US 5,148,489 AGrant
Method for Spectral Estimation to Improve Noise Robustness for Speech Recognition
Issue Date:1992-09-15
•15 Claims
•2 Drawing Sheets
Abstract
A method is disclosed for use in preprocessing noisy speech to minimize likelihood of error in estimation for use in a recognizer. The computationally-feasible technique, herein called Minimum-Mean-Log-Spectral-Distance (MMLSD) estimation using mixture models and Marlov models, comprises the steps of calculating for each vector of speech in the presence of noise corresponding to a single time frame, an estimate of clean speech, where the basic assumptions of the method of the estimator are that the probability distribution of clean speech can be modeled by a mixture of components each representing a different speech class assuming different frequency channels are uncorrelated within each class and that noise at different frequency channels is uncorrelated. In a further embodiment of the invention, the method comprises the steps of calculating for each sequence of vectors of speech in the presence of noise corresponding to a sequence of time frames, an estimate of clean speech, where the basic assumptions of the method of the estimator are that the probability distribution of clean speech can be modeled by a Markov process assuming different frequency channels are uncorrelated within each state of the Markov process and that noise at different frequency channels is uncorrelated.
Metadata
Assignee
- SRI International
Inventors
- Adoram Erell
- Mitchel Weintraub
Application Information
Application Number:US 8478759
Filing Date:1992-03-09
Priority Date:1990-02-28
Art Unit:231
Classifications
IPC:
G10L 500
Field of Search:
38139546-48;432
Patent Drawings (2 sheets)
Description
COPYRIGHT NOTICE
A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever.
BACKGROUND OF THE INVENTION
This invention was supported in part by a grant from the National Science Foundation (IRI-8720403) and in part by SRI International of Menlo Park, Calif.
This invention relates to speech recognition in the presence of noise, and more particularly to a method for preprocessing speech for use in connection with a speech recognition system.
Speech recognition systems are very sensitive to differences between a training condition which is free of noise and operating conditions in the presence of noise. In particular, speech recognition systems can be trained to recognize specific speech patterns in the absence of noise and are therefore trained on high-quality speech. However, such systems degrade drastically in noisy environments.
Several methods for handling this problem are known, among them are methods of supplementing the acoustic preprocessing of a speech recognizer with a statistical estimator. A statistical estimator as used herein is intended to provide to a speech recognizer input values or signals which can be assumed to be clean speech information.
The task of designing a statistical estimator for speech recognition is that of defining an optimality criterion that will match the recognizer and of deriving an algorithm to compute the estimator based on this criterion. Defining the optimality criterion is easier for speech recognition than it is for speech enhancement for human listeners, since the signal processing technique is known in the former but not in the latter. For a recognition system which is based on a distance metric, whether for template matching or vector quantization, it is reasonable to assume that the optimality criterion is to minimize the average distortion as measured by that distance metric. Achieving this criterion is frequently computationally infeasible.
With discrete Fourier transform (DFT), filter-bank based systems, the distance measure which is typically used is a weighted Euclidean distance on the cosine transform of the logarithm of the output energy of the filters, often referred to as the "liftered cepstral distance." (The cepstrum in a filter-bank system is defined as a transform of the filter energies.) Achieving this estimation criterion using this distance metric is computationally difficult with additive noise. Published estimation algorithms which have been applied to filter-bank based systems are the minimum mean square error (MMSE) algorithm and the spectral subtraction algorithm, applied to either discrete Fourier transform (DFT) coefficients or filter-bank output energies. (Reference to Porter et al. and Van Compernolle 1 and 2 discussed below.) A basic difference between the multiple-dimensional cepstral distance optimality criterion and the single frequency channel minimum mean square error (MMSE) distance criterion is that the cepstral distance implies a joint estimation of a feature vector whereas the MMSE distance implies an independent estimation of scalar quantities. Because the speech spectral energies at different frequencies are in fact correlated, use of an independent estimate of individual frequency channels results in suboptimal estimation.
