Ari Abramson

Simultaneous Detection and Estimation Approach for Speech Enhancement

In this paper, we present a simultaneous detection and estimation approach for speech enhancement. A detector for speech presence in the short-time Fourier transform domain is combined with an estimator, which jointly minimizes a cost function that takes into account both detection and estimation errors. Cost parameters control the tradeoff between speech distortion, caused by missed detection of speech components and residual musical noise resulting from false-detection. Furthermore, a modified decision-directed a priori signal-to-noise ratio (SNR) estimation is proposed for transient-noise environments. Experimental results demonstrate the advantage of using the proposed simultaneous detection and estimation approach with the proposed a priori SNR estimator, which facilitate suppression of transient noise with a controlled level of speech distortion.

ON THE STATIONARITY OF MARKOV-SWITCHING GARCH PROCESSES

Generalized autoregressive conditional heteroskedasticity (GARCH) models with Markov-switching regimes are often used for volatility analysis of financial time series. Such models imply less persistence in the conditional variance than the standard GARCH model and potentially provide a significant improvement in volatility forecast. Nevertheless, conditions for asymptotic wide-sense stationarity have been derived only for some degenerated models. In this paper, we introduce a comprehensive approach for stationarity analysis of Markov-switching GARCH models, which manipulates a backward recursion of the models second-order moment. A recursive formulation of the state-dependent conditional variances is developed, and the corresponding conditions for stationarity are obtained. In particular, we derive necessary and sufficient conditions for the asymptotic wide-sense stationarity of two different variants of Markov-switching GARCH processes and obtain expressions for their asymptotic variances in the general case of m-state Markov chains and (p,q)-order GARCH processes.The authors thank Professor Rami Atar for helpful discussions. The authors thank the co-editor Bruce Hansen and the three anonymous referees for their helpful comments and suggestions and in particular the referee who proposed a generalization of the proof in Appendix B. This research was supported by the Israel Science Foundation (grant 1085/05).

Enhancement of Speech Signals Under Multiple Hypotheses using an Indicator for Transient Noise Presence

In this paper, we formulate a speech enhancement problem under multiple hypotheses, assuming an indicator or detector for the transient noise presence is available in the short-time Fourier transform (STFT) domain. Hypothetical presence of speech or transient noise is considered in the observed spectral coefficients, and cost parameters control the trade-off between speech distortion and residual transient noise. An optimal estimator, which minimizes the mean-square error of the log-spectral amplitude, is derived, while taking into account the probability of erroneous detection. Experimental results demonstrate the improved performance in transient noise suppression, compared to using the optimally-modified log-spectral amplitude estimator.

Dual-microphone speech dereverberation using GARCH modeling

In this paper, we develop a dual-microphone speech dereverberation algorithm for noisy environments, which is aimed at suppressing late reverberation and background noise. The spectral variance of the late reverberation is obtained with adaptively-estimated direct path compensation. A Markov-switching generalized autoregressive conditional heteroscedasticity (GARCH) model is used to estimate the spectral variance of the desired signal, which includes the direct sound and early reverberation. Experimental results demonstrate the advantage of the proposed algorithm compared to a decision-directed-based algorithm.

Recursive Supervised Estimation of a Markov-Switching GARCH Process in the Short-Time Fourier Transform Domain

In this paper, we introduce a Markov-switching generalized autoregressive conditional heteroscedasticity (GARCH) model for nonstationary processes with time-varying volatility structure in the short-time Fourier transform (STFT) domain. The expansion coefficients in the STFT domain are modeled as a multivariate complex GARCH process with Markov-switching regimes. The GARCH formulation parameterizes the correlation between sequential conditional variances while the Markov chain allows the process to switch between regimes of different GARCH formulations. We obtain a necessary and sufficient condition for the asymptotic wide-sense stationarity of the model, and develop a recursive algorithm for signal restoration in a noisy environment. The conditional variance is estimated by iterating propagation and update steps with regime conditional probabilities, while the model parameters are evaluated a priori from a training data set. Experimental results demonstrate the performance of the proposed algorithm.

Single-Sensor Audio Source Separation Using Classification and Estimation Approach and GARCH Modeling

In this paper, we propose a new algorithm for single-sensor audio source separation of speech and music signals, which is based on generalized autoregressive conditional heteroscedasticity (GARCH) modeling of the speech signals and Gaussian mixture modeling (GMM) of the music signals. The separation of the speech from the music signal is obtained by a simultaneous classification and estimation approach, which enables one to control the tradeoff between residual interference and signal distortion. Experimental results on mixtures of speech and piano music signals have yielded an improved source separation performance compared to using Gaussian mixture models for both signals. The tradeoff between signal distortion and residual interference is controlled by adjusting some cost parameters, which are shown to determine the missed and false detection rates in the proposed classification and estimation approach.

State smoothing in Markov-switching time-frequency GARCH models

In this letter, we propose a state smoothing algorithm for path-dependent Markov-switching generalized autoregressive conditional heteroscedasticity (GARCH) processes. Our smoothing technique extends the forward-backward recursions of Chang and Hancock and the stable backward recursion of Lindgren, Askar and Derin. We derive two recursive steps for the evaluation of conditional densities of future observations. The first step is an upward recursion that manipulates the future observations for the evaluation of their conditional densities, and the second step is a backward recursion that integrates over the possible future paths. Experimental results demonstrate the improvement in performance, compared to using causal estimation.

Simultaneous Detection and Estimation Approach for Speech Enhancement and Interference Suppression

In this chapter, we present a simultaneous detection and estimation approach for speech enhancement. A detector for speech presence in the short-time Fourier transform domain is combined with an estimator, which jointly minimizes a cost function that takes into account both detection and estimation errors. Cost parameters control the trade-off between speech distortion, caused by missed detection of speech components, and residual musical noise resulting from false-detection. Furthermore, a modified decision-directed a priori signal-to-noise ratio (SNR) estimation is proposed for transient-noise environments. Experimental results demonstrate the advantage of using the proposed simultaneous detection and estimation approach with the proposed a priori SNR estimator, which facilitate suppression of transient noise with a controlled level of speech distortion.