US 5,379,355 AGrant
Data Encoding Using One or More Adaptive Decision Trees
Issue Date:1995-01-03
•29 Claims
•17 Drawing Sheets
Abstract
A method and apparatus for quantizing a stream of data at a predetermined bit compression ratio. A binary decision tree is established for classifying the error between a predicted and actual data value. The binary decision tree comprising a root node and multiple binary nodes represented by a pair of threshold values around the root node, a member of each pair representing a node in the binary decision tree and a threshold value indicative of a range of data values. The range in which the data values lies is then determined and a binary code representing the quantized error (token) between the predicted and actual data values. The quantized error symbol (token) is then encoded and a bit string corresponding to the error symbol is output, thereby representing compressed data. After a predetermined number of errors have been quantized (and encoded), the bit rate of the compressed data is compared to a predetermined (target) compression ratio. The ranges used to quantize the error are then adjusted to maintain the predetermined compression ratio.
Metadata
Assignees
- Ricoh Corporation
- Ricoh Company Ltd.
Inventor
- James D. Allen
Application Information
Application Number:US 934764&
Filing Date:1992-08-24
Priority Date:1992-08-24
Art Unit:266
Classifications
IPC:
G06K 936H04B 166
Field of Search:
38235834137556;49;36;37;38432;433;135;136;13379;86;94;77;14330;122
Patent Drawings (17 sheets)
Description
Field of the Invention
The present invention relates to the field of data encoding; more particularly, the present invention relates to image coding for fixed-rate compression.
Background of the Invention
Data compression is defined as the reduction in the space required for a set of data. Various methods of data compression are known in the art. Each data compression method includes an encoding scheme to encode the set of data. The purpose of encoding schemes is to reduce the data storage or transmission requirements for the representation of a set of data. Associated with the encoding (compression) method is a decoding (decompression) method to reconstruct the data from its encoded representation.
Quantization is an integral part of many data compression techniques. One quantization technique is the quantization of a sample sequence using information from neighboring samples. This is commonly referred to as sequential quantization. Two types of sequential quantizers are utilized: predictive coders and multipath search coders. Predictive coders predict the next sample and then quantize the difference between the predicted value and the actual value. The prediction is based on a combination of previously predicted values. Two well-known predictive coding schemes include delta modulation and differential pulse code modulation (DPCM).
DPCM is a class of lossy encoding schemes for signals. In a lossy encoding scheme, the reconstructed image does not match the original image exactly. Basically, in DPCM systems, the difference between a given sample and its predicted value is quantized and transmitted. The predicted value, which is obtained from previous predicted values and quantized differences, is also available at the receiver, since an identical predictor is used there. The receiver adds this predicted value to the received quantized difference in order to produce an approximation to the original sample in each case.
There are two types of DPCM coding schemes: fixed-rate and variable-rate. Fixed-rate schemes encode a given signal quantum (e.g., millisecond or pixel) with a fixed number of bits, such as eight bits. Fixed-rate schemes offer the advantages of simplicity, synchronous real-time encoding and decoding, and predictable buffer size or transmission time. Variable-rate schemes, on the other hand, require fewer or more bits in the less or more complex regions of the signal respectively. Variable-rate schemes offer the advantage of better compression for a given fidelity. In other words, variable-rate schemes offer better fidelity for a given compression ratio.
The operation of a DPCM system begins by filtering the signal to remove short-term excursions. For example, a noise removal filter or a low-pass filter can be applied. It should be noted that this type of filtering can be done as a separate first step or a similar effect can be achieved by modifying the primary encoding process. The purpose of removing noise is not solely to enhance the image, although this is a desirable side effect, but more importantly to improve signal fidelity at a given coded bit rate by suppressing the bit-expensive coding of such excursions.
The encoding process for each input sample comprises prediction, error quantization and code generation. Prediction includes predicting the next sample value based on some previous predicted values or differences. The predicted sample value is subtracted from the actual value of the sample. This results in an "error" value. The error value is replaced with (i.e., quantized as) a close value (e.g., the closest) in magnitude to the error value from a set of allowable values. The set of allowable values, which is denoted here as V={a1, a2, a3, ..., ak}, is usually small, often as small as two. The quantized error value is whichever of the a1, a2, ... ak is numerically closest to the actual error value. This is the quantization. The value chosen is used for subsequent prediction so that the state can be learned by the decoder. Often the set of allowable values varies depending on the state of the previous encodings. For example, in one scheme where V is of size 2 and a fixed 1-bit per point encoding is achieved, the values a1 and a2 are skewed in the direction of the immediately prior encodings. This provides a "momentum" effect and allows an accelerating signal to be encoded.
The quantized error value is encoded in some fashion to form the compressed signal. Bit encoding can be fixed or adaptive. In fixed bit encoding, a given quantized error value is always encoded with the same sized bit string. In adaptive bit encoding, the encoding varies adaptively to achieve near-optimal compression given a statistical history. Thus, in adaptive bit encoding, the encoding varies, thereby allowing variable sized bit strings to represent the quantized error value (in DPCM systems). Bit encoding can also be instantaneous or non-instantaneous. In the instantaneous encoding, the appropriate output code bits in a given context can be determined immediately from the token (e.g., quantized error value) to be encoded. In non-instantaneous encoding, state information is retained in the bit encoder such that a given output bit may be determined by a plurality of encoded tokens (e.g., quantized error values). Examples of non-instantaneous coding include arithmetic coding. Non-instantaneous adaptive bit encoding offers improved compression. For simplicity, most of these codes operate only on binary decisions. Such binary non-instantaneous adaptive entropy codes are known in the art, often referred to as arithmetic codes. The encoded quantized error values form the compressed signal data (e.g., image) which is stored or transmitted.
When the compressed signal is decoded (decompressed), the signal is reconstructed in the same order and similar state information is constructed. Each sample is again predicted and the quantized error value decoded. As done previously, the predicted and error values are added to form the reconstructed sample value. All of the reconstructed sample values form the decoded signal.
In the prior art, some DPCM systems are adaptive. These adaptive designs consist of either adaptive predictors or adaptive quantization techniques. One adaptive quantization technique is referred to as error signal normalization and involves a memoryless quantizer which changes the quantizer intervals and levels according to the standard deviation of the signal, which is known to it. Another technique referred to as a switched quantizer changes the quantizer characteristics to match the difference signal and uses a few previous sample differences, two in the case of video, to determine the state of the difference signal.
Another technique, specifically applicable to images and referred to as spatial masking, uses both the previous samples on the scan line and samples from the previous scan line. A masking function is developed from the weighted sum of the gradients around a given picture element.
Multipath search coders (MSCs) use both previous and future sample values to select a quantized version of a given input sample. One type of MSC technique is tree coding. Tree coding makes use of a tree structure, where each typical sample sequence is stored as a sequence of branches in the tree. When the sequence is selected, its corresponding tree path is transmitted as a binary sequence, with each bit indicating a direction to follow at each sequential node of the tree. In other words, while proceeding through the samples, the subsequent samples are usually less correlated to the first sample and, thus, have more possible values. In this manner, this MSC technique resembles a tree structure.