This art presumes a basic familiarity with statistics and Markov processes, as well as familiarity with the state of the art in speech recognition systems using hidden Markov models. By way of example of the state of the art, reference is made to the following patents and publications, which have come to the attention of the inventors in connection with the present invention. Not all of these references may be deemed to be relevant prior art.
Papers
Rabiner, "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition," Proc. IEEE, Vol. 77, No. 2, February, 1989.
Nadas et al., "Speech Recognition Using noise-adaptive prototypes," IEEE Trans. on ASSP, Vol. 37, No. 10, October, 1989.
Stern et al., "Acoustical pre-processor for robust speech recognition," Proc. DARPA Speech and Natural Language Workshop, Session, October, 1989.
Ephraim et al., "Speech Enhancement Using a Minimum Mean-Square Error Short-Time Spectral Estimator," IEEE Trans. ASSP, Vol. 32, pp. 1109-1112 (December, 1984).
Ephraim et al., "Speech Enhancement Using a Minimum Mean-Square Error Log-Spectral Amplitude Estimator," IEEE Trans. ASSP. Vol. 33, pp. 443-447 (April, 1985).
Porter et al., "Optimal Estimators for Spectral Restoration of Noisy Speech," Proc. ICASSP, Vol. 2, pp. 18A2.1-2.4 (1984).
Van Compernolle, "Noise Adaptation in a Hidden Markov Model Speech Recognition System," Computer Speech and Language, Vol. 3, pp. 151-167, 1989.
Van Compernolle, "Spectral Estimation Using a Log-Distance Error Criterion Applied to Speech Recognition," Proc. ICASSP, Vol. 1, pp. 258-261 (1989).
Gray, "Vector Quantization," The ASSP Magazine, Vol. 1, No. 2, pp. 3-29 (April, 1984).
The Rabiner paper is a survey article on Hidden Markov Model applications to speech recognition which is background for understanding the present invention. It does not address the noise problem. It is incorporated herein by reference.
The remaining patents and publications describe other work in the general field.
The Nadas et al. paper describes a method that addresses the noise problem. It is not however a preprocessing method.
The Stern et al. paper describes a method that addresses the noise problem using a preprocessor based on spectral subtraction.
The Van Compernolle (1) is a description of a spectral subtraction type of preprocessor.
The Van Compernolle (2) is a description of a preprocessor using Minimum Mean Square Error independent estimation of single channels.
The Porter et al. and Ephraim et al. papers describe preprocessors for use in speech recognition techniques using the minimum mean square error estimation of various functions of the digital Fourier transform (DFT) coefficients, including the logarithm of the DFT amplitude. These techniques deal only with single DFT coefficients.
Sedgwick et al. describes work at the National Resource Development Corporation on a noise compensation apparatus for speech recognition system, wherein input signals corresponding to levels in frequency spectrum regions are derived and the (Euclidean) distance for noisy input cells is determined to take advantage of noise level during both recognition and training. In both recognition and training processes, signals reaching a microphone are digitized and passed through a filter bank to be separated into frequency channels. In training, a noise estimator and a masker are used with a recognizer to prepare and store probability density functions (PDFs) for each channel partially defining Markov models of words to be recognized. The PDFs are derived only from input signals above noise levels, but derivation is such that the whole of each PDF is represented. In recognition, "distance" measurements on which recognition is based are derived for each channel. If the signal in one channel is above the noise level, then the distance is determined by the recognizer from the negative logarithm of the PDF. If a channel signal is below a noise level, then the distance is determined from the negative logarithm of the cumulative distance of the PDF to the noise level. This publication describes a recognition system with noise compensation, but it does not address preprocessing to address the noise problem.
Bahl et al. '156 describes IBM work on apparatus and method for training the statistics of a Markov model speech recognizer to a subsequent speaker. Therein, the invention determines label output probabilities at transitions in the Markov models corresponding to the subsequent speaker where there is sparse training data. This patent does not address the noise problem.
