Itakura-Saito Distortion Measure Research Articles

Noise Estimation and Suppression Using Nonlinear Function withA PrioriSpeech Absence Probability in Speech Enhancement

This paper proposes a noise-biased compensation of minimum statistics (MS) method using a nonlinear function anda priorispeech absence probability (SAP) for speech enhancement in highly nonstationary noisy environments. The MS method is a well-known technique for noise power estimation in nonstationary noisy environments; however, it tends to bias noise estimation below that of the true noise level. The proposed method is combined with an adaptive parameter based on a sigmoid function anda prioriSAP for residual noise reduction. Additionally, our method uses an autoparameter to control the trade-off between speech distortion and residual noise. We evaluate the estimation of noise power in highly nonstationary and varying noise environments. The improvement can be confirmed in terms of signal-to-noise ratio (SNR) and the Itakura-Saito Distortion Measure (ISDM).

A modified weighted overlap and add-based spectral subtraction method

The Weighted Overlap and Add (WOLA) method is an optimization of frequency modulated DFT filter banks. However, the decrement in frequency resolution of speech signal caused by WOLA leads to noise estimation error. In this study, a speech power compression and gain compensation method was proposed to solve the low-resolution problem from the WOLA process. Finally, a multi-band spectral subtraction method was developed by combining the WOLA and the spectral subtraction algorithm in frequency domain. The noise reduction degrees were determined by the individual Signal-to-Noise Ratios (SNRs) in each frequency bands. Objective evaluation of the proposed noise reduction method was performed based on Itakura-Saito Distortion Measure under different types of noise. Statistical results showed that this proposed method could improve noisy speech by 5 dB SNR with little distortion. This noise reduction method has an advantage on low computation load, real-time processing and good performance on noise reduction. So this method can be implemented in embedded devices, e.g. hearing aid and cochlear implants. # This work is supported by National Natural Science Foundation of China (11104316). and Shanghai Natural Science Foundation (11ZR1446000).

Quantifying filter bank decorrelating performance via matrix diagonality

An important number of signal processing applications require decomposing a discrete-time signal into decorrelated frequency channels. Several algorithms have been used for this purpose. One of the most popular is the DFT, which is known to be far from optimal due to the presence of overlap between adjacent channels. Filter banks are an interesting alternative as they can be designed for reduced frequency overlap, which results in an approximately tridiagonal autocorrelation matrix. In order to compare the decorrelating ability of different transforms, we propose simple but useful measures via autocorrelation matrix diagonality. We develop analytical expressions and numerical examples to show that our measures are equivalent for well decorrelated signals, and related to the well known Itakura–Saito distortion measure.

Disordered Speech Assessment Using Automatic Methods Based on Quantitative Measures

Speech quality assessment methods are necessary for evaluating and documenting treatment outcomes of patients suffering from degraded speech due to Parkinson's disease, stroke, or other disease processes. Subjective methods of speech quality assessment are more accurate and more robust than objective methods but are time-consuming and costly. We propose a novel objective measure of speech quality assessment that builds on traditional speech processing techniques such as dynamic time warping (DTW) and the Itakura-Saito (IS) distortion measure. Initial results show that our objective measure correlates well with the more expensive subjective methods.

Distortion Measures for Speech Coding

In this article, we have reviewed some of the existing subjective and objective measures used in the area of speech coding. The mean opinion score and the diagnostic acceptability measure are two of the widely used subjective measures. The most popular class of the time-domain measures is the signal-to-noise ratio (SNR) with its variants such as the segmental SNR, the granular segmentsal SNR etc. Among the spectral distortion measures, the log likelihood ratio measure, the log area ratio measure, the log spectral distortion measure, the cepstral distance and the Itakura-Saito distortion measure are quite well-known. Some of the more recently proposed objective measures place emphasis on the perceptually significant aspects. Three such classes of the psychoacoustically-motivated measures are the information index, the Bark spectral distortion measure and the neural distance measure (e.g., the cochlear discrimination information, the cochlear hidden Markovian measues). The merit of considering important perceptual events is evident in the success of these measures.

Marker-free estimation of hip joint position

An important number of signal processing applications require decomposing a discrete-time signal into decorrelated frequency channels. Several algorithms have been used for this purpose. One of the most popular is the DFT, which is known to be far from optimal due to the presence of overlap between adjacent channels. Filter banks are an interesting alternative as they can be designed for reduced frequency overlap, which results in an approximately tridiagonal autocorrelation matrix. In order to compare the decorrelating ability of different transforms, we propose simple but useful measures via autocorrelation matrix diagonality. We develop analytical expressions and numerical examples to show that our measures are equivalent for well decorrelated signals, and related to the well known Itakura–Saito distortion measure.