As will be shown, the present invention provides a fixed-rate scheme for encoding data which allows a variable number of bits in regions of varying complexity of the signal. Thus, the present invention encodes a set of data samples using fewer or more bits with less or more probable samples while providing nearly constant bit rate compression.
Summary of the Invention
It is an object of the present invention to provide a scheme which obtains the advantages of both fixed-rate and variable-rate DPCM encoding.
It is another object of the present invention to provide an adaptive quantization scheme which updates the model as data is compressed.
It is yet another object of the present invention to provide a compression scheme which varies the quantization levels to achieve approximately fixed-rate encoding.
It is still another object of the present invention to provide a method of heuristically controlled quantization fineness according to the type of data to be compressed.
It is a further object of the present invention to provide a scheme for determining the error classification set for quantizing data symbols.
These and other objects are provided by a method and apparatus for quantizing a stream of data at a predetermined bit compression ratio. A binary decision tree is established for classifying the error between a predicted and actual data value. The binary decision tree comprising a root node and multiple binary nodes represented by a pair of threshold values around the root node, a member of each pair representing a node in the binary decision tree and a threshold value indicative of a range of data values. The range in which the data values lies is then determined and a binary code representing the quantized error (token) between the predicted and actual data values is produced. The quantized error symbol (token) is then encoded and a bit string corresponding to the error symbol is output, thereby representing compressed data.
After a predetermined number of errors have been quantized (and encoded), the bit rate of the compressed data is compared to a predetermined (target) compression ratio. If the bit rate is greater than that dictated by the predetermined compression ratio, the size of the ranges is increased to encompass a wider range of data values, thereby decreasing the bit rate. If the bit rate utilized is less than the number of bits dictated by the predetermined compression ratio, the size of the ranges is decreased, thereby increasing the number of bits output per data value (i.e., increasing the bit rate). Thus, the present invention allows the error token to be quantized according to a set of error classifications in order to maintain a predetermined compression ratio.
Brief Description of the Drawings
The present invention will be understood more fully from the detailed description given below and from the accompanying drawings of the preferred embodiment of the invention, which, however, should not be taken to limit the invention to the specific embodiments, but are for explanation and understanding only.
FIG. 1 is illustrative of a binary decision tree.
FIG. 2 is a block diagram illustration of a coder/decoder employed in the preferred embodiment of the present invention.
FIG. 3 is a flow diagram of one embodiment of the present invention.
FIG. 4a is a flow diagram representative of the functions performed by a coder configured in accordance with the present invention and FIG. 4b is a flow chart of the functions performed by a decoder in accordance with the present invention.
FIGS. 5A-5C illustrates an array of threshold values for different size ranges utilized in the preferred embodiment of the present invention.
FIG. 6 illustrates the adjustment of threshold values to vary the ranges in accordance with the present invention.
Detailed Description of the Invention
A compression/decompression system is described. In the following description, numerous specific details are set forth, such as specific numbers of bits, types of data symbols, tokens, etc., in order to provide a thorough understanding of the preferred embodiment of the present invention. It will be obvious to those skilled in the art that the present invention may be practiced without these specific details. Also well-known devices have been shown in block diagram form, rather than in detail, in order to avoid unnecessarily obscuring the present invention.
Although the present invention has applications to all types of data value sets to be compressed, an important application of the invention is color image compression. The compression/decompression system of the present invention will be described in terms of a system for compressing and decompressing image signals. However, it should be noted that the present invention is applicable to all types of signal quantum. In the following discussions, the term "pixel" is used to denote a scalar signal value. It should be noted that the scalar signal values could represent a variety of attributes, such as luminance, chromaticity, etc. The term "color pixel" is used to represent a tristimulus pixel.
In the image compression application, pixels are processed sequentially pixel by pixel, first by predicting the pixel value from prior retained values and then by encoding a quantized form of the prediction error, firstly into the bits of the path address of a "leaf" in one of multiple binary decision trees and then, secondly, into the productions of a binary entropy encoder. During the encoding, the image pixels are scanned in some fixed order. In one embodiment, a square-lattice array of pixels is used and is scanned in raster (lexicographic) order. However, it should be noted that the order could be hierarchical-raster, zigzag raster or other orders known in the art. It should be noted that the present invention is not limited to a square-lattice array of pixels. Other pixel compositions can be used, such as a hexagonal lattice array. Thus, the image signals are encoded pixel by pixel, while retaining information of prior pixel values (i.e., state information) synopsizing the already-encoded portion of the image.
In one embodiment, the state information comprises two line buffers of pixels. The first line buffer contains the line currently being encoded, and the second line buffer holds the line immediately prior.
The encoding process for each input point comprises prediction, error quantization and code generation. The present invention does not require a specific prediction method. In the currently preferred embodiment for image compression, a 3-pel prediction method is used in which the pixel at location (x,y) is predicted with the formula:
where A=R(x--1,y--1), B=R(x--1, y), C=R(x, y--1), where R() represents the reconstructed pixel value that the encoder uses. Alternative prediction formulas can be used such as (A+B+C)/3 or (B+C)/2.
Optionally, a dithering term can be added to the predicted value. The dithering term should be a pseudo-random value with a zero mean and a standard deviation of about one-third the smallest distance between the allowable values a1, a2, etc. Use of a dithering term is well-known in the art. It should be noted that dithering is not utilized in the currently preferred embodiment.
Using the prediction method, a value is predicted for the pixel. The predicted pixel value is then subtracted from the actual original pixel value, resulting in an "error" value. The error value is quantized using a set of allowable values. Each set of allowable values in the present invention are referred to as an error class. In the currently preferred embodiment, one of the allowable values is always zero. However, it should be noted that there is no requirement that a zero value be allowed. In another embodiment, the value nearest to zero fluctuates periodically among two or more values which average to zero. This alternate embodiment, in effect, is an alternate means of achieving the effects of dithering.
The ability to vary the set of allowable values (V={a1, a2, ..., ak}) serves to provide improved fidelity for a given compression rate. The present invention varies the allowable values dynamically to approximate a fixed compression ratio. Thus, in regions of high signal activity, the allowable values V are spread out to improve compression at the expense of greater quantization error, while in regions of low activity the values are compacted to improve fidelity at the expense of compression. In one embodiment, this dynamic adjustment proceeds slowly (i.e., the feedback is time-averaged, "damped", or "low-passed"). It should be noted that the "quantization error" mentioned above is not the "prediction error", but rather the difference between the actual prediction error and its quantized (approximated) encoding.