Levinson et al. describes AT&T Bell Labs work on a speech recognizer which includes a plurality of stored constrained hidden Markov model reference templates and a set of stored signals representative of prescribed acoustic features of the plurality of reference patterns. This patent does not address the noise problem.
Juang et al. describes further AT&T Bell Labs work on a hidden Markov model speech recognition arrangement. Markov model speech pattern templates are formed by analyzing identified speech patterns to generate frame sequences of acoustic feature signals. This patent does not address the noise problem.
Bahl et al. '036 describes IBM work in a speech recognition system whereby discrimination between similar sounding uttered words is improved by weighting the probability vector data stored for the Markov model representing the reference word sequence of phones. The weighting vector is derived for each reference word by comparing similar sounding utterances using Viterbi alignment and multivariate analysis which maximizes the differences between correct and incorrect recognition multivariate distributions. This patent does not address the noise problem.
None of the prior art teaches how to approximate the cepstral distance optimality criterion in preprocessing of noisy speech in a speech recognition system in a computationally feasible manner.
SUMMARY OF THE INVENTION
In accordance with the invention, a computationally-feasible method is provided for use in preprocessing noisy speech to minimize likelihood of error in estimation for use in a speech recognizer. The computationally-feasible technique, herein called Minimum-Mean-Log-Spectral-Distance (MMLSD) estimation using mixture models and Markov models, comprises the steps of calculating for each vector of speech in the presence of noise corresponding to a single time frame, an estimate of clean speech, where the basic assumptions of the method of the estimator are that the probability distribution of clean speech can be modeled by a mixture of components each representing a different speech class assuming different frequency channels are uncorrelated within each class and that noise at different frequency channels is uncorrelated. (EQ. 11 and FIG. 2). In a further embodiment of the invention, the method comprises the steps of calculating for each sequence of vectors of speech in the presence of noise corresponding to a sequence of time frames, an estimate of clean speech, where the basic assumptions of the method of the estimator are that the probability distribution of clean speech can be modeled by a Markov process assuming different frequency channels are uncorrelated within each state of the Markov process and that noise at different frequency channels is uncorrelated. (EQ. 21 and FIG. 3)
The invention will be better understood upon reference to the following detailed description, taken in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a block diagram of a speech recognition system incorporating a preprocessor employing a method in accordance with the invention.
FIG. 2 is a block diagram of a single frame MMLSD estimator using a mixture model according to a first method in accordance with the invention.
FIG. 3 is a flow chart illustrating a computation of a mixture of Gaussians model used in connection with the invention.
FIG. 4 is a block diagram of a MMLSD estimator for a sequence of time frames using a Markov model according to a second method in accordance with the invention.
DESCRIPTION OF SPECIFIC EMBODIMENTS
FIG. 1 is a block diagram of a speech recognition system 10 incorporating a preprocessing estimator 22 employing a method in accordance with the invention. The system 10 depicted is a filter-bank-based system employing a hidden Markov process recognizer. Alternatively, a template matching system could be employed for speech recognition. The recognition system 10 receives an analog time-domain signal representing speech in the presence of noise at an input 12, which in turn is applied to a feature extractor comprising an analog to digital converter (ADC) 14 and a filter bank 18. The ADC 14 converts the analog signal to digitized speech which are then applied on digital signal lines 16 to a time segmenter 15. The time segmenter 15 segments the digitized signal into time frames for subsequent processing. Output on lines 17 are applied to a filter bank 18. The filter bank 18 categorizes the speech+noise (noisy speech) components into a vector of filter log energies (or more generally spectral log energies) S' with components S'.sub.k for each time frame, each component representing one filter channel of speech information. The vector S' is then applied via lines 20 to a preprocessor 22 which functions as an estimator of the clean speech. The output of the preprocessor 22 is in the form of a estimate of clean speech, a vector S.
The vector S is optionally applied on lines 24 to an acoustic labeler 26 or directly to a speech recognizer 30.
