Most contemporary automatic speech recognition (ASR) systems use MFCCs (Mel-frequency cepstral coefficients) and their derivatives as speech features, and a set of Gaussian mixture continuous density hidden Markov models (CDHMMs) for modeling basic speech units. The models are trained with clean speech. However, in practice, speech is often not clean but corrupted by noise and/or distortion.
It is well known that the performance of such an automatic speech recognition system trained with clean speech will degrade significantly when later dealing with speech that is corrupted by additive noises from the surrounding environment. Recognition performance will also degrade because of convolutional distortions, such as resulting from the use of a different type of microphone/transducer than the type used in training, and/or from the speech traveling over different transmission channels.
Various approaches to deal with the corrupted speech problem have been attempted. Any improvement over existing technology in dealing with the corrupted speech problem is desirable for use in automatic speech recognition systems.
This Summary is provided to introduce a selection of representative concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used in any way that would limit the scope of the claimed subject matter.
Briefly, various aspects of the subject matter described herein are directed towards a technology by which a feature compensation mechanism receives feature vectors corresponding to (possibly) corrupted speech, and uses a high-order vector Taylor series approximation to approximate a model of distortions to modify the feature vectors into compensated feature vectors corresponding to a clean speech estimate. The clean speech estimate, such as in the form of normalized feature vectors, is provided to a speech recognizer for recognition.
In one aspect, a feature extraction mechanism extracts a series of Mel-frequency cepstral coefficient feature vectors from frames of input speech. The feature compensation mechanism includes an inverse discrete cosine transform mechanism that uses a clean-speech trained Gaussian mixture model to compute log spectrum Gaussian mixture model components from the input feature vectors of cepstral domain. The high-order vector Taylor series approximation is used to calculate statistics from the Gaussian mixture model components. A discrete cosine transform mechanism transforms the statistics back to the cepstral domain, where they are used to re-estimate noise parameters. The re-estimation may be performed a plurality of times (e.g., three or four) by iterating accordingly.
Other advantages may become apparent from the following detailed description when taken in conjunction with the drawings.
The present invention is illustrated by way of example and not limited in the accompanying figures in which like reference numerals indicate similar elements and in which:
Various aspects of the technology described herein are generally directed towards improving speech recognition accuracy by compensating for additive noise and/or convolutional distortion using a high-order vector Taylor series (HOVTS) approximation of an explicit model of distortions. This provides a compensation approach to robust speech recognition that consistently and significantly improves recognition accuracy compared to traditional first-order (simple linear approximation) VTS-based feature compensation approaches. Also described is deriving formulations for maximum likelihood (ML) estimation of noise model parameters and minimum mean squared error (MMSE) estimation of clean speech.
It should be understood that the components and steps described herein are only examples of a suitable implementation. As such, the present invention is not limited to any particular embodiments, aspects, concepts, structures, functionalities or examples described herein. Rather, any of the embodiments, aspects, concepts, structures, functionalities or examples described herein are non-limiting, and the present invention may be used various ways that provide benefits and advantages in computing and speech processing in general.
Turning to
In the training stage, given clean training samples 102, feature extraction 104 based upon Mel-frequency cepstral coefficients (MFCC) obtains MFCC feature vectors in a known manner. The feature vectors are used to train one or more Gaussian mixture model (GMMs) 106 as a reference of the clean speech model, used as described below. Note that in one implementation, the GMMs are not given a filter meaning for each Gaussian component, but rather a in a feature space for all sounds in the particular language being recognized. Further, the feature vectors are normalized (via cepstral mean normalization, or CMN 108), for use in maximum likelihood (ML) training 110 to provide acoustic Hidden Markov Models 112 for later online use by a recognizer 120.
In the recognition stage, an unknown utterance 122, which may or may not be clean with respect to noise or distortion, is recognized. In general, MFCC feature extraction 124 provides a sequence of MFCC feature vectors for a set of input frames. The sequence of frames are modified by a feature compensation using HOVTS mechanism 126 (as described in detail below) into another sequence of MFCC feature vectors, which generally have at least some of any additive noise/convolutional noise removed. The compensated feature vectors are normalized via cepstral mean normalization 140 for recognition by the recognizer 120, using the training acoustic HMMs, into an output result in a known manner.
y[t]=x[t]{circle around (*)}h[t]+n[t] (1)
where independent signals x[t], h[t] and n[t] represent the tth sample of clean speech, the convolutional (e.g., transducer and transmission channel) distortion and the additive (e.g., environmental) noise, respectively.
