Yariv Ephraim

A signal subspace approach for speech enhancement

A comprehensive approach for nonparametric speech enhancement is developed. The underlying principle is to decompose the vector space of the noisy signal into a signal-plus-noise subspace and a noise subspace. Enhancement is performed by removing the noise subspace and estimating the clean signal from the remaining signal subspace. The decomposition can theoretically be performed by applying the Karhunen-Loeve transform (KLT) to the noisy signal. Linear estimation of the clean signal is performed using two perceptually meaningful estimation criteria. First, signal distortion is minimized while the residual noise energy is maintained below some given threshold. This criterion results in a Wiener filter with adjustable input noise level. Second, signal distortion is minimized for a fixed spectrum of the residual noise. This criterion enables masking of the residual noise by the speech signal. It results in a filter whose structure is similar to that obtained in the first case, except that now the gain function which modifies the KLT coefficients is solely dependent on the desired spectrum of the residual noise. The popular spectral subtraction speech enhancement approach is shown to be a particular case of the proposed approach. It is proven to be a signal subspace approach which is optimal in an asymptotic (large sample) linear minimum mean square error sense, assuming the signal and noise are stationary. Our listening tests indicate that 14 out of 16 listeners strongly preferred the proposed approach over the spectral subtraction approach. >

Hidden Markov processes

An overview of statistical and information-theoretic aspects of hidden Markov processes (HMPs) is presented. An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel. In recent years, the work of Baum and Petrie (1966) on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet. In particular, statistical properties and ergodic theorems for relative entropy densities of HMPs were developed. Consistency and asymptotic normality of the maximum-likelihood (ML) parameter estimator were proved under some mild conditions. Similar results were established for switching autoregressive processes. These processes generalize HMPs. New algorithms were developed for estimating the state, parameter, and order of an HMP, for universal coding and classification of HMPs, and for universal decoding of hidden Markov channels. These and other related topics are reviewed.

A Bayesian approach to robust adaptive beamforming

An adaptive beamformer that is robust to uncertainty in source direction-of-arrival (DOA) is derived using a Bayesian approach. The DOA is assumed to be a discrete random variable with a known a priori probability density function (PDF) that reflects the level of uncertainty in the source DOA. The resulting beamformer is a weighted sum of minimum variance distortionless response (MVDR) beamformers pointed at a set of candidate DOAs, where the relative contribution of each MVDR beamformer is determined from the a posteriori PDF of the DOA conditioned on previously observed data. A simple approximation to the a posteriori PDF results in a straightforward implementation. Performance of the approximate Bayesian beamformer is compared with linearly constrained minimum variance (LCMV) beamformers and data-driven approaches that attempt to estimate signal characteristics or the steering vector from the data.

Extended Ziv-Zakai lower bound for vector parameter estimation

The Bayesian Ziv-Zakai bound on the mean square error (MSE) in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than MSE. The extended bound is evaluated for some representative problems in time-delay and bearing estimation. The resulting bounds have simple closed-form expressions, and closely predict the simulated performance of the maximum-likelihood estimator in all regions of operation.

On second-order statistics and linear estimation of cepstral coefficients

Explicit expressions for the second-order statistics of cepstral components representing clean and noisy signal waveforms are derived. The noise is assumed additive to the signal, and the spectral components of each process are assumed statistically independent complex Gaussian random variables. The key result developed here is an explicit expression for the cross-covariance between the log-periodograms of the clean and noisy signals. In the absence of noise, this expression is used to show that the covariance matrix of cepstral components representing N signal samples, is a fixed signal independent matrix, which approaches a diagonal matrix at a rate of 1/N. In addition, the cross-covariance expression is used to develop an explicit linear minimum mean square error estimator for the clean cepstral components given noisy cepstral components. Recognition results on the English digits using the fixed covariance and linear estimator are presented.

Revisiting autoregressive hidden Markov modeling of speech signals

Linear predictive hidden Markov modeling is compared with a simple form of the switching autoregressive process. The latter process captures existing signal correlation during transitions of the Markov chain. Parameter estimation is described using naturally stable forward-backward recursions. The switching autoregressive model outperformed the linear predictive model in a digit recognition task and provided comparable performance to a cepstral-based recognizer.

Spectrum Sensing Using a Hidden Bivariate Markov Model

A new statistical model, in the form of a hidden bivariate Markov chain observed through a Gaussian channel, is developed and applied to spectrum sensing for cognitive radio. We focus on temporal spectrum sensing in a single narrowband channel in which a primary transmitter is either in an idle or an active state. The main advantage of the proposed model, compared to a standard hidden Markov model (HMM), is that it allows a phase-type dwell time distribution for the process in each state. This distribution significantly generalizes the geometric dwell time distribution of a standard HMM. Measurements taken from real data confirm that the geometric dwell time distribution characteristic of the HMM is not adequate for this application. The Baum algorithm is used to estimate the parameter of the proposed model and a forward recursion is applied to online estimation and prediction of the state of the cognitive radio channel. The performance of the proposed model and spectrum sensing approach are demonstrated using numerical results derived from real spectrum measurement data.

On Ryde/spl acute/n's EM algorithm for estimating MMPPs

Two aspects of Rydens expectation-maximization algorithm for estimating the parameter of a Markov modulated Poisson process are addressed. First, a scaling procedure is developed for the forward-backward recursions that circumvents the need for customized floating-point software. Second, evaluation of integrals of matrix exponentials is facilitated by applying a result due to Van Loan. For an MMPP of order four, a speedup of over two orders of magnitude was observed.

An EM Algorithm for Markov Modulated Markov Processes

An expectation-maximization (EM) algorithm for estimating the parameter of a Markov modulated Markov process in the maximum likelihood sense is developed. This is a doubly stochastic random process with an underlying continuous-time finite-state homogeneous Markov chain. Conditioned on that chain, the observable process is a continuous-time finite-state nonhomogeneous Markov chain. The generator of the observable process at any given time is determined by the state of the underlying Markov chain at that time. The parameter of the process comprises the set of generators for the underlying and conditional Markov chains. The proposed approach generalizes an earlier approach by Ryden for estimating the parameter of a Markov modulated Poisson process.

Hidden Markov process based dynamic spectrum access for cognitive radio

Cognitive radio is an emerging technology for sensing and dynamic access of spectrum in mobile radio environments. It aims at dynamically allocating unused bandwidth among secondary users without causing harmful interference to the primary users. This approach, which has clear economical benefits, has recently attracted significant research effort. In this paper, we propose a new approach to dynamic spectrum access in which the occupancy state of each frequency band at each time instant is estimated, and available bands are allocated accordingly. Estimation is performed from power spectral density measurements which are assumed to obey a hidden Markov process. The value of the hidden state represents the status of a given frequency band which could be free or occupied. We have trained the system using real spectrum measurements, and tested it on simulated data for which the occupancy state of each frequency band at each time instant is known. We demonstrate the performance of the proposed approach and compare it with a simple energy detector which has previously been proposed for this application.1