The preprocessor 22 functions such that all subsequent processing treats input signals as if no noise is present. Three possible speech recognizers can be used with the preprocessor 22 in accordance with the invention. The speech recognizer 30 may be a discrete density Hidden Markov Model (HMM) recognizer with an acoustic labeler using a distance metric for acoustic labeling. Alternatively, it may use a continuous density HMM recognizer which uses a probabilistic algorithm for acoustic labeling but no distance metric. Still further, the speech recognizer 30 may use template matching, such as dynamic time warping, which uses a distance metric for the template matching. The output of the speech recognizer 30 on lines 32 is the recognized speech.
Referring now to FIG. 2, there is shown a first embodiment of a preprocessor 22 in accordance with the invention. The preprocessor 22 of FIG. 2 computes an estimate, for each time frame, of the vector of clean speech S from the vector of noisy speech S' based on:
1) the assumption that the probability distribution of clean speech can be modeled by a mixture of components as a mixture model, each component representing a different speech class assuming different frequency channels are uncorrelated within each class, and based on
2) a conditional probability function of a vector of noisy speech around a vector of clean speech which is based on the assumption that noise at different frequency channels is uncorrelated.
The estimator is a minimum mean square error (MMSE) estimation of the vector S, where the mean square error is in the vector Euclidean sense. The minimum Euclidean distance on the vector S of K filter log-energies yields the following vector estimator, (where boldface indicates a vector):
Using Bayes' Rule, the estimator is therefore of the form: ##EQU1## where the probability for the vector S' is given by:
This estimator is considerably more complex than a single channel-type estimator because it requires integration of K-dimensional probability distributions, e.g., 25 dimensions for 25 frequency channels. In accordance with the invention, approximated models for both the probability of S and the probability of S' around S can be used in the computation, since the assumptions are that the noise is additive and that the vector S is the vector of filter-bank log-energies.
First, the conditional probability of the vector S' around the vector S, or P(S'.vertline.S), can be modeled simply as the product of the marginal probabilities, or: ##EQU2## since it is assumed that Gaussian noise is uncorrelated in the frequency domain and since the energy value of a given noisy filter S'.sub.k depends only on the clean energy S.sub.k and on the noise level at that frequency (i.e., within the passband of the filter at that frequency). This model is merely an approximation, however, where the passbands of the filters overlap.
The conditional probability P(S'.sub.k .vertline.S.sub.k) can be modeled as follows:
Assume that the noise associated with the speech to be estimated can be represented by a stationary, ARMA (autoregressive moving average) stochastic process (i.e, viewed as white noise colored by linear filtering). Therefore, at each time frame, the coefficients of the discrete Fourier transform (DFT) for the noise are uncorrelated complex Gaussian random variables. Assume further that the filter output energy can be approximated by a sum of M coefficients. Finally, assume that the noise spectral power is uniform within the range of summation. With only noise present (i.e., no speech), the sum extends over a total of 2M random variables which are Gaussian, of zero mean and of a variance:
where N.sub.k is the expected value of the noise filter energy. Under these conditions, the variance-normalized filter energy will obey a chi-squared probability distribution (PD) with 2M degrees of freedom.
In the presence of speech and noise, the filter energy is given by:
where DFT.sub.s refers to speech coefficients and DFT.sub.n refers to noise coefficients.
The random variable given by Equation 6 divided by Equation 5, or E'.sub.k /.sigma..sup.2, will then obey a different probability distribution, namely, a probability distribution of noncentral chi-squared with 2M degrees of freedom and noncentral parameter .lambda..
Thus the conditional probability of the filter energy is given by: ##EQU3## where ##EQU4## With the following normalized log-energy variable defined, ##EQU5## the conditional probability for S'.sub.k is finally given by ##EQU6##
The value S'.sub.k is the filter log-energy value of observed speech in the presence of noise for the k.sup.th filter, and value S.sub.k is the filter log-energy value of clean speech.
The conditional probability of S'.sub.k around S.sub.k given by Equation 9 provides the needed "fuzziness" in the probability distribution to account for the uncertainty around the speech element S in the presence of noise.
