Multiple-input/output Inverse Theorem Research Articles

Multichannel Online Dereverberation Based on Spectral Magnitude Inverse Filtering

This paper addresses the problem of multichannel online dereverberation. The proposed method is carried out in the short-time Fourier transform (STFT) domain, and for each frequency band independently. In the STFT domain, the time-domain room impulse response is approximately represented by the convolutive transfer function (CTF). The multichannel CTFs are adaptively identified based on the cross-relation method, and using the recursive least square criterion. Instead of the complex-valued CTF convolution model, we use a nonnegative convolution model between the STFT magnitude of the source signal and the CTF magnitude, which is just a coarse approximation of the former model, but is shown to be more robust against the CTF perturbations. Based on this nonnegative model, we propose an online STFT magnitude inverse filtering method. The inverse filters of the CTF magnitude are formulated based on the multiple-input/output inverse theorem (MINT), and adaptively estimated based on the gradient descent criterion. Finally, the inverse filtering is applied to the STFT magnitude of the microphone signals, obtaining an estimate of the STFT magnitude of the source signal. Experiments regarding both speech enhancement and automatic speech recognition are conducted, which demonstrate that the proposed method can effectively suppress reverberation, even for the difficult case of a moving speaker.

Multichannel Speech Separation and Enhancement Using the Convolutive Transfer Function

This paper addresses the problem of speech separation and enhancement from multichannel convolutive and noisy mixtures, \emph{assuming known mixing filters}. We propose to perform the speech separation and enhancement task in the short-time Fourier transform domain, using the convolutive transfer function (CTF) approximation. Compared to time-domain filters, CTF has much less taps, consequently it has less near-common zeros among channels and less computational complexity. The work proposes three speech-source recovery methods, namely: i) the multichannel inverse filtering method, i.e. the multiple input/output inverse theorem (MINT), is exploited in the CTF domain, and for the multi-source case, ii) a beamforming-like multichannel inverse filtering method applying single source MINT and using power minimization, which is suitable whenever the source CTFs are not all known, and iii) a constrained Lasso method, where the sources are recovered by minimizing the $\ell_1$-norm to impose their spectral sparsity, with the constraint that the $\ell_2$-norm fitting cost, between the microphone signals and the mixing model involving the unknown source signals, is less than a tolerance. The noise can be reduced by setting a tolerance onto the noise power. Experiments under various acoustic conditions are carried out to evaluate the three proposed methods. The comparison between them as well as with the baseline methods is presented.

Improving the conditioning of the optimization criterion in acoustic multi-channel equalization using shorter reshaping filters

In acoustic multi-channel equalization techniques, such as complete multi-channel equalization based on the multiple-input/output inverse theorem (MINT), relaxed multi-channel least-squares (RMCLS), and partial multi-channel equalization based on MINT (PMINT), the length of the reshaping filters is generally chosen such that perfect dereverberation can be achieved for perfectly estimated room impulse responses (RIRs). However, since in practice the available RIRs typically differ from the true RIRs, this reshaping filter length may not be optimal. This paper provides a mathematical analysis of the robustness increase of equalization techniques against RIR perturbations when using a shorter reshaping filter length than conventionally used. Based on the condition number of the (weighted) convolution matrix of the RIRs, a mathematical relationship between the reshaping filter length and the robustness against RIR perturbations is established. It is shown that shorter reshaping filters than conventionally used yield a smaller condition number, i.e., a higher robustness against RIR perturbations. In addition, we propose an automatic non-intrusive procedure for determining the reshaping filter length based on the L-curve. Simulation results confirm that using a shorter reshaping filter length than conventionally used yields a significant increase in robustness against RIR perturbations for MINT, RMCLS, and PMINT. Furthermore, it is shown that PMINT using an optimal intrusively determined reshaping filter length outperforms all other considered techniques. Finally, it is shown that the automatic non-intrusively determined reshaping filter length in PMINT yields a similar performance as the optimal intrusively determined reshaping filter length.

Signal-Dependent Penalty Functions for Robust Acoustic Multi-Channel Equalization

Acoustic multi-channel equalization techniques, which aim to achieve dereverberation by reshaping the room impulse responses (RIRs) between the source and the microphone array, are known to be highly sensitive to RIR perturbations. In order to increase the robustness against RIR perturbations, several signal-independent methods have been proposed, which only rely on the available perturbed RIRs and do not incorporate any knowledge about the output signal. This paper presents a novel signal-dependent method to increase the robustness of equalization techniques by enforcing the output signal to exhibit spectro-temporal characteristics of a clean speech signal. Motivated by the sparse nature of clean speech, we propose to extend the cost function of state-of-the-art least squares equalization techniques, i.e., the multiple-input/output inverse theorem (MINT), relaxed multi-channel least squares (RMCLS), and partial multi-channel equalization based on MINT (PMINT), with a signal-dependent penalty function promoting sparsity of the output signal in the short-time Fourier transform domain. Three conventionally used sparsity-promoting penalty functions are investigated, i.e., the $l_0$ -norm, the $l_1$ -norm, and the weighted $l_1$ -norm, and the sparsity-promoting reshaping filters are iteratively computed using the alternating direction method of multipliers. Simulation results for several acoustic systems and RIR perturbations demonstrate that incorporating sparsity-promoting penalty functions significantly increases the robustness of MINT, RMCLS, and PMINT, with the weighted $l_1$ -norm typically outperforming the $l_0$ -norm and the $l_1$ -norm. Furthermore, it is shown that the weighted $l_1$ -norm sparsity-promoting PMINT technique outperforms the other sparsity-promoting techniques in terms of perceptual speech quality. Finally, it is shown that the signal-dependent weighted $l_1$ -norm sparsity-promoting PMINT technique yields a similar or better dereverberation performance than the signal-independent regularized PMINT technique, confirming the advantage of using signal-dependent penalty functions for robust dereverberation filter design.

