Akihide Horita

A learning algorithm for convolutive blind source separation with transmission delay constraint

A learning algorithm is proposed for fully recurrent convolutive blind source separation. Let s/sub i/(n) and x/sub j/(n) be the signal sources and the observations. H/sub ji/(z) expresses a transfer function from s/sub i/(n) to x/sub j/(n). It is assumed that the transmission delay time of H/sub ji/(z), j/spl ne/i is longer than that of H/sub ii/(z). In many practical applications, this assumption is acceptable. Based on this assumption, s/sub i/(n) in the output y/sub j/(n), j/spl ne/i of an unmixing block is cancelled through the feedback C/sub ji/(z) from the ith output to the jth observation. However, s/sub i/(n) in the output y/sub i/(n) cannot be cancelled, because a noncausal C/sub ij/(z) is required. A cost function E[q(y/sub j/(n))] can be used, where q is an even function with a single minimum point. The coefficients of C/sub ji/(z), i.e. c/sub ji/(l) are updated following a gradient descent method. The correction term is expressed uq/spl dot/[y/sub j/(n)]y/sub i/(n-l). q/spl dot/ is a partial derivative of q. Two-channel blind source separation has been simulated using speech signals. 100th- and 70th-order FIR filters are used for C/sub 12/(z) and C/sub 21/(z), respectively. The power ratio of the main signals and the cross-components is about 15 dB.

A learning algorithm with adaptive exponential stepsize for blind source separation of convolutive mixtures with reverberations

First, convergence properties in blind source separation (BSS) of convolutive mixtures are analyzed. A fully recurrent network is taken into account. Convergence is highly dependent on relation among signal source power, transmission gain and delay in a mixing process. Especially, reverberation degrade separation performance. Second, a learning algorithm is proposed for this situation. In an unmixing block, feedback paths have an FIR filter. The filter coefficients are updated through the gradient algorithm starting from zero initial guess. The correction is exponentially scaled along the tap number. In other words, stepsize is exponentially weighted. Since the filter coefficients with a long delay are easily affected by the reverberations, their correction is suppressed. Exponential weighting is automatically adjusted by approximating an envelop of the filter coefficients in a learning process. Through simulation, good separation of performance, which is the same as in no reverberations condition, can be achieved by the proposed method.

Analysis of signal separation and signal distortion in feedforward and feedback blind source separation based on source spectra

Source separation and signal distortion in three kinds of BSSs with convolutive mixture are analyzed. They include a feedforward BSS, trained in the time domain and in the frequency domain, and a feedback BSS, trained in the time domain. First, an evaluation measure of signal distortion is discussed. Second, conditions for source separation and distortion free are derived. Based on these conditions, source separation and signal distortion are analyzed. The feedforward BSS has some degree of freedom, and the output spectrum can be changed. The feedforward BSS, trained in the frequency domain, has weighting effect, which can suppress signal distortion. This weighting is, however, effective only when the source spectra are similar to each other. Since, the feedforward BSS, trained in the time domain, does not have any constraints on signal distortion free, its output signals can he easily distorted. A new learning algorithm with a distortion free constraint is proposed. On the other hand, the feedback BSS can satisfy both source separation and distortion free conditions simultaneously. Simulation results support the theoretical analysis.

A Distortion Free Learning Algorithm for Feedforward BSS and ITS Comparative Study with Feedback BSS

Source separation and signal distortion are theoretically analyzed for the FF-BSS systems implemented in both the time and frequency domains and the FB-BSS system. The FF-BSS systems have some degree of freedom, and cause some signal distortion. The FB-BSS has a unique solution for complete separation and distortion free. Next, the condition for complete separation and distortion free is derived for the FF-BSS systems. This condition is applied to the learning algorithms. Computer simulations by using speech signals and stationary colored signals are carried out for the conventional methods and the new learning algorithms employing the proposed distortion free constraint. The proposed method can drastically suppress signal distortion, while maintaining high separation performance. The FB-BSS system also demonstrates good performances. The FF-BSS systems and the FB-BSS system are compared based on the transmission time difference in the mixing process. Location of the signal sources and the sensors are rather limited in the FB-BSS system.

Analysis and comparative study of source separation performances in feed-forward and feed-back BSSs based on propagation delays in convolutive mixture

Feed-Forward (FF-) and Feed-Back (FB-) structures have been proposed for Blind Source Separation (BSS). The FF-BSS systems have some degrees of freedom in the solution space, and signal distortion is likely to occur in convolutive mixtures. On the other hand, the FBBSS structure does not cause signal distortion. However, it requires a condition on the propagation delays in the mixing process. In this paper, source separation performance in the FB-BSS is theoretically analyzed taking the propagation delays into account. Simulation is carried out by using white signals and speech signals as the signal sources. The FF-BSS system and the FB-BSS system are compared. Even though the FB-BSS can provide good separation performance, there exits some limitation on location of the signal sources and the sensors.

A Distortion-Free Learning Algorithm for Feedforward Multi-Channel Blind Source Separation

FeedForward (FF-) Blind Source Separation (BSS) systems have some degree of freedom in the solution space. Therefore, signal distortion is likely to occur. First, a criterion for the signal distortion is discussed. Properties of conventional methods proposed to suppress the signal distortion are analyzed. Next, a general condition for complete separation and distortion-free is derived for multi-channel FF-BSS systems. This condition is incorporated in learning algorithms as a distortion-free constraint. Computer simulations using speech signals and stationary colored signals are performed for the conventional methods and for the new learning algorithms employing the proposed distortion-free constraint. The proposed method can well suppress signal distortion, while maintaining a high source separation performance.

A blind source separation with exponentially weighted stepsize and its convergence analysis in convolutive mixture with reverberations

Abstract A blind source separation (BSS) method with an exponentially weighted (EW) stepsize has been proposed for convolutive mixtures with reverberations. The EW stepsize is also useful for general adaptive filters under the conditions without reverberations. This paper analyzes usefulness of the EW stepsize on the reverberations. In simulations, high-order lters are used in a separation block. Two kinds of conditions for a mixing process, that is with and without reverberations, and two kinds of stepsizes, that is a constant and the EW stepsizes, are taken into account. In the mixing process without reverberations, the EW stepsize can realize fast convergence, however, the final separation results are the same as using the constant stepsize. When reverberations are included, the EW stepsize can provide fast convergence and the good final results. A constant stepsize cannot suppress effects of reverberations. From these results, usefulness of the EW stepsize for reverberations is confirmed.