There may be less than 2M degrees of freedom in actual practice due to deviations from the model assumptions. In particular, the filters are typically defined with trapezoidal frequency windows (rather than box-car or rectangular frequency windows), and the Hamming window of the discrete Fourier transform introduces correlations between the noise DFT coefficients. In addition, the noise spectrum of very broad filters may not be flat within the range of a single filter.
Second, a model is required for the probability distribution (PD) of the clean speech vector P(S). The clean-speech PD cannot be represented in the frequency domain as a product of the marginal probabilities. Rather, this PD can be modeled by a mixture model in the form: ##EQU7## where C.sub.n are mixture coefficients, and N is the number of mixture components or classes.
This model is based on the idea that the acoustic space can be divided into classes within which the correlation between different frequency channels is significantly smaller than within the space as a whole. The classes can represent either mutually exclusive or overlapping regions of the acoustic space. As hereinafter explained, the estimator for clean speech is given by: ##EQU8## where index n is a class and where the first term (estimate of S.sub.k around n) is the n.sup.th class-conditioned MMSE estimator given in a computationally-feasible form by: ##EQU9## where
and the second term (the a posteriori probability of n given the vector S', i.e., that the clean speech vector belonged to the n.sup.th class) is given by: ##EQU10## where ##EQU11## Thus the estimator can be viewed as a weighted sum of class-conditioned MMSE estimators. Where N=1, the resulting estimator is identical to an MMSE estimator of individual channels.
In order to realize a computationally-feasible estimator according to the invention, it is necessary to employ a mixture model to model P(S) by equation 10. Several implementation of the mixture model may be employed, depending on the application.
The simplest implementation of the mixture model is by vector quantization. The vector quantization mixture model identifies the classes with rigid-boundary partitions of the acoustic space and creates the partitions by vector quantization. A codebook of size N is created using the Lloyd algorithm. (The Lloyd algorithm is given in the literature in Gray.) The codebook minimizes the distortion as measured by the Euclidean distance, and P.sub.n (S.sub.k) is estimated from a histogram of all speech frames quantized into codeword n.
Another implementation of the mixture model which provides a better fit within computationally-feasible methods is a mixture of Gaussians model. This model is a parametric model for the PDs adjusted so as to maximize the likelihood of observed data given the model.
Parameterization with a mixture of Gaussians model begins with the assumptions that the probabilities P.sub.n (S.sub.k) are Gaussian distributions, each with a mean value of .mu..sub.nk and a standard deviation .sigma..sub.nk. The maximum likelihood problem thus becomes a problem of estimating Hidden Markov Model (HMM) parameters with continuous densities, where the model comprises a single state with N multivariate Gaussian components of diagonal covariance matrices. FIG. 3 illustrates steps for parameter estimation using an iterative procedure as follows:
Make initial estimates of C, .mu. and .sigma. (Step AA). A reasonable starting point for these "seed" values would be the classification by vector quantization using as values the relative numbers of vectors in each class, their mean and their standard deviation.
Next, perform a loop on all speech frames and for each frame "t" compute the probability .gamma..sub.n (t) according to the equations: ##EQU12## where P.sub.n (S.sub.t) is computed using the current values of .mu. and .sigma. (Step AB). The new parameter estimates are then given by the following time averages ##EQU13##
Finally, test for convergence of the total likelihood given by:
(Step AC). If convergence is not attained, then Step AB is repeated, and the convergence test (Step AC) is repeated until convergence is attained.
The above methods have potential difficulties in practice. First, filter-bank-based systems have filters with passbands that typically overlap, and second, the computational load, even in the foregoing model, may be excessive, particularly for interactive or near real-time recognition systems. With overlapping filters, the assumptions regarding statistical independence of channels are incorrect. While overlapping filters can be replaced with non-overlapping filters, it is also possible to apply a "Broadband" mixture model to reduce the computational load.
