System and method for encoding three-dimensional signals using a matching pursuit algorithm

[0001] This application claims the benefit under 35 USC 119(c) of U.S. provisional application No. 60/334,521, which was filed on Nov. 30, 2001. The application also relates to the co-pending patent application entitled System and Method for Equal Perceptual Relevance Packetization of Data, Ser. No. ______, which claims the benefit under 35 USC 119(c) of U.S. provisional application No. 60/334,521, filed Nov. 30, 2001, as well as the co-pending patent application entitled Transcoding Proxy and Method for Transcoding Encoded Streams, Ser. No. ______, which claims the benefit under 35 USC 119(c) of U.S. provisional application No. 60/334,514, filed Nov. 30, 2001.

[0002] This invention relates generally to digital signal representation, and more particularly to an apparatus and method to compress a video signal for improved source quality versus decoding complexity for a given compression bit rate and improved resistance against data loss when delivered over an error-prone network. Further, the invention provides an apparatus and method to improve the delivery quality of digital multimedia streams over a lossy packet network.

[0003] The purpose of source coding (or compression) is data rate reduction. For example, the data rate of an uncompressed NTSC (National Television Systems Committee) TV-resolution video stream is close to 170 Mbps, which corresponds to less than 30 seconds of recording time on a regular compact disk (CD). The choice of a compression standard depends primarily on the available transmission or storage capacity as well as the features required by the application. The most often cited video standards are H.263, H.261, MPEG-1 and MPEG-2 (Moving Picture Experts Group). The aforementioned video compression standards are based on the techniques of discrete cosine transform (DCT) and motion prediction, even though each standard targets a different application (i.e., different encoding rates and qualities). The applications range from desktop video-conferencing to TV channel broadcasts over satellite, cable, and other broadcast channels. The former typically uses H.261 or H.263 while MPEG-2 is the most appropriate compression standard for the video broadcast applications.

[0004] Motion prediction operates to efficiently reduce the temporal redundancy inherent to most video signals. The resulting predictive structure of the signal, however, makes it vulnerable to data loss when delivered over an error-prone network. Indeed, when data loss occurs in a reference picture, the lost video areas will affect the predicted video areas in subsequent frame(s), in an effect known as temporal propagation.

[0005] Tri-dimensional (3-D) transforms offer an alternative to motion prediction. In this case, temporal redundancy is reduced the way spatial redundancy is; that is, using a mathematical transform for the third dimension (e.g., wavelets, DCT). Algorithms based on 3-D transforms have proven to be as efficient as coding standards such as MPEG-2, and comparable in coding efficiency to H.263. In addition, error resilience is improved since compressed 3-D blocks are self-decodable.

[0006] Non-orthogonal transforms present several properties that provide an interesting alternative to orthogonal transforms like DCT or wavelet. Decomposing a signal over a redundant dictionary improves the compression efficiency, especially at low bit rates where most of the signal energy is captured by few elements. Moreover, video signals issued from decomposition over a redundant dictionary are more resistant to data loss. The main limitation of non-orthogonal transforms is encoding complexity.

[0007] Matching pursuit algorithms provide a way to iteratively decompose a signal into its most important features with limited complexity. The matching pursuit algorithm will output a stream composed of both atom parameters and their respective coefficients. The problem with the state-of-the-art in matching pursuit is that the dictionaries do not address the need for decomposition along both the spatial and temporal domains, and also the optimization of source coding quality versus decoding complexity for a given bit rate.