Robust Multichannel Dereverberation using Relaxed Multichannel Least Squares

A novel approach is proposed for robust multichannel dereverberation in the presence of system identification error (SIEs), based on channel shortening. A mathematical link is derived between the well known multiple-input/output inverse theorem (MINT) algorithm and channel shortening. The relaxed multichannel least squares (RMCLS) algorithm is then proposed as an efficient realization within the channel shortening paradigm and is shown through experimental results to outperform MINT in the presence of SIEs. While the RMCLS is robust to SIEs, the coloration of the output cannot be controlled. Two extensions to RMCLS are proposed to control the level of coloration and the performances of both extensions are evaluated comparatively. It is shown that both substantially maintain the dereverberation performance and robustness to SIEs obtained from RMCLS while effectively controlling the level of coloration introduced.

Multichannel Equalization in the KLT and Frequency Domains With Application to Speech Dereverberation

Equalization of acoustic channels usually involves inversion of acoustic impulse responses (AIRs), and generally employs multichannel techniques. In this paper, we propose three equalization algorithms, one in the Karhunen-Loève transform (KLT) domain and the other two in the frequency domain. Our proposed algorithm in the KLT domain provides a platform to achieve equalization in conjunction with denoising. Existing multiple-input/output inverse theorem (MINT)-based non-adaptive algorithms require the inversion of a matrix with dimension that is proportional to the AIR length, and is computationally expensive. To overcome this limitation, we propose the frequency-domain algorithm which is computationally very efficient and thus can be employed for the equalization of high-order AIRs in practical applications. In addition, the frequency-domain method is more robust to AIR estimation errors. To achieve further reduction in the complexity without significant performance degradation, we then propose a modified version of the frequency-domain algorithm.

Regularization for Partial Multichannel Equalization for Speech Dereverberation

Acoustic multichannel equalization techniques such as the multiple-input/output inverse theorem (MINT), which aim to equalize the room impulse responses (RIRs) between the source and the microphone array, are known to be highly sensitive to RIR estimation errors. To increase robustness, it has been proposed to incorporate regularization in order to decrease the energy of the equalization filters. In addition, more robust partial multichannel equalization techniques such as relaxed multichannel least-squares (RMCLS) and channel shortening (CS) have recently been proposed. In this paper, we propose a partial multichannel equalization technique based on MINT (P-MINT) which aims to shorten the RIR. Furthermore, we investigate the effectiveness of incorporating regularization to further increase the robustness of P-MINT and the aforementioned partial multichannel equalization techniques, i.e., RMCLS and CS. In addition, we introduce an automatic non-intrusive procedure for determining the regularization parameter based on the L-curve. Simulation results using measured RIRs show that incorporating regularization in P-MINT yields a significant performance improvement in the presence of RIR estimation errors, whereas a smaller performance improvement is observed when incorporating regularization in RMCLS and CS. Furthermore, it is shown that the intrusively regularized P-MINT technique outperforms all other investigated intrusively regularized multichannel equalization techniques in terms of perceptual speech quality (PESQ). Finally, it is shown that the automatic non-intrusive regularization parameter in regularized P-MINT leads to a very similar performance as the intrusively determined optimal regularization parameter, making regularized P-MINT a robust, perceptually advantageous, and practically applicable multichannel equalization technique for speech dereverberation.

A Fast Frequency-Domain Algorithm for Equalizing Acoustic Impulse Responses

The multiple-input/output inverse theorem (MINT) algorithm for multichannel equalization is computationally demanding. Although adaptive MINT reduces the computational complexity, it suffers from slow convergence. In this letter, we propose a low-complexity fast-converging adaptive algorithm for multichannel equalization. The novelty of the approach lies in the adaptive equalization for each frequency bin and its ability to achieve fast convergence in a single step. The proposed algorithm can achieve better equalization of high-order acoustic impulse responses with significant reduction in complexity.

On Microphone-Array Beamforming From a MIMO Acoustic Signal Processing Perspective

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Although many microphone-array beamforming algorithms have been developed over the past few decades, most such algorithms so far can only offer limited performance in practical acoustic environments. The reason behind this has not been fully understood and further research on this matter is indispensable. In this paper, we treat a microphone array as a multiple-input multiple-output (MIMO) system and study its signal-enhancement performance. Our major contribution is fourfold. First, we develop a general framework for analyzing performance of beamforming algorithms based on the acoustic MIMO channel impulse responses. Second, we study the bounds for the length of the beamforming filter, which in turn shows the performance bounds of beamforming in terms of speech dereverberation and interference suppression. Third, we address the connection between beamforming and the multiple-input/output inverse theorem (MINT). Finally, we discuss the intrinsic relationships among different classical beamforming techniques and explain, from the channel condition perspective, what the prerequisites are for those techniques to work. </para>

Inverse filtering of room acoustics

A novel method is proposed for realizing exact inverse filtering of acoustic impulse responses in room. This method is based on the principle called the multiple-input/output inverse theorem (MINT). The inverse is constructed from multiple finite-impulse response (FIR) filters (transversal filters) by adding some extra acoustic signal-transmission channels produced by multiple loudspeakers or microphones. The coefficients of these FIR filters can be computed by the well-known rules of matrix algebra. Inverse filtering in a sound field is investigated experimentally. It is shown that the proposed method is greatly superior to previous methods that use only one acoustic signal-transmission channel. The results prove the possibility of sound reproduction and sound reception without any distortion caused by reflected sounds. >