With overlapping filters, a K-dimensional vector of filter log-energies can be represented by a vector of less than K dimensions assuming a fewer number of filters with broad yet non-overlapping passbands. Quantization using the VQ mixture model is thereby simplified, and a new, lower-dimensional vector is introduced as a ["]wideband spectral vector [quantization mixture model" as follows:] R, defined as the log energy in a number of frequency bands.
The classification of speech frames proceeds by quantizing the vectors R with a codebook of size N. The mixture components P.sub.n (S.sub.k) of Equation 10 are then estimated based on these classes, and the a posteriori class probability is conditioned on the vector R' rather than on the vector S' as in Equation 11. ##EQU14## Equation 21 replaces Equation 11 and the a posteriori class probabilities replacing Equations 14 and 15 are given by: ##EQU15## where ##EQU16## where j is a broadband channel, R.sub.j is the log-energy in channel j, and the total number of bands is J.
P(R'.sub.j .vertline.n) is computed similarly to Equation (13), where R.sub.j and R'.sub.j replace S.sub.k and S'.sub.k. P.sub.n (R.sub.j)) can be either estimated from histograms of the speech frames quantized into codeword n, using vector quantization or it can be modeled by a Gaussian, similar to Gaussian Mixture modeling. P(R'.sub.j .vertline.R.sub.j) can similarly be modeled after P(S'.sub.k .vertline.S.sub.k) of Equation 9. The advantage of this method is therefore in the smaller number of integrals to be computed and multiplied in Equation (22), relative to Equation (14).
Referring now to FIG. 4, there is illustrated a second embodiment of a preprocessor 22 in accordance with the invention. The preprocessor 22 of FIG. 4 computes an estimate, for a sequence of time frames, of the vectors of clean speech, S.sub.O to S.sub.T from the sequence of vectors of noisy speech, S'.sub.O to S'.sub.T, based on:
1) the assumption that the probability distribution of clean speech can be modeled by a Markov model, each state of the Markov model representing a different speech class assuming different frequency channels are uncorrelated within each class, and based on
2) a conditional probability function of a vector of noisy speech around a vector of clean speech which is based on the assumption that noise at different frequency channels is uncorrelated.
The estimator is a minimum mean square error (MMSE) estimation of a sequence of vectors S.sub.O to S.sub.T, where the mean square error is in the vector Euclidean sense. The minimum Euclidean distance estimator of vector S of K filter log-energies given the sequence of noisy vectors S'.sub.O to S'.sub.T, yields the following vector estimator:
This vector estimator is computed using the following assumptions. The speech can be modeled by a Markov process so that the speech at any time t is in any one of N different states. The output probability distribution (PD) for state "n" is given by: ##EQU17##
The state output probability distributions and the transition probabilities between states are computed by identifying the states with partitions of the acoustic space. These partitions are exactly the same as those used in the vector quantization mixture model or the wideband vector quantization mixture model hereinabove. The transition probabilities are estimated from speech data by counting the number of transitions from one state to another.
With additive noise, the noisy speech is modeled by a Hidden Markov Model (HMM) where the states correspond to the states of the clean speech, and the output probability distributions are given by: ##EQU18## where P(S'.sub.k .vertline.n) is given by
and where P.sub.n (S.sub.k) is the output probability distribution of the k.sup.th component of the clean speech vector S for state "n". The probability of S'.sub.k given S.sub.k is computed using equations 7-9 hereinabove.
Given all of these assumptions, the estimator of FIG. 4 is given by:
The probability of state "n" given the sequence of noisy speech vectors in Equation 28 is computed by the forward-backward algorithm applied to the HMM of the noisy speech defined above. (The forward-backward algorithm is for example given in the Rabiner (1989) review article, referenced above, which is incorporated herein by reference and made a part hereof.)
A sample of one implementation of the six different preprocessor estimators in accordance with the present invention is presented in Appendix A attached hereto. The appendix is source code written in the LISP programming language.