[0008] The art in Matching Pursuit (MP) coding is limited. A publication by S. G. Mallat and Z. Zhang, entitled Matching Pursuits With Time-Frequency Dictionaries, Transactions on Signal Processing, Vol. 41, No. 12, December 1993 details one application of matching pursuit coding. In addition, the publication entitled Very Low Bit-Rate Video Coding Based on Matching Pursuits, by R. Neff and A. Zakhor, Circuits and Systems for Video Technology, Vol. 7, No. 1, February 1997, the publication entitled Decoder Complexity and Performance Comparison of Matching Pursuit and DCT-Based MPEG-4 Video Codecs, by R. Neff, T. Nomura and A. Zakhor, Circuits and Systems for Video Technology, Vol. 7, No. 1, February 1997, and U.S. Pat. No. 5,699,121, detail using a 2-D matching pursuit coder to compress the residual prediction error resulting from motion prediction.

[0009] The shortcomings of the prior art include, first, that matching pursuit has never been proposed for coding 3-D signals. Second, the basic functions have been limited to Gabor functions because they were proven to minimize the uncertainty principle. However these functions are generally isotropic (same scale along x- and y-axes) and do not address image characteristics such as contours and textures.

[0010] What is needed, therefore, is a system and method to represent a video signal for improved source quality versus decoding complexity for a given compression rate and improved resistance to data loss when delivered over an error prone network.

[0011] The foregoing and other objectives are realized by the present invention, which alleviates the problems related to hybrid DCT/motion prediction coding by using a 3-D matching pursuit algorithm. The invention defines a separable 3-D structured dictionary. The resulting representation of the input signal is highly resistant to data loss (non-orthogonal transforms). Also, it improves the source coding quality versus decoding requirements for a given target bit rate (anisotropy of the dictionary). The invention disclosed herein provides an apparatus and method to compress a video signal for improved source quality versus decoding complexity for a given compression rate and improved resistance against data loss when delivered over an error-prone network. The method relies on a 3-D matching pursuit algorithm with an improved 3-D dictionary. The 3-D MP encoder transforms blocks of frames into a set of spatio-temporal functions from the improved dictionary. The 3-D coder outputs a video stream that is highly resistant to data loss. Also, the proposed dictionary is optimized for source quality versus decoding complexity for a given compression rate. The present invention mainly targets asymmetric applications (high-end PC for encoding and a wide range of devices for decoding).

[0012] The advantages of the present invention will become readily apparent to those ordinarily skilled in the art after reviewing the following detailed description and accompanying drawings, wherein:

[0013] FIG. 1 is a block diagram illustrating the overall architecture in which the present invention takes place;

[0014] FIG. 2 illustrates the Signal Transform Block 100 from FIG. 1;

[0015] FIG. 3 is a flow graph illustrating the Matching Pursuit iterative algorithm of FIG. 2;

[0016] FIG. 4 shows an example of a spatio-temporal dictionary function in accordance with the present invention;

[0017] FIG. 5 shows an example of video signal reconstruction after 100 Matching Pursuit iterations; and

[0018] FIG. 6 shows an example of video signal reconstruction after 500 Matching Pursuit iterations.

[0019] The present invention alleviates the problems related to hybrid DCT/motion prediction coding by using a 3-D matching pursuit algorithm. The invention defines a separable 3-D structured dictionary. The resulting representation of the input signal is highly resistant to data loss (non-orthogonal transforms). Also, it improves the source coding quality versus decoding requirements for a given target bit rate (anisotropy of the dictionary).

[0020] Matching Pursuit (MP) is an adaptive algorithm that iteratively decomposes a function L²(e.g., image, video) over a possibly redundant dictionary of functions called atoms (see FIG. 3). Let Dg be such a dictionary with g1. is first decomposed into:

[0021] where <g₀>g₀ represents the projection of onto g₀ and R is the residual component. Since all elements in D have a unit norm, g₀ is orthogonal to R, and this leads to:

[0022] In order to minimize R and thus optimize compression, one must choose g₀ such that the projection coefficient <g₀> is maximum. Applying the same strategy to the residual component carries the pursuit further. After N iterations, one has the following decomposition for : $f=\underset{n=0}{\overset{N-1}{}}{g}_n|R^{n}f{g}_n+R^{N}f,$

[0023] with, R⁰. Similarly, the energy ² is decomposed into: $f^2=\underset{n=0}{\overset{N-1}{}}|g_n|R^{n}f{|}^2+{R^{N}f}^2.$

[0024] Although matching pursuit places very few restrictions on the dictionary set, the structure of the latter is strongly related to convergence speed and thus to coding efficiency. The decay of the residual energy Rⁿ² has indeed been shown to be upper-bounded by an exponential, whose parameters depend on the dictionary. However, true optimization of the dictionary can be very difficult. Any collection of arbitrarily sized and shaped functions can be used, as long as completeness is respected.