After quantization, the quantized error value is encoded in some fashion to form the compressed signal. The quantized error value is added to the predicted value and the sum replaces the original pixel value in the buffer. If the data values being quantized were originally derived from image data, the sum is saved in the buffer as R(x,y). The encoded quantized error values form the compressed image which is stored and transmitted.
When the image is decoded (decompressed), the image is reconstructed in the same order and the same state information is constructed. Each pixel is again predicted, and the quantized error value decoded. Again the predicted and error values are added to form the reconstructed pixel value R(x,y). Collectively, the R(x,y) values form the decoded image. If a preliminary low-pass filter was performed during encoding to improve code efficiency, it may be appropriate to include an image-sharpening process after the decoding.
Overview of the Present Invention
In the present invention, the multiple sets of allowable values define a plurality of classes. The plurality of classes correspond to nodes of a binary tree. Each pixel is encoded with such a class, denoted as the pixel's class code. There may be a plurality of such trees (zones), with the encoder and the decoder agreeing on which tree to use. Each class code is a binary value having a length of a number of bits. The bits of the code represent the binary decisions down the binary tree from the root node to the node corresponding to the threshold value indicative of the range of data values within which the input data value (symbol) lies. It should be noted that although a range is defined by a lower threshold and an upper threshold, it may be simplified by identifying the range by a single threshold, e.g. the lower threshold wherein the threshold for the adjacent range identifies the upper threshold.
The trees of the binary decisions provide the present invention with flexibility. A plurality of trees allows for better probability estimates to be produced and also heuristic control over quantization fineness. An example of the structure of a decision tree in the present invention is shown in FIG. 1.
After the prediction error, d=D(original)--D(prediction), is determined, it is quantized into a range. The input data values to be encoded are quantized into a succession of binary events. Referring to FIG. 1, the root node of the tree 100 contains two branch nodes 110 and 111 which correspond respectively to a binary zero and binary one of the code. Node 101 represents the range ("quantization range") -k1<=d<=k1. Tree 100 also includes nodes 102, 103, 104, 105, and 106 and others which are not depicted. Node 102 is coupled to node 101 by branch 111 an corresponds to the "0" quantization. Branches 113 and 112 couples nodes 103 and 104 respectively to node 102. Nodes 103 and 104 (via branches 118 and 115 respectively) represent the ranges of -k2<=d<-k1 and k1<d<=k2 respectively. Furthermore, branch 118 and branch 115 are represented by the binary code 101 and 110. Branches 119 and 114 couple nodes 105 and 106 respectively to nodes 103 and 104 respectively. Node 105 corresponds to the range -k3<=d<-k2 and a binary code of 1001. Node 106 corresponds to the range k2<d<-k3 and a binary code of 1110. The ranges continue on both the positive and negative side.
Each node has a range of threshold values associated with it. The threshold values used in a particular system are dependent on the character and range of data values. For example, when quantizing image data, it is often desirable to provide greater precision in certain ranges of color and intensity because the eye is more sensitive to changes at particular ranges. In particular, if the data values are symbols identified by numbers in the range of 100-300, the three threshold values will be in the range of 100-300. If the data values are translated to probability or error values prior to coding, the range of threshold values will be much smaller, reselecting a fine quantization. In the following description of the preferred embodiment, error values, reflecting the error determined between a predicted data value and the actual data value are coded. Therefore, the threshold values reflect a range of possible error values. However, it will be obvious to one skilled in the art that the data types can be varied as well as the range of threshold values, without departing from the spirit and scope of the invention.
Referring to FIG. 1, a modified unbalanced binary tree employed in the preferred embodiment is shown in FIG. 1. The first binary decision determines whether the value to be compressed is in the region between +k1 and -k1. If the data value is in the region, the quantization is complete (a binary 1 is output) and the process proceeds to the next data value to be quantized. If the data value is not within the region delineated by .+-.k1, the next decision determines the sign of the data value indicating which side of the binary tree and the region the value lies within. If the value is positive and not within the range of .+-.k1, the next test determines whether the value is in the region between k1 and k2 by determining whether the data value is less than k2. If it is not, then the next decision in the tree is to determine whether the input data value is in the region between k2 and k3 by determining whether the data value is less than k3. Similarly, if the value is negative, the same steps will be performed with respect to -k2 and -k3.
When the regions are decreased in size by decreasing the threshold values, other regions will be increased, increasing the likelihood that the data value will be within one of the increased ranges. Furthermore, in the present invention, as the regions are decreased, additional regions are added to the outside ranges. Thus, as the regions are decreased, the number of regions are increased. For example, if the value of k1 is decreased, the region defined by k1 and k2 will be increased, thereby increasing the probability that the data value will be in the region k1-k2. Also, other regions are added to the outside probability ranges. Similarly if the threshold values k1 and k2 are decreased in value, the region defined by k1 and k2 will be decreased while increasing the range defined by k2 and k3. Also, in this case, the number of ranges is decreased. The value of k2 may also be decreased, thereby not only decreasing the region between k1 and k2, but increasing the region between k 2 and k3 and, therefore, increasing the likelihood that an input value will fall into a range greater than k3 which requires more bits to represent the path of the binary tree to the node of the region. The values of k1, k2 and k3 are dependent upon the range of possible values to be compressed and the type of data to be compressed. Moreover, the total number of ranges in one embodiment of the present invention is dependent upon the range of positive values to be compressed and the type of data to be compressed.
In the currently preferred embodiment, the data values and threshold values for the binary tree are representative of the prediction error for a pixel. In this embodiment, the pixels are processed by predicting the pixel value, for example, the luminance value, from prior luminance values and comparing the predicted value to the actual value to generate a prediction error. This prediction error is then quantized according to the path address for the node indicative of the range the prediction error falls in. It will be understood that a certain level of precision and accuracy is required for luminance, but a different level may be required for chromaticity. Therefore, a plurality of binary trees may be utilized and selected according to the type of data and, furthermore, according to the initial input value. The initial value must be known by the decoder. An illustration would be that chromaticity requires high accuracy in the brown and purple regions but can be relaxed somewhat in the green regions. Thus, the data could be tested for the color regions and a binary tree selected according to the region that is determined.
As previously mentioned, the selected range is viewed as being determined by a sequence of binary decisions. The range values can be any threshold values. In the currently preferred embodiment, the threshold values are chosen by selecting symmetric thresholds (-k3, -k2, -k1, k1, k2, k3), although the thresholds, could have been asymmetric. Each node in the binary decision tree contains an associated probability estimate. In FIG. 1, these probability estimates are labeled P1-P6. The probability estimates are the only storage cost associated with each node. In the currently preferred embodiment, the probability estimates are stored as B-bit values.
Specifically with regard to image compression, because of subjective image considerations, the thresholds are chosen as multiples of the other thresholds. For instance, in the currently preferred embodiment, the thresholds are chosen as:
In general, there will be a "runt" error range at each extreme point. For a slight performance improvement in the currently preferred embodiment, this "runt" error range may be coalesced with the adjacent range if it is less than half its size. In other words, if any of the prediction error values are outside the range of thresholds, then the range which is nearest to the values are used to quantize the prediction error.