The invention has now been described with reference to specific embodiments. Other embodiments will be apparent to those of ordinary skill in the art. It is therefore not intended that this invention be limited, except as indicated in the appended claims. ##SPC1##
Claims
We claim:
1. In a speech recognition system for responding to signals representative of digitized speech, a method for preprocessing a noisy speech signal to estimate a clean speech signal, comprising the steps of: categorizing each time-invariant segment of digitized speech and noise into a noisy speech vector, each element of said noisy speech vector representing one frequency channel of speech information in the presence of noise, said noise being assumed to be additive, time invariant and uncorrelated to the frequency domain; estimating a clean speech signal comprising a clean speech vector for each said element from said noisy speech vector by (1) determining the probability distribution of clean speech by applying the noisy speech vector to a mixture model composed of a mixture of components, each component representing a different speech class assuming different frequency channels are uncorrelated within each class, (2) modelling the conditional probability function of a vector of noisy speech around a vector of clean speech as uncorrelated at different frequency channels; and storing the estimated clean speech signal in memory.
2. The method according to claim 1 wherein said estimating step comprises: estimating filter log spectral energies on a multiple-frequency channel probability according to the function: ##EQU19## where index n is a class and where the estimate of S.sub.k around n is the n.sup.th class-conditioned MMSE estimator given by: ##EQU20## where (S.sub.k) dS.sub.k.
3. The method according to claim 2 wherein said estimating step comprises applying a minimum mean-log-spectral-distance estimation to said vector of noisy speech to obtain an estimation of Euclidean distance.
4. The method according to claim 1 wherein said conditional probability of a noisy speech vector around a clean speech vector P(S'.sub.k .vertline.S.sub.k) is modeled as follows: 1) noise associated with said speech to be estimated is assumed to be a stationary, autoregressive moving average stochastic process such that, at each time frame, coefficients of a discrete Fourier transform (DFT) for said noise are uncorrelated complex Gaussian random variables; 2) filter output energy is assumed to be approximated by a sum of M coefficients; 3) noise spectral power is assumed to be uniform within a range of passbands of filters; such that, in the presence of noise alone, said summation extends over a total of 2M random variables which are Gaussian, of zero mean and of a variance: where N.sub.k is the expected value of the noise filter energy wherein variance-normalized filter energy obeys a chi-squared probability distribution (PD) with 2M degrees of freedom, and such that, in the presence of speech and noise, filter energy is given by: (i).vertline..sup.2 where DFT.sub.x refers to speech coefficients and DFT.sub.n refers to noise coefficients, wherein said variance-normalized filter obeys a probability distribution of noncentral chi-squared with 2M degrees of freedom and noncentral parameter .lambda.; in order that the conditional probability of the filter energy is given by: ##EQU21## where ##EQU22## so that, with the following normalized log-energy variable defined as: ##EQU23## the conditional probability for S'.sub.k is given by ##EQU24##
5. The method according to claim 1 wherein said mixture model is implemented as a vector quantization mixture model where classes are identified with rigid boundary partitions of the acoustic space and the partitions are created by vector quantization.
6. The method according to claim 1 wherein said mixture model is implemented as a mixture of Gaussians mixture model with the assumptions that the probabilities Pn(Sk) are Gaussian distributions and the mean and standard deviations of these Gaussians are adjusted so as to maximize the likelihood of speech data given the mixture model.
7. The method according to claim 2 wherein the vector S' of said mixture model is replaced by a vector R', where the vector R' is a lower dimensional vector of log spectral energies in wide frequency bands and wherein the probability of class n conditioned on S' is replaced by the probability of new class n conditioned on R' such that new class n components refer to classes in a mixture model for a vector R.
8. The method according to claim 7 wherein the mixture model for vector R is implemented as a vector quantization mixture model where classes are identified with rigid boundary partitions of acoustic space and the partitions are created by vector quantization and wherein S k in the expression for the estimator for clean speech: ##EQU25## is conditioned on new class n.