[0025] The method of the present invention is useful in a variety of applications where it is desired to produce a low to medium bit rate video stream to be delivered over an error-prone network and decoded by a set of heterogeneous devices.

[0026] Let first the dictionary define the set of basic functions used for the signal representation. The basic functions are called atoms. The atoms are represented by a possibly multi-dimensional index , and the index along with a correlation coefficient c_i forms an MP iteration.

[0027] The method of the present invention then is as follows. As illustrated in FIG. 2, the original video signal is first passed to a Frame Buffer 101 to form groups of K video frames of dimension XY. The method of the present invention thus decomposes the input video sequence into K-frames long independent 3D blocks. The dictionary 102 is composed of atoms, which are also 3-D functions of the same size, i.e., KXY. The method as shown in FIG. 3 iteratively compares the residual 3-D function with the dictionary atoms and elects in the Pattern Matcher 103 the 3-D atom that best matches the residual signal (i.e., the atom which best correlates with the residual signal). The parameters of the elected atom, which are the index and the coefficient c_i are sent across to the following block performing the Coding (i.e., quantization, entropy coding probably followed by channel coding, as shown in FIG. 1). The pursuit continues up to a predefined number of iterations N, which is either imposed by the user, or deduced from a rate constraint and/or a source coding quality constraint.

[0028] The method relies on a structured 3-D dictionary 102, which allows for a good trade-off between dictionary size and compression efficiency. In our method, the dictionary is constructed from separable temporal and spatial functions, since features to capture are different in spatial and temporal domains. An atom dictionary is therefore written as g(x,y,k)¹S_s(x,y)T_t(k), where corresponds to the parameters that transform the generating function. The parameter is chosen so that each atom is normalized, i.e., g(x,y,k)²1. Each entry of the dictionary therefore consists in a series of 7 parameters. The first 5 parameters specify position, dilation and rotation of the spatial function of the atom, S_s(x,y). The last 2 parameters specify the position and dilation of the temporal part of the atom, T_t(k).

[0029] The spatial function in a preferred embodiment of the present invention is generated using B-splines, which provides the advantages of having a limited and calculable support, and optimizes the trade-off between compression efficiency (i.e., source coding quality for a given target bit rate) and decoding requirements (i.e., CPU and memory requirements to decode the input bit Stream). A B-spline of order n is given by: ${}^n\left(x\right)=\frac{1}{n!}\underset{k=0}{\overset{n+1}{}}\left(\begin{array}{c}n+1\\ k\end{array}\right){{\left(-1\right)}^k\left[x-k+\frac{n+1}{2}\right]}_{+}^n,$

[0030] where yⁿ represents the positive part of yⁿ.

[0031] The 2-D B-spline is formed with a 3rd order B-spline in one direction, and its first derivative in the orthogonal direction to catch edges and contours. Rotation, translation and anisotropic dilation of the B-spline generates an overcomplete dictionary. The anisotropic refinement permits to use different dilation along the orthogonal axes, in opposition to Gabor atoms. Thus the spatial dictionary maximizes the trade-off between coding quality and decoding complexity for a specified source rate. The spatial function of the 3-D atoms can be written as S_sS_x^xS_y^y, with: $\begin{array}{c}{S}_x^x\left(x\right)={}^3\left(\frac{\cos \left(\right)\left(x-p_x\right)+\sin \left(\right)\left(y-p_y\right)}{d_x}\right),\\ \begin{array}{c}{S}_y^y\left(y\right)={}^2\left(\frac{\sin \left(\right)\left(x-p_x\right)-\cos \left(\right)\left(y-p_y\right)}{d_y}+\frac{1}{2}\right)-\\ {}^2\left(\frac{\sin \left(\right)\left(x-p_x\right)-\cos \left(\right)\left(y-p_y\right)}{d_y}-\frac{1}{2}\right).\end{array}\end{array}$