In one embodiment, the threshold values (k1, k2, k3, ... ) are taken from one row in a quantization table. The quantization table (T table) is an array of threshold values for different size ranges for quantizing the input. An illustrative table is shown in FIG. 5. In one embodiment, there are about 100 such rows, preferably numbered by increasing quantization coarseness. The selected row index may be given by:
where Rg is a global variable controlled to achieve a preset fixed bit rate and Rt is a per-tree heuristic. Various heuristics can be used in selecting trees.
Referring to FIGS. 5A-5C, a T table of 152 rows, each row representative of the threshold values for a binary tree. The number of threshold values ranges from 13 threshold values down to a single threshold value. In the preferred embodiment, the process may start with the tree as representative of the 52nd row containing threshold values 13, 45, 84, 129, 180, 236 and 299. Depending upon the input values and the target bit range, the ranges may be compressed by going to a lower numbered row such as 51 or expanded by going to a higher numbered row. In one embodiment, the ranges are varied a single row at a time.
FIGS. 6A-6K is a sample output generated according to the preferred embodiment out of the present invention. Five hundred and seventy-five lines of an image are encoded as compressed output. For each line, the number of bits utilized to encode the line are identified followed by the actual bit rate per line and the T table row value (referred to as the throttle) is identified. Thus, as illustrated in FIG. 6, with respect to line 1, only 905 bits were utilized. Thus, it is desirable to decrease the size of the ranges in order to increase the bit rate as reflected in the net T value being set to 19. The next line shows 2,788 bits utilized resulting in an actual bit rate of 1.98 and a throttle of 16, identifying that the number of rows moved which reflects the change in sizes of the ranges of the binary tree changed 16 steps. Looking further down the lines from line 8 through 159, the actual bit rate is within the allowable range of the target bit rate and, therefore, the threshold values are not adjusted as reflected by the net T value equal to zero. As the image changes, so may the number of bits utilized to represent the image at a line and, therefore, it may be required to change the threshold values of the binary tree in order to adapt to the actual data being compressed. This is shown by the changes in the vicinity of line 225 as well as the changes in the vicinity of lines 279 through 550 reflecting a large difference in the number of bits utilized.
Bit Encoding
The present invention is capable of using either a fixed or adaptive bit encoding in conjunction with instantaneous or non-instantaneous encoding. The following embodiment is a simple scheme which achieves near-optimal compression with a fixed rate of 2.0 bits per pixel using fixed-string instantaneous encoding. Assuming that five allowable error values with fixed encodings and occurrence frequencies are as follows:
If the indicated occurrence frequencies are achieved two goals are satisfied: (1) the entropy coding is optimal (for a certain quantization) in the sense of the Shannon limit, and (2) a rate of exactly 2.0 bits per pixel is achieved. In one embodiment, the target occurrence frequencies are achieved by calculating the decaying averages of the actual frequencies and slowly migrating the values of -A, -B, +C, +D in the direction to compensate for any difference between target and actual frequencies.
Non-instantaneous adaptive bit encoding offers improved compression and is used in the currently preferred embodiment. For simplicity, the codes operate only on binary decisions. Binary non-instantaneous adaptive entropy codes are known in the art, often referred to as arithmetic codes or binary entropy codes. Any such code can be used with the present invention. An example of such an entropy code is the Q-Coder. It should be noted that the only constraints on the present invention is that such codes operate on binary decisions made in any of a plurality of contexts and where the constructed bit output encodes each such decision. A variety of encoding processes can be utilized. The encoded quantized error values form the compressed image which is stored or transmitted.
When an error class set has size greater than two, the quantized error must be represented as a leaf in a binary tree in order to conform to the requirements of such a binary entropy code. Each non-leaf node in the tree denotes an encodable binary decision. The quantized error class is denoted as the path address of the corresponding leaf node. In one embodiment, the binary leaf address may be used as the actual output bit string (instantaneous non-adaptive code) or, in another embodiment, the decisions may be submitted one-by-one to a non-instantaneous adaptive code.
Numerous methods can be employed to achieve entropy coding in the present invention. First, renaming the allowable value set V to be equal to:
where N(k)<N(k-1)<...<N(1)<Z<P(1)<... P(k) and where Z is the element nearest to zero. This renaming results in multiple possible embodiments of trees which are preferred for organizing these elements to be the leafs of a binary tree. In one embodiment, the root of the tree divides the set into one set which contains Z and another set which contains all of the other elements. The latter set is then subdivided into a set which contains all elements greater than Z and a set which contains all of the elements less than Z. The positive elements, depicted P(1), P(2), etc., then branch off as singletons in order of smallest to largest. Similarly for the negative elements, denoted N(1), N(2), etc., branch off from the lowest negative value in magnitude to the highest.
In another embodiment, the root of the tree separates Z into its own set. However, in contrast with the previous embodiment, the sets {P(1), N(1)},{P(2), N(2)}, etc. are separated off as doubletons in the order from those having magnitudes closest to Z to those having magnitudes farthest from Z. In using the tree, the final decision is whether the current decision is greater than Z.
In yet another embodiment of the tree, the root of the tree separates V into those elements greater (or less) than Z into one set. The element Z is then separated, with the separation proceeding as in the first embodiment, wherein the positive elements branch off as singletons in order of smallest to largest and the negative elements branch off from the lowest negative value in magnitude to the highest.
The present invention is sensitive to the number of bits output as compressed data and can adapt itself to output at a bit rate consistent with a target bit rate specified by the user or the system. This is preferable, for example, when memory for storing data is of a predetermined and limited size or when the bit transmission rate of an input/output device cannot exceed a certain limit.
In the system of the present invention, after a predetermined number of data values have been quantized (and subsequently output in a compressed form), the number of bits output is compared to the target bit rate or target compression ratio. If the actual bit rate is greater than the target bit rate, the size of the quantization ranges are increased such that the classes closer to the root node, which utilize a smaller number of bits as its class code, are used more frequently thereby decreasing the bit rate. Similarly, if the target bit rate is less than the actual bit rate, the ranges will be decreased in size to increase the frequency that the input data value lies within the ranges further away from the root node that utilize a greater number of bits.
With respect to image compression, at the end of every scan line in the one embodiment, the target bit rate is compared with the actual bit rate and the values of the elements of each error class set (i.e., the "quantization ranges") are adjusted slightly in an attempt to migrate the actual bit rate towards the target. For example, the elements of the set v might be the elements of:
multiplied by Rg+Rt where Rg is a global throttling term adjusted slowly to achieve the target bit rate and Rt is the constant associated with the selected tree when a plurality of trees are in use. In this example, for all of the elements, N(k)=-P(k). It should be noted that this is not required. Note that in the example above, the elements of V become more divergent as they become more distant from Z. This is appropriate both because it reduces net quantization error for typical distributions as shown by Lloyd-Max and in view of the sub-linear character of human perception. For more information on Lloyd-Max Quantizer, see Gersho, Allen. and Robert M. Gray, Vector Quantization and Signal Compression, Kluwer Academic Press 1992, pg. 165. Also human visual perception does not require accurate luminance rendition in the vicinity of edges. In the preferred implementation, the value Rg+Rt is taken to be the row index of a table containing the precomputed values of Z, N(K) and P(K).