Two new robust nonlinear signal restoration algorithms

Signal restoration is a well-known problem is many scientific fields such as image processing and geophysics. Here, we process a signal to enhance its quality in order to uncover features about the original or system input signal z that are not apparent in the noisy and distorted output of the system, u. Once the model is specified, the signal restoration problem is then to find a signal z” that is as close as possible to the original one subject to a suitable optimality criterion. The assumed givens are the output u, system model h, and any a priori knowledge about the solution in the form of constraints. Various methods that relied on different criteria showed attractive results in well-defined situations. Minimum meansquare error, maximum entropy, maximum likelihood, and maximum a posteriori probability are a few criteria that have proven useful. Here, regularization theory is used to tackle the problem. Especially, the stabilizing functional approach is considered [ 1,2 ] . The problem is formulated as the constrained minimization of a certain stabilizing functional a( z, P) [1,2]. The choice of the stabilizing functional or criterion based on the problem at hand is still an open question. In a recent paper [l] , Karayiannis and Venetsanopoulos investigated the choice of a stabilizing functional in the case of 2-D ill-posed inverse problems. These authors emphasized the use of a certain class of quadratic functionals as stabilizing functionals. The use of global nonquadratic functionals was discouraged due to several problems. One main problem is the justification of the choice of a particular nonquadratic functional [l] . Recently, a step toward reducing the set of nonquadratic functionals to an optimal class of functionals useful in speech and image compression, cluster analysis, and pattern classification was presented by Jones [ 31. The considered functionals satisfy an orthogonality condition similar to that enjoyed by linear projections in Hilbert space. The concept of directed orthogonality is known as the correlation matching property in speech analysis and as expected value matching within the space of probability densities [ 41. Jones demonstrates that the Itakura-Saito distortion measure (ISD) of communication theory and the Kullback-Leilber distance measure ( KLM ) of statistics are the only functionals in the smooth Ali-Silvey-Csiszar class and the class of regular ratio distortion measures, respectively, to obey the directed orthogonality principle. Therefore, our focus in this paper is to investigate further these two functionals, i.e., Qisn and RkLM. In Section II, a regularized solution for the ill-posed inverse problem of signal restoration is developed through the use of the stabilizing function approach that uses the entropic stabilizing functionals &, and !l kLM, respectively. These functionals are minimized subject to a mean-squared-error constraint equation. This produces two iterative schemes, called the ISD and KLM algorithms, through which the signal is obtained. In Section III, the derived iterative algorithms are shown to be theoretically sound, leading to a unique, robust solution. In Section IV, examples that demonstrate the restoration achieved by the new methods in several signal-to-noise-ratio (SNR) environments are presented. Finally, we note that this work is an extension of that presented in [ 61.

Discrete all-pole modeling

A method for parametric modeling and spectral envelopes when only a discrete set of spectral points is given is introduced. This method, called discrete all-pole (DAP) modeling, uses a discrete version of the Itakura-Saito distortion measure as its error criterion. One result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values, such as in voiced speech. An iterative algorithm for DAP modeling that is shown to converge to a unique global minimum is presented. Results of applying DAP modeling to real and synthetic speech are also presented. DAP modeling is extended to allow frequency-dependent weighting of the error measure, so that spectral accuracy can be enhanced in certain frequency regions. >

A bit-level systolic architecture for implementing a VQ tree search

A bit-level systolic array system for performing a binary tree Vector Quantization codebook search is described. This consists of a linear chain of regular VLSI building blocks and exhibits data rates suitable for a wide range of real-time applications. A technique is described which reduces the computation required at each node in the binary tree to that of a single inner product operation. This method applies to all the common distortion measures (including the Euclidean distance, the Weighted Euclidean distance and the Itakura-Saito distortion measure) and significantly reduces the hardware required to implement the tree search system.

Approximation–Theoretic Derivation of Logarithmic Entropy Principles for Inverse Problems and Unique Extension of the Maximum Entropy Method to Incorporate Prior Knowledge

The minimum distance approach for reconstructing a positive function based on knowledge of finitely many linear functional values is examined. Two important classes of directed distances for signal processing and statistical inference are discussed. By imposing conditions analogous to those satisfied by linear projections in Hilbert space, two logarithmic entropy principles are derived. One of these involves the Itakura–Saito distortion measure of communication theory and uniquely extends Burg's maximum entropy method to incorporate prior knowledge. The other uses the Kullback–Leibler distance of statistics.

Asymptotic minimum discrimination information measure for asymptotically weakly stationary processes

An explicit expression is derived for the minimum discrimination information (MDI) measure with respect to Gaussian priors for sources characterized by their mean and by any principal leading block of their covariance matrix. An explicit expression is provided for the MDI extension of the given partial covariance of the source with respect to a Gaussian prior. For zero-mean sources and zero-mean Gaussian priors that are asymptotically weakly stationary (AWS) processes, it is shown that the asymptotic MDI measure equals half the Itakura-Saito distortion measure between the asymptotic power spectral densities of the source and prior. Asymptotic MDI modelling of a given AWS source by autoregressive and autoregressive moving average models, which are AWS models, is considered, and conditions are given for convergence of the sample covariance estimator of the source to the stationary covariance used in the modelling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rate-distortion bounds for quotient-based distortions with application to Itakura- Saito distortion measures