9. The method according to claim 7 wherein the mixture model for vector R is implemented as a mixture of Gaussians mixture model with the assumptions that the probabilities P.sub.n (R.sub.j) are Gaussian distributions and the mean and standard deviations of these Gaussians are adjusted so as to maximize the likelihood of speech data given the mixture model and wherein S.sub.k in the expression for the estimator for clean speech: ##EQU26## is conditioned on new class n.
10. In a speech recognition system for responding to signals representative of digitized speech, a method for preprocessing speech in the presence of noise to produce an estimated clean speech signal, comprising the steps of: providing a data base of clean speech; training a Markov model with said clean speech data base, each state of said Markov model representing a different speech class assuming different frequency channels are uncorrelated within each class, to produce parameters for said Markov model; categorizing each time-invariant segment of digitized speech and noise into a noisy speech vector, each element of said noisy speech vector representing one frequency channel of speech information in the presence of noise, said noise being assumed to be frequency independent and time invariant; estimating a clean speech signal comprising a clean speech vector for each vector of a sequence of said noisy speech vectors S'.sub.O to S'.sub.T by 1) determining a probability distribution of the clean speech vector by applying the noisy speech vector to the Markov model using said parameters, and 2) modelling a conditional probability function of a vector of noisy speech around a vector of clean speech as uncorrelated at different frequency channels.
11. The method according to claim 10 wherein said estimating step comprises: estimating filter log spectral energies on a multiple-frequency channel probability according to .vertline.n.multidot.P(n.vertline.S'.sub.O, . . . ,S'.sub.t . . . S'.sub.T) where index n is a state and where the estimate of S.sub.k around n is the n.sup.th MMSE estimator given by: ##EQU27## where (S.sub.k) dS.sub.k where a Hidden Markov model is assumed for the speech, and the Hidden Markov state output probabilities are specified by: ##EQU28## and where a forward-backward algorithm is applied to compute P(n.vertline.S'.sub.O. . . . ,S'.sub.t . . . S'.sub.T).
12. The method according to claim 10 wherein said conditional probability of a noisy speech vector around a clean speech vector P(S'.sub.k .vertline.S.sub.k) is modeled as follows: 1) noise associated with said speech to be estimated is assumed to be a stationary, autoregressive moving average stochastic process such that, at each time frame, coefficients of a discrete Fourier transform (DFT) for said noise are uncorrelated complex Gaussian random variables; 2) filter output energy is assumed to be approximated by a sum of M coefficients; 3) noise spectral power is assumed to be uniform within a range of summation; such that, in the absence of noise, said summation extends over a total of 2M random variables which are Gaussian, of zero means and of a variance: where N.sub.k is the expected value of the noise filter energy wherein variance-normalized filter energy obeys a chi-squared probability distribution (PD) with 2M degrees of freedom, and such that, in the presence of speech and noise, filter energy is given by: (i).vertline..sup.2 where DFT.sub.s refers to speech coefficients and DFT.sub.n refers to noise coefficients, wherein said variance-normalized filter obeys a probability distribution of noncentral chi-squared with 2M degrees of freedom and noncentral parameter .lambda.p in order that the conditional probability of the filter energy is given by: ##EQU29## where ##EQU30## so that, with the following normalized log-energy variable defined as: ##EQU31## the conditional probability for S'.sub.k is given by ##EQU32##
13. The method according to claim 10 wherein said Markov model is implemented as a vector quantization Markov model where states are identified with rigid boundary partitions of the acoustic space and the partitions are created by vector quantization.
14. The method according to claim 11 wherein the vector S' of said mixture model is replaced by a vector R', where the vector R' is a lower dimensional vector of log spectral energies in wide frequency bands and wherein the probability of state n conditioned on sequence of S'(t) where t is from zero to T is replaced by the probability of new state n conditioned on sequence of R'(t) where t is from zero to T such that new state n components refer to states in a Markov model for a vector R.
15. The method according to claim 14 wherein the mixture model for vector R is implemented as a vector quantization Markov model where states are identified with rigid boundary partitions of the acoustic space and the partitions are created by vector quantization and S.sub.k is conditioned on new state n.
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