Some binary entropy codes operate non-optimally for very likely decisions (i.e., decisions which assume a given actual value more than 99% of the time). in this instance, compression can be improved with a simple heuristic. When the statistics bin of a decision context indicates that the decision assumes a given value more than 99% of the time, the decision is forced to that state regardless of its actual value, and no action is performed by the bit encoder. The statistics bin is then put in a special state such that this heuristic is bypassed on its next encounter. (This allows the continued recording of and adjustment to changing statistics. This heuristic is also bypassed whenever it has already been used at another node in the encoding of the pixel. This prevents the decoding of divergent wrong pixels.
Error Class Set Determination
It should be noted that a single tree could suffice in principle. However, in the currently preferred embodiment, multiple trees are used to achieve improved compression for a given quality (or equivalently improved quality for a given compression) by giving better probability estimates and also allowing heuristic control over quantization fineness. The same signal decision model which predicts pixel values is also responsible for determining a pixel context group. For tristimulus (color) images, there is one group of pixel context groups for luminance and one or two groups for chromaticity.
When the predicted pixel value is near the upper limit of its range (e.g., high luminance), a large positive error value is impossible. Similarly, a large negative error value is impossible when the prediction is for low luminance. A good compression system should take advantage of this. Moreover, since each pixel class context has its own set of statistics bins, probability estimation is made more accurate by grouping similar image areas into the same bins and differing areas into different bins.
One preferred embodiment for signals whose valid range is (0,1 , ..., 255) provides 6 context groups for luminance, depending on the predicted pixel value (pv):
Multiple trees provide better probability estimates and also allow heuristic control over the degree of quantization. This is especially critical in some applications. For instance, in image compression, chromaticity must be very accurate in the brown and purple regions and not so accurate in dark green areas. Therefore, in this case, the pixel values in the brown and purple regions use trees having probability estimates which have smaller ranges, thereby reducing the degree of quantization, while pixels in the dark green areas can be quantized using probability estimates that encompass larger ranges, which raises the degree of quantization.
One Embodiment of the System of the Present Invention
FIG. 2 illustrates an exemplary system in accordance with the preferred embodiment of the present invention. Illustrated is the combined compression/decompression system for image data such as that required for facsimile transmission. However, the system is not limited solely to this application and can be easily adapted to operate with respect to any type of data, in the compression mode, the original image 416 is ordered and sub-sampled by scanner/sample 417 to yield the sequence of digital data values. The scanner/sample device 417 preferably includes a scanner which translates the physical image into signals and a sampler which samples the signals at a predetermined frequency to generate digital image data. However any device which generates an output of digital data for compression can be used. The type of sampling performed is dependent on the image and application. For example, the image can be sampled in a zigzag raster order or in the form of a hexagon sampled grid. Furthermore, the pixels comprising each image preferably has a plurality of components, such as luminance, chromaticity, and x,y coordinate location which, when sub-sampled, are interweaved in a deterministic way such as a single raster or a zigzag scan.
Each data value is subtracted by the subtracter 419 from a predicted data value 402. The predictor 402 predicts the value of the component, i.e. data value to be encoded from some of the already processed components which are returned in prior image state buffer 401. The prediction is typically made on the basis of neighboring data values. The predictor may consist of a simple state machine or processor with the predicted value determined on an ad hoc basis or random access memory in which a look-up table is stored containing possible predicted values which are indexed according to input information (e.g., the values of k1, k2 and k3).
The predicted value generated by the predictor 402 and the actual value output by the scanner sampler 417 are subtracted by subtracter 419 to generate the difference which corresponds to the error value. This error value is input to the classification (quantization) mechanism 406. Also input to the classification (quantization) mechanism 406 is a row of the T table 420 (FIG. 6). The values in the T table 420 are threshold values and preferably contain the midpoint values between adjacent values in the corresponding row of the R table (discussed below). Using the threshold values provided by the T table 420 and comparing the error value output by the subtracter 419, the quantization range or class in which the error value lies is determined and the quantization range is input to an encoder/decoder 41 3. Encoder/decoder 13, in response, encodes the class and outputs it as part of the output bit stream. The entropy coding of the quantization range depends on probability estimates selected from a look-up table 415 in memory which are maintained separately for each tree. The tree is determined by the magnitude of the predicted component, its horizontal position in the image and its quantity value. The tree select mechanism 412 outputs a signal to the look-up table to select the probability estimates.
It should be noted that the embodiment described encodes the quantized error value to generate the bits output as part of the bit stream. The encoder is not limited to any type of encoder, but preferably may be an encoder of the type described earlier. Alternately, the system may be configured not to include an encoder, but rather the quantized error value (i.e., delta class) itself is output as part of the output bit stream.
The output of the encoder/decoder 413 is also input to a buffer which stores the number of bits output in order to generate a number corresponding to the actual bit rate 410. For example, when a line of image data is encoded and output, the number of bits utilized to encode the scan line of data, as maintained by the buffer 410, is subsequently output to comparator/adjuster 408 which compares the target bit rate 409 to the actual bit rate 410. This determines the difference between the target bit rate and actual bit rate, referred to as the overall coarseness value.
The overall coarseness value output by the adjuster 408 is added to any tree bias (at 407) provided by the tree bias register 411. Tree bias is determined in part by the user and may be set according to the type of data or the particular application. The particular tree bias term is dependent upon the selected tree. The tree bias added to the overall coarseness term produces the quantization coarseness term, which is then input to the T table to select a proper row used to determine class threshold values to be used with processing of subsequent pixels.
The result of the addition of the overall coarseness value is input to the R table. The output of the quantization 406 selects an R value and adds (405) it to the prediction from 402 (compression) to form the reconstructed component values. The reconstructed component values are then stored in prior image buffer 401 and the reconstructed image buffer 423 (decompression).
In the decompression mode, the compressed bit stream 414 is input to the encoder/decoder 41 3 to perform a decode operation. As with the encoding sequence, the same procedure is utilized in the reverse fashion. The compressed image is input and determines the quantization range, the R value and the reconstructed component (405). The quantization range is output to the classification mechanism 406. The quantization range is then input to the R table in conjunction with the quantization coarseness term output by adder 407 to index the R table. The R table is a random access memory (RAM) having a look-up table comprising representative error values for each quantization range. In one embodiment, the R table contains error values which are the midpoints of each quantization range. As the T table contains the threshold values identifying the ranges for each quantization range, the R table can be viewed as the midpoint value between adjacent values in a corresponding row of the T table. The output of the R table 404 is an R value which is input to the adder 405 which, along with the value generated by the predictor 402, produce the reconstructed image after processing through the inverse procedure of the scan/sampler 417.