[0032] The index _s is thus given by 5 parameters; these are two parameters to describe an atom's spatial position (p_x,p_y), two parameters to describe the spatial dilation of the atom (d_x,d_y), and the rotation parameter .

[0033] The temporal function is designed to efficiently capture the redundancy between adjacent video frames. Therefore T_t(k) is a simple rectangular function written as: $T_t\left(k\right)=\left\{\begin{array}{cc}1& \mathrm{if}{p}_{k}k<p_k+d_k\\ 0& \mathrm{otherwise}\end{array}\right\}.$

[0034] The temporal index _t is here given by 2 parameters; these are one parameter to describe the atom's temporal position p_k and one parameter to describe the temporal dilation d_k.

[0035] The index parameters range (p_x,py,p_k,d_x,d_y,d_k,) is designed to cover the size of the input signal. Spatial-temporal positions allow to completely browse the 3D input signal, and the dilations values follow an exponential distribution up to the 3D input signal size. The basis functions may however be trained on typical input signal sets to determine a minimal dictionary, trading off the compression efficiency.

[0036] FIG. 1 is a block diagram illustrating the overall architecture in which the present invention takes place. The Signal Transform block 100 is the focus of this invention at which the foregoing transformation takes place. After transformation, the digital signal is quantized 200, entropy coded 300 and packetized 400 for delivery over the error-prone network 500. A wide range of decoding devices are targeted; from a high-end PC 600, to PDAs 700 and wireless devices 800.

[0037] FIG. 2 illustrates the Signal Transform Block 100. The video sequence is fed into a frame buffer 101, and where a spatio-temporal signal is formed. This signal is iteratively compared to functions of a Pattern Library 102 through a Pattern Matcher 103. The parameters of the chosen atoms are then sent to the quantization block 200, and the corresponding features are subtracted from the input spatio-temporal signal.

[0038] FIG. 3 is a flow chart illustrating the Matching Pursuit iterative algorithm of FIG. 2. The Residual signal 101, which consists in the input video signal at the beginning of the Pursuit, is compared to a library of functions and a Pattern matcher 103 elects the best matching atom. The contribution of the chosen atom is removed from the residual signal 104 to form the residual signal of the next iteration.

[0039] The Pattern Matcher 303 basically comprises an iterative loop within the MP algorithm main loop, as shown in FIG. 3. The residual signal is compared with the functions of the dictionary by computing, pixel-wise, the correlation coefficient between the residual signal and the atom. The square of the correlation coefficient represents the energy of the atom (107). The atom with the highest energy (112) is considered as the atom that best matches the residual signal characteristics and is elected by the Pattern Matcher. The atom index and parameters and sent across (118) the Entropy Coder as shown in FIG. 2, and the residual signal is updated in consequence (104). To increase the speed of the encoding, the best atom search can be performed only on a well-chosen subset of the dictionary functions. However, such a method may result in a sub-optimal signal representation.

[0040] FIG. 4 shows an example of a spatio-temporal dictionary unction. FIG. 5 shows an example of video signal reconstruction after 100 Matching Pursuit iterations. FIG. 6 shows an example of video signal reconstruction after 500 Matching Pursuit iterations. Clearly the amount of signal information improves with successive iterations.

[0041] The invention has been detailed in terms of a preferred embodiment. One having skill in the art will recognize that modifications may be made without departing from the spirit and scope of the invention as set forth in the appended claims.