Then, a frame of speech as represented by its feature vector in the cepstral domain may be transformed into a feature vector in the log power-spectrum domain. More particularly, by ignoring correlations between different filter banks, the distortion model in the log power-spectrum domain can be expressed approximately as
exp(y)=exp(x+h)+exp(n) (2)
where y, x, h and n are log power-spectrums in a particular channel of the filterbank of clean speech, convolutional term and noise, respectively.
However, the nonlinear nature of the above distortion model makes statistical modeling and inference of the above variables difficult, whereby certain approximations are made. Traditional approximation was performed via a first-order (simple linear approximation) VTS-based feature compensation approach. As described herein, a more accurate approximation is based upon HOVTS, and provides improved recognition accuracy.
To this end, the above nonlinear distortion function may be expanded using HOVTS. Then a linear function is found to approximate the above HOVTS by minimizing the mean-squared error incurred by this approximation. Given the linear function, the remaining inference is the same as in using the traditional first-order VTS to approximate the nonlinear distortion function directly. HOVTS is used to approximate the nonlinear portion of the distortion function by expanding with respect to n−x instead of (x, n). In one implementation, both approaches work for each feature dimension independently by ignoring correlations among different channels of filterbank. Note however that correlations among different channels of the filterbank may be considered in alternative implementations.
The above nonlinear distortion function may be approximated by a second-order VTS. Using this relation, the mean vector of the relevant noisy speech feature vector can be derived, which includes a term related to the second order term in HOVTS. Note however that the nonlinear distortion function can be approximated by HOVTS with any order (that is, not only a second order).
In the above-described training stage, a Gaussian mixture model (GMM) 106,
was trained from clean speech using MFCC features without cepstral mean normalization (CMN), where
and wm are mean vector, diagonal covariance matrix and mixture weight of the mth component, respectively. Assume that for each sentence, the noise feature vector nc in cepstral domain follows a Gaussian PDF (probability density function) with a mean vector μnc and a diagonal covariance matrix Σnc, which can be estimated in the recognition stage as represented in the steps 201-206 of
Step 201 represents initialization, wherein in general, the mechanism 126 initializes parameters by using the first j (e.g., ten) frames to obtain a noise/channel estimation. More particularly, one implementation estimates the initial noise model parameters in the cepstral domain by taking the sample mean and covariance matrix of the MFCC features from the first j (e.g., ten) frames of the unknown utterance, and sets hc as a zero vector.
Step 202 is performed in order to more easily calculate the statistics that are later used to re-estimate noise. As h is deterministic, and x is assumed to follow the GMM, the inverse discrete cosine transform (IDCT) block 130 transforms the parameters from cepstral domain to log power-spectral domain. To this end, a new random vector, zc=xc+hc, is defined, whose PDF can be derived as follows:
More particularly, the parameters are transformed from the cepstral domain to the log-power-spectral domain (represented by the GMMs 131 of
where C+ is the Moore-Penrose inverse of the discrete cosine transform (DCT) matrix C, and the superscripts ‘I’ and ‘c’ indicate the log-power-spectral domain and cepstral domain, respectively.
Step 203 of
which are used for noise re-estimation and clean speech estimation, using HOVTS approximation in the log-power-spectral domain. Additional details of this calculation are described below.
Step 204 of
Step 205 of
Note that in the above equations, the cepstral domain indicator “c” was dropped in relevant variables for notational convenience. Further,
is the PDF of the noisy speech yt, where the true py(yt|m) is approximated by a Gaussian PDF, N(yt; μy,m, Σy,m), via “moment-matching”. En[nt|yt, m], En[ntntT|yt, m] and Ez[zt|yt, m] are the relevant conditional expectations evaluated as follows:
Step 206 of
Given the noisy speech and noise estimation, the minimum mean-squared error (MMSE) estimation of clean speech feature vector in the cepstral domain can be calculated (step 208 of
where Ex[xt|yt, m] is the conditional expectation of xt given yt for the mth mixture component, and can be evaluated as follows:
E
x
[x
t
|y
t
,m]=E
z
[z
t
|y
t
,m]−h (19)
For completeness, step 210, along with the cepstral mean normalization block 140 and the recognizer 120, represent normalizing the compensated feature vectors, recognizing the speech, and outputting results (e.g., text).