Although the above discussion refers to a single binary tree, the data values may be predicted, quantized and encoded/decoded utilizing a separate binary tree for individual data values (e.g., for different data types and ranges of data values) and subsequently output as a single output bit stream.
Referring to FIG. 3, process flow for one embodiment of the present invention is illustrated. At step 300, the ranges of the binary tree are determined and delineated by the threshold values which correspond to the nodes of the binary tree. At step 305, each range is identified as a class code (i.e., quantization range). As will be shown later, this code is encoded and output as the bit stream for transmission or storage of compressed data. At step 310, the first data value to be compressed is retrieved. Comparison is made between the ranges and the data value digits to determine the range the data value is within. The actual comparison is performed by comparing the data value to the threshold values. At step 320, the corresponding class code is selected and encoded for output as part of the output bit stream.
At step 325, a comparison is made to determine whether a predetermined number of data values have been processed and output as compressed data. For example, a count may be made to determine a block of data representative of a scan line of image data. If the predetermined number of data values have been output, then a comparison is made to determine the relationship between the number of bits output to the target bit rate, which is the preferable number of bits to be output per a predetermined number of data values such as a scan line. At step 345, if the number of bits output is greater than the target bit rate, then, at step 350, the ranges are expanded. If the number of bits is less than the target bit rate (step 355), then the ranges are contracted (step 360).
By expanding the ranges, the ranges encompassing the area around the root node will be wider, thereby increasing the probability that the data value falls within those ranges. This, in turn, reduces the number of bits required to output because the class code, which in this embodiment corresponds to the data path through the binary tree, requires a fewer number of bits because a fewer number of nodes are included in the data path for those nodes closest to the root node. Correspondingly, if the ranges are contracted, then this decreases the likelihood that the data value falls within those ranges closest to the root node, but instead falls within those ranges further away from the root node, thereby requiring a greater number of bits to be output representative of the path of nodes through the binary tree. In turn, this increases the actual bit rate. Preferably, the ranges are expanded and contracted by modifying the index into the T table which contain the threshold values for a range of different quantization coarseness. For example, the index to the current row of threshold values can be decreased to index a row of threshold values narrower in spacing. Alternately, the index to the T table can be increased to index a row of threshold values spaced wider apart.
Once the ranges have been expanded or contracted, the next data value is retrieved (step 330), and if all data values have been compressed (step 335), the process is terminated. If all data values have not been compressed, the process continues again for each data value starting at block 315 until all data values have been compressed. Thus, the ranges are expanded and contracted as needed in view of the type of data and the ranges of data values for a particular set of data values to be quantized yielding a bit rate which is close to the target bit rate.
FIGS. 4a and 4b show another embodiment of the present invention. FIG. 4a illustrates the process flow for encoding data values and FIG. 4b illustrates the process flow for decoding data values. Referring to FIG. 4a (at step 400), the ranges are identified with their class codes which represent the binary decisions through the binary tree to reach the node corresponding to the threshold value of the range the data value is within. At step 405, the first actual data value is retrieved and, at step 410, a predicted data value is generated. This predicted data value may be determined from data values in the vicinity of the data value, such as the adjacent data values or the predetermined number of previous data values. At step 470, which tree to use is determined. At step 415, the predicted data value and the actual data value are compared and an error value is generated as the difference between the actual data value and the predicted data value. This error value is compared to the ranges of the binary tree to determine the range the error value falls within. The corresponding class code, at step 425, is encoded and output as part of the output bit stream.
At step 430, a check is made to determine whether a predetermined number of data values have been output. If a predetermined number of data values have been output, at step 435, a determination is made as to whether the output bit stream is greater than the target bit rate. (The target bit rate is the predetermined bit rate determined to be desirable for this particular application. ) If the output bit stream is greater than the target bit rate, the ranges are expanded in order to decrease the number of bits output as part of the output bit stream. At step 445, if the output bit stream is less than the target bit rate, the ranges are compressed in order to increase the number of bits output as part of the output bit stream step 450. This process is continued until all the data values have been processed at which time the process is terminated 465.
The corresponding decoder is illustrated by the flow chart of FIG. 4b. At step 500, the ranges are identified and the class codes determined. At step 505, the first compressed class code is retrieved. At step 51 0, the class code is decoded. A predicted data value is generated using the same process utilized in the encoder and, at step 520, and error value is determined. This error value preferably is a mid-point error value for the range of values corresponding to the class code. At step 525, the actual data value is generated from the predicted data value and selected error value using the reverse process employed in the encoder. As in the encoder, the ranges are adapted according to the type of data. Thus, at step 530, if a predetermined number of data values have been reconstructed, the input stream, that is the compressed class code, is compared to the target bit rate and, at step 535, if the input stream is greater than the target bit rate, the ranges are expanded, step 550, and if the input stream is less than the target bit rate, step 540, at step 545, the ranges are compressed. This process will continue for the remainder of the compressed class codes to reconstruct the data values until all class codes have been processed at which time the process is terminated (step 565).
While the invention has been described in conjunction with the preferred embodiment, it is evident that numerous alternatives, modifications, variations and uses will be apparent to those skilled in the art in light of the foregoing description.
A method and apparatus for encoding data has been described.
Claims
I claim:
1. A method for compressing a plurality of data at a predetermined compression ratio comprising the steps of: providing a first class set having a first plurality of error value ranges, wherein each error range covers a sequential set of error values and is identified by a class code representing the sequential set of error values associated with said each range, and further wherein a class code encompassing error values having a greater frequency of occurrence employs a lesser number of bits than a class code for a class encompassing error values having a lesser frequency of occurrence; quantizing said data using said at least one class set, wherein the step of quantizing includes generating for each data value an error value representing a difference between said data value and a predicted data value, identifying one of the plurality of error value ranges encompassing the error value, and assigning class codes to each data value, such that each data value is associated with a class code; generating an output representative of the class code as part of an output data stream; and varying said first class set after a predetermined number of class codes have been represented as part of the data stream, wherein the step of varying includes adjusting the first class set to provide a second class set having a second plurality of error value ranges different in size from the first plurality of error value ranges, such that error value ranges are adapted to maintain the compressed data stream in the proximity of the predetermined compression ratio.
2. The method as defined in claim 1 wherein said step of varying includes comparing a number of bits of the output utilized to represent the class code in the data stream with the predetermined compression ratio.
3. The method as defined in claim 2 wherein if the number of bits utilized is greater than the predetermined compression ratio then the ranges of error values is modified in size for the first class set such that error value ranges encompassing error values having a greater frequency of occurrence are increased in size to encompass a wider range of error values, thereby decreasing the compression ratio, and if the number of bits utilized is less than the predetermined compression ratio then the range of error value ranges for the first class set is modified in size, such that error value ranges encompassing error values having a greater frequency of occurrence are decreased in size to encompass a narrower range of error values thereby increasing the compression ratio.