In many linear predictive coding (LPC) speech compression systems the encoding of the LPC parameters is performed using a product code book scheme. One possible approach consists in organizing the set of LPC reproduction models as the Cartesian product of a vector code book describing the shape of each reproduction LPC model and a scalar codebook describing the gain or energy. We first present a formal development of rate-distortion theoretic results for distortion functions based on quotients of input and reproduction symbols. We also obtain theoretical bounds for the rate-distortion function of the gain term of LPC systems (which, depending on the quantization scheme, can use about <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10-25</tex> percent of the transmission rate), as well as asymptotic (small distortions) approximations to the performance of the optimal scalar quantizer for these gain terms, when the overall fidelity criterion is the Itakura-Saito distortion measure, which is a member of the class of quotient distortion measures. The approximations and bounds are compared finally with experimental results.

Comparative study of several distortion measures for speech recognition

Local spectral distortion measures are commonly used to measure the similarity (or spectral distance) between two given short-time spectra. In this study we compared several different spectral distortion measures including the Itakura-Saito distortion measure, the log likelihood ratio (LLR) distortion measure, the likelihood ratio (LR) distortion measure, the cepstral (CEP) distortion measure, and two proposed perceptually based distortion measures, the weighted likelihood ratio (WLR) and the weighted slope metric (WSM) distortion measures, in terms of their effects on the performance of standard dynamic time warping (DTW) based, isolated word, speech recognizer. Two modifications of the basic forms of each measure were also investigated, namely a Bark-scale frequency warping and the incorporation of suprasegemental energy information. All distortion measures and their modifications were tested on an alpha-digit vocabulary, 4-talker, telephone recording data base. The results can be summarized as: (1) All LPC-based distortion measures performed reasonably well. The log likelihood ratio and weighted slope metric distortion measures gave the highest recognition accuracy, while the Itakura-Saito distortion measure gave the lowest score; (2) Whereas the addition of suprasegmental energy information helped the recognition performance, the use of gain and absolute loudness degraded the performance; (3) Bark-scale frequency warping did not, at least for the highly bandlimited telephone data base we tested, performed as well as its unwarped counterpart; (4) The weighted likelihood ratio distortion measure did not perform as well as its unweighted counterpart.

Matrix quantizer design for LPC speech using the generalized Llyod algorithm

Rate-distortion theory provides the motivation for using data compression techniques on matrices of N LPC vectors. This leads to a simple extension of speech coding techniques using vector quantization. The effects of using the generalized Lloyd algorithm on such matrices using a summed Itakura-Saito distortion measure are studied, and an extension of the centroid computation used in vector quantization is presented. The matrix quantizers so obtained offer substantial reductions in bit rates relative to full-search vector quantizers. Bit rates as low as 150 bits/s for the LPC matrix information (inclusive of gain, but without pitch and voicing) have been achieved for a single speaker, having average test sequence and codebook distortions comparable to those in the equivalent full-search vector quantizer operating at 350 bits/s. Preliminary results indicate that higher quality or lower bit rates may be achieved with enough computational resources.

An Algorithm for the Design of Labeled-Transition Finite-State Vector Quantizers

A finite-state vector quantizer (FSVQ) is a switched vector quantizer where the sequence of quantizers selected by the encoder can be tracked by the decoder. It can be viewed as an adaptive vector quantizer with backward estimation, a vector generalization of an AQB system. Recently a family of algorithms for the design of FSVQ's for waveform coding application has been introduced. These algorithms first design an initial set of vector quantizers together with a next-state function giving the rule by which the next quantizer is selected. The codebooks of this initial FSVQ are then iteratively improved by a natural extension of the usual memoryless vector quantizer design algorithm. The next-state function, however, is not modified from its initial form. In this paper we present two extensions of the FSVQ design algorithms. First, the algorithm for FSVQ design for waveform coders is extended to FSVQ design of linear predictive coded (LPC) speech parameter vectors using an Itakura-Saito distortion measure. Second, we introduce a new technique for the iterative improvement of the next-state function based on an algorithm from adaptive stochastic automata theory. The design algorithms are simulated for an LPC FSVQ and the results are compared with each other and to ordinary memoryless vector quantization. Several open problems suggested by the simulation results are presented.

Product code vector quantizers for waveform and voice coding

Memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding (LPC). One approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the Cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy. Such shape-gain vector quantizers can be applied both to waveform coding using a quadratic-error distortion measure and to voice coding using an Itakura-Saito distortion measure. In each case, the minimum distortion reproduction vector can be found by first selecting a shape code-word, and then, based on that choice, selecting a gain codeword. Several algorithms are presented for the design of shape-gain vector quantizers based on a traning sequence of data or a probabilistic model. The algorithms are used to design shape-gain vector quantizers for both the waveform coding and voice coding application. The quantizers are simulated, and their performance is compared to that of previously reported vector quantization systems.