Turning to additional details on calculating the statistics
using the HOVTS approximation of the nonlinear distortion function of Equation (2), note that z in Equations (1) through (19) is represented by x in the following description. For notational convenience, the indices related to the frame number, mixture component, and channel index of the filterbank are dropped.
The explicit distortion model in Equation (2) may be reformulated in the scalar form as follows:
y=f(x,n)=log(exp(x)+exp(n)). (20)
Then, the K-order Taylor series of f(x; n) with the expansion point (μx; μn) may be represented as:
where
and
When k>1 and k≧p≧1, the coefficients B(k; p) in Equation (23) can be evaluated by using the following recursive relation
B(k,p)=(p−1)B(k−1,p−1)−pB(k−1,p) (24)
with the initial condition
B(1,1)=−1,B(k,0)=B(k,k+1)=0,k≧1. (25)
For convenience, the following expectations are defined:
E
xn
i
[g(x,n)]=∫∫g(xi,ni)pxn(xi,ni)dxidni (26)
E
xn
ij
[g(x,m), h(x,n)]=∫∫∫∫g(xi,ni)h(xj,nj)pxn(xi,xj, ni,nj)dxidxjdnidnj (27)
where g(xi, ni) and h(xj, nj) are two general functions, i and j are dimensional indices. Given the above notations and results, the main statistics required in implementing the feature compensation approach are summarized.
To calculate μy(i), which denotes the ith element of the vector μy, using the definition of the mean parameter gives
where Δ represents ‘x’ or ‘n’. Ai(k; r) is the value of Equation (22) for the ith dimension.
To calculate σy2(i; j) to denote the (i; j)th element of the matrix Σy, using the definition of the covariance gives
where
To calculate σxy2(i; j) to denote the (i; j)th element of the matrix Σxy, using the definition of the covariance parameter gives
To calculate σny2(i; j) to denote the (i; j)th element of the matrix Σny, using the definition of the covariance parameter gives
The invention is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well known computing systems, environments, and/or configurations that may be suitable for use with the invention include, but are not limited to: personal computers, server computers, hand-held or laptop devices, tablet devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments that include any of the above systems or devices, and the like.
The invention may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, and so forth, which perform particular tasks or implement particular abstract data types. The invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in local and/or remote computer storage media including memory storage devices.
With reference to
The computer 310 typically includes a variety of computer-readable media. Computer-readable media can be any available media that can be accessed by the computer 310 and includes both volatile and nonvolatile media, and removable and non-removable media. By way of example, and not limitation, computer-readable media may comprise computer storage media and communication media. Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by the computer 310. Communication media typically embodies computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” means a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of the any of the above may also be included within the scope of computer-readable media.
The system memory 330 includes computer storage media in the form of volatile and/or nonvolatile memory such as read only memory (ROM) 331 and random access memory (RAM) 332. A basic input/output system 333 (BIOS), containing the basic routines that help to transfer information between elements within computer 310, such as during start-up, is typically stored in ROM 331. RAM 332 typically contains data and/or program modules that are immediately accessible to and/or presently being operated on by processing unit 320. By way of example, and not limitation,
The computer 310 may also include other removable/non-removable, volatile/nonvolatile computer storage media. By way of example only,
The drives and their associated computer storage media, described above and illustrated in
The computer 310 may operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 380. The remote computer 380 may be a personal computer, a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to the computer 310, although only a memory storage device 381 has been illustrated in
When used in a LAN networking environment, the computer 310 is connected to the LAN 371 through a network interface or adapter 370. When used in a WAN networking environment, the computer 310 typically includes a modem 372 or other means for establishing communications over the WAN 373, such as the Internet. The modem 372, which may be internal or external, may be connected to the system bus 321 via the user input interface 360 or other appropriate mechanism. A wireless networking component 374 such as comprising an interface and antenna may be coupled through a suitable device such as an access point or peer computer to a WAN or LAN. In a networked environment, program modules depicted relative to the computer 310, or portions thereof, may be stored in the remote memory storage device. By way of example, and not limitation,
An auxiliary subsystem 399 (e.g., for auxiliary display of content) may be connected via the user interface 360 to allow data such as program content, system status and event notifications to be provided to the user, even if the main portions of the computer system are in a low power state. The auxiliary subsystem 399 may be connected to the modem 372 and/or network interface 370 to allow communication between these systems while the main processing unit 320 is in a low power state.
While the invention is susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents failing within the spirit and scope of the invention.