4. The method as defined in claim 1 wherein the step of quantizing the data includes the steps of: generating a predicted data value for the data value to be quantized; determining the difference between the predicted data value and the data value, such that an error value is generated for the data value; and identifying the class for the data value to be quantized by determining the range of error values the error value is within.
5. The method as defined in claim 1 wherein the step of outputting includes the step of encoding the class code.
6. The method as defined in claim 1 wherein the step of providing comprises the step of providing at least one binary decision tree having a root node and a plurality of binary nodes represented by pairs of threshold values, each member of each pair of threshold values representing a node in the binary decision tree and a threshold of a range of data values.
7. The method as defined in claim 1,2, 3, 4, 5 or 6 wherein the step of providing comprises the step of providing at least one binary decision tree having a plurality of leaf nodes and at least one non-leaf node arranged into a rooted binary tree, each leaf node represented by pairs of threshold error values, each member of each pair of threshold error values representing a node in the binary decision tree and a threshold of a range of data values and each said at least one non-leaf node representing a binary decision required to arrive at an appropriate one of the plurality of leaf nodes.
8. The method as defined in claim 7 wherein said step of providing at least one binary decision tree includes converting a root node in the rooted binary tree directly to one leaf node containing a predetermined quantization range and another leaf node is further subdivided into a first sub-tree containing all thresholds greater than the predetermined quantization range and a second set containing all threshold less than the predetermined quantization range.
9. The method as defined in claim 7 wherein said step of providing at least one binary decision tree includes connecting a root node in the rooted binary tree directly to one leaf node containing a predetermined quantization range and another leaf node containing quantization ranges other than the predetermined quantization range, wherein said another leaf node is further subdivided into a sub-tree containing threshold error values, having equal magnitude and opposite signs.
10. The method as defined in claim 7 wherein said step of providing at least one binary decision tree includes connecting a root node in the rooted binary tree directly to one leaf node containing quantization ranges greater or less than a predetermined threshold error value and another leaf node containing the remaining quantization range.
11. The method as defined in claim 1 wherein said step of varying occurs at the end of a predetermined number of scan lines.
12. The method as defined in claim 11 wherein said predetermined number of scan lines equal 1, such that said step of varying occurs at the end of every scan line.
13. A method for compressing a stream of data at a predetermined compression ratio, said method comprising the steps of: providing a first class set having a first plurality of error value ranges, wherein each error value range covers a sequential set of error values arid is identified by a class code representing the sequential set of error values associated said each error value range and further wherein a class code encompassing error values having a greater frequency of occurrence employs a lesser number of bits than a class code for a class encompassing error values having a lesser frequency of occurrence; generating a predicted data value for the data value to be quantized; determining an error value as the difference between the predicted data value and the data value to be compressed; identifying a class code for the data value by determining an error value range in the plurality of error value ranges the error value is within; encoding the class code to a first code comprising at least one bit, such that the data value is quantized; outputting the first code as part of a compressed data stream; after outputting the first code for a predetermined number of data values, comparing a number of bits utilized to output the compressed data stream representing data values to the predetermined compression ratio; if the number of bits utilized is greater than the predetermined compression ratio, modifying the first plurality of error value ranges in size for the first class set to provide a second class set having a second plurality of error value ranges different in size from the first plurality of error value ranges, such that error value ranges encompassing error values having a greater frequency of occurrence are increased in size to encompass a wider range of error values, thereby decreasing the compression ratio; and if the number of bits utilized is less than the predetermined compression ratio, modifying the first plurality of error value ranges for the first class set to provide a second class set having a second plurality of error value ranges different in size from the first plurality of error value ranges, such that error value ranges encompassing error values having a greater frequency of occurrence are decreased in size to encompass a narrower range of error values, thereby increasing the compression ratio; such that error value ranges are adapted to maintain the compressed data stream in the proximity of the predetermined compression ratio.
14. A method for compressing a stream of data values at a predetermined compression ratio, said method comprising the steps of: establishing at least one binary decision tree for the data values, said binary decision tree having a plurality of leaf nodes and at least one non-leaf node arranged in a binary rooted tree, each leaf node represented by pairs of threshold error values, each member of each pair of threshold error values representing a leaf node in the binary decision tree and a threshold of a range of data values and each said at least one non-leaf node representing a binary decision required to arrive at the appropriate leaf node; identifying a range of error values that the data value is within; quantizing the data value, wherein the step of quantizing the data value includes the step of generating a binary code according to the range of error values the data value is within and a path address of the node corresponding to the range threshold; entropy coding said binary code, such that the stream of data values are output as a compressed bit stream after outputting a binary code for a predetermined number of data values, comparing a number of bits utilized to output the compressed bit stream representing data values to the predetermined compression ratio; if the number of bits utilized is greater than the number of bits dictated by the predetermined compression ratio, increasing the ranges of error values in size by increasing the values of the threshold values, such that ranges represented by nodes closer to a root node in the binary rooted tree, and therefore identified by a binary code having a lessor number of bits, are increased in size to encompass a wider range of data values, thereby decreasing the compression ratio; and if the number of bits utilized is less than the number of bits dictated by the predetermined compression ratio, decreasing the ranges of error values in size by decreasing the values of the threshold values, such that ranges represented by nodes closer to the root node are decreased in size to encompass a narrower range of data values, thereby increasing the compression ratio; such that ranges of error values are adapted to maintain the compressed data stream in the proximity of the predetermined compression ratio.
15. The method for compressing a stream of data values as set forth in claim 14, further comprising the steps of: predicting the value of the data value to be quantized, wherein a predicted data value is produced; and generating an error value from the difference between the predicted data value and the data value to be quantized, said threshold values representative of threshold values for ranges of error values, such that said binary decision tree represents a range of error values and binary codes are generated for the error values.
16. The method for compressing a stream of data values as set forth in claim 14 or 15, wherein the data values comprise a plurality of pixels representative of a digital image.
17. The method as set forth in claim 14, wherein the threshold values are determined according to a set of possible data values and a desired quantization granularity of zones.
18. The method as set forth in claim 13, further comprising decompressing the compressed data, comprising the steps of: decoding the class code to identify the class code of the data value; determining the range of error values from the encoded class code; selecting an error value from the range of error values; generating a predicted data value for the data value to be decompressed; constructing the compressed data value from the selected error value and the predicted data value.
19. The method as set forth in claim 18 further comprising the steps of determining the midpoint of the range determined from the encoded class code as the selected error value, and further comprising the step of adding error value to the predicted value to decompress the compressed data.
20. The method as set forth in claim 14, further comprising decompressing the compressed data, comprising the steps of: decoding the class code to identify the class code of the data value; determining the range of error values from the encoded class code; selecting an error value from the range of error values; generating a predicted data value for the data value to be decompressed; constructing the compressed data value from the selected error value and the predicted data value.
21. The method as set forth in claim 20 further comprising the steps of determining the midpoint of the range determined from the encoded class code as the selected error value, and further comprising the step of adding the selected error value to the predicted value to decompress the compressed data.
22. An apparatus for compressing a stream of data values at a predetermined compression ratio comprising: at least one binary decision tree for encoding the data error values, said binary decision tree comprising a root node and a plurality of binary nodes represented by pairs of threshold values, each member of each pair of threshold values representing a node in the binary decision tree and a threshold of a range of data error values; a first look-up table for storing threshold values for different quantization granularities, each of said threshold values representing a threshold of a range of values and organized in groups according to the quantization granularity, said range of values identified by a class code identifying a binary path from the root node to the node corresponding to the threshold value. selection means for selecting a first quantization granularity to index the first look-up table; comparison means for identifying a range of values in the selected quantization granularity within which the input data value lies, said comparison means comparing the data value to the threshold values of the group selected according to the first quantization granularity from the first lookup table; generation means for generating a binary code, said binary code comprising at least one bit and determined according to the range the data value is within and the path address of the node corresponding to the range; output means for outputting a compressed data stream wherein said compressed stream includes data representing the binary code subjected to entropy encoding; counting means for counting a number of bits output as part of the compressed data stream; comparison means for comparing the number of bits utilized to output the compressed data stream to the predetermined compression ratio; quantization granularity control means for updating the quantization granularity of the group of threshold values, if the number of bits utilized is greater than the predetermined compression ratio, said control means controls said selections means to select a second quantization granularity that is coarser than the first quantization granularity, such that groups encompassing error values having a greater frequency of occurrence having a class code employing a lessor number of bits are increased in size to encompass a wider range of error values thereby decreasing the compression ratio; and if the number of bits utilized is less than the predetermined compression ratio, said control means controls said selections means to select a second quantization granularity that is finer than the first quantization granularity such that groups encompassing error values having a greater frequency of occurrence having a class code employing a lessor number of bits are decreased in size to encompass a narrower range of error values thereby increasing the compression ratio, such that error ranges are adapted to maintain the compressed data stream in the proximity of the predetermined compression ratio.
23. The apparatus as set forth in claim 22, further comprising a zone bias which is input to the selection means to bias the quantization granularity to index the first look-up table.
24. The apparatus as set forth in claim 22 further comprising: a predictor for generating a predicted data value for the data value to be quantized; subtraction means for determining the error value for the data value to be quantized to be the difference between the data value and the predicted data value, wherein said threshold values are representative of threshold values for ranges of error values, and said binary decision tree represents a range of error values and binary codes are generated for the error values.
25. The apparatus as set forth in claim 24, wherein the data values to be compressed comprise a plurality of pixels representative of a digital image.
26. The apparatus as set forth in claim 24, further comprising a decompressor for reconstructing the data value from the class code, comprising: a decoder for decoding the class code to identify the class code of the data value; a second look up table comprising error values corresponding to the class codes at a predetermined quantization coarseness, the quantization granularity determined by the selection means; retrieval means for retrieving a representative error value from the second look up table according to the class code and the quantization coarseness; said predictor generating a predicted data value for the data value to be reconstructed; reconstruction means for generating the data value from the predicted data value and the class code.
27. The apparatus as set forth in claim 26, wherein the representative error value is an error value at the midpoint of the range of the error values determined from the class code.
28. A method for decompressing a stream of bits representative of data values at a predetermined decompression ratio, wherein the data values include encoded class codes used to quantize the original data values, said method comprising the steps of: establishing a first binary decision tree for decoding the data error values, said binary decision tree comprising a root node and a plurality of binary nodes represented by pairs of symmetric threshold values, symmetric around the root node, each member of each pair of symmetric threshold values representing a node in the binary decision tree and a threshold of a range of data values, each node identified by a class code comprising bits representing a path address from the root node to the node; decoding a stream of bits to determine the node corresponding to the error value range the data value is within; reconstructing the data value from the error value range corresponding to the decoded node; after decompressing a predetermined number of data values, comparing a number of input bits in the stream of bits utilized to represent the compressed data to the predetermined compression ratio; if the number of bits utilized is greater than the number of bits dictated by the predetermined compression ratio, increasing the error value ranges in size by increasing the value of the symmetric threshold values to produce a second binary decision tree for decoding data error values such that error value ranges represented by nodes closer to the root node and identified by a binary code having a lessor number of bits, are increased in size to encompass a wider range of data error values thereby decreasing the compression ratio; and if the number of bits utilized is less than the number of bits dictated by the predetermined compression ratio, decreasing the error value ranges in size by decreasing the value of the symmetric threshold values to produce a second binary decision tree for decoding data error values such that error value ranges represented by nodes closer to the root node and identified by a binary code having a lessor number of bits, are decreased in size to encompass a narrower range of data error values thereby increasing the compression ratio; such that the error ranges change to maintain the compressed data stream in the proximity of the predetermined compression ratio and accurately reconstruct the data values.
29. An apparatus for decompressing a stream of bits representative of data values, wherein said data values include encoded class codes used in quantizing original data values said data values compressed at a predetermined compression ratio, said apparatus comprising: a first look-up table for storing error values for different quantization granularities, each of said error values representing a threshold of a range of data error values and organized in groups according to the quantization granularity, each said range of error values identified by a class code; selection means for selecting a first quantization granularity to index the first look-up table and retrieve a group of error values; means for generating a predicted data value for the data value to be quantized; a decoder for decoding a portion of the stream of bits to produce a class code corresponding to the data value to be reconstructed; means for determining a representative error value for the class code decoded at the selected quantization granularity from group of values retrieved from the look up table; reconstruction means for reconstructing the data value from the predicted data value and representative error value; counting means for counting the number of bits of the input bit stream utilized to encode class codes; comparison means for comparing the number of bits utilized to the predetermined compression ratio; quantization granularity control means for updating the quantization granularity of the group of threshold values, if the number of bits utilized is greater than the predetermined compression ratio, said control means controls said selections means to select a second quantization granularity that is coarser than the first quantization granularity such that the classes encompassing error values having a greater frequency of occurrence having a class code employing a lessor number of bits are increased in size to encompass a wider range of error values thereby decreasing the compression ratio; and if the number of bits utilized is less than the predetermined compression ratio, said control means controls said selections means to select a second quantization granularity that is finer than the first quantization granularity such that the classes encompassing error values having a greater frequency of occurrence having a class code employing a lessor number of bits are decreased in size to encompass a narrower range of error values thereby increasing the compression ratio; such that error value ranges are adapted by selecting another quantization granularity to maintain the compressed data stream in the proximity of the predetermined compression ratio and accurately reconstruct the data values.