A cascade form blind source separation connecting source separation and linearization for nonlinear mixtures

A network structure and its learning algorithm have been proposed for blind source separation applied to nonlinear mixtures. The network has a cascade form consists of a source separation block and a linearization block in this order. The conventional learning algorithm is employed for the separation block. A new learning algorithm is proposed for the linearization block assuming 2nd-order nonlinearity. After, source separation, the outputs include the nonlinear components for the same signal source. This nonlinearity is suppressed through the linearization block. Parameters in this block are iteratively adjusted based on a process of solving a 2nd-order equation of a single variable. Simulation results, using 2-channel speech signals and an instantaneous nonlinear mixing process, show good separation performance

BLIND SOURCE SEPARATION USING MAXIMUM ENTROPY PDF ESTIMATION BASED ON FRACTIONAL MOMENTS

Abstract. Recovering a set of independent sources which are linearly mixed is the main task of the blind source separation. Utilizing different methods such as infomax principle, mutual information and maximum likelihood leads to simple iterative procedures such as natural gradient algorithms. These algorithms depend on a nonlinear function (known as score or activation function) of source distributions. Since there is no prior knowledge of source distributions, the optimality of the algorithms is based on the choice of a suitable parametric density model. In this paper, we propose an adaptive optimal score function based on the fractional moments of the sources. In order to obtain a parametric model for the source distributions, we use a few sampled fractional moments to construct the maximum entropy probability density function (PDF) estimation . By applying an optimization method we can obtain the optimal fractional moments that best fit the source distributions. Using the fractional moments (FM) instead of the integer moments causes the maximum entropy estimated PDF to converge to the true PDF much faster . The simulation results show that unlike the most previous proposed models for the nonlinear score function, which are limited to some sorts of source families such as sub-gaussian and super-gaussian or some forms of source distribution models such as generalized gaussian distribution, our new model achieves better results for every source signal without any prior assumption for its randomness behavior

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

金沢大学理工研究域　電子情報学系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 be 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. © 2005 IEEE

A distortion free learning algorithm for feedforward BSS and its comparative study with feedback BSS

金沢大学理工研究域　電子情報学系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. © 2006 IEEE

A distortion free learning algorithm for feedforward BSS and its comparative study with feedback BSS

金沢大学大学院自然科学研究科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. © 2006 IEEE

周波数領域フィードフォワード形ブラインド信号源分離における信号歪みを抑制する学習法

金沢大学理工研究域　電子情報学系ブラインド信号源分離(BSS)では、出力を独立にするように学習が行われるため信号歪みが発生する可能性があることが知られている.また, フィードフォワード形ブラインド信号源分離(FF-BSS)は分離回路における自由度が高く, 出力信号を互いに独立にする学習が信号歪みを生じる可能性がある.そこで信号歪みの低減のために完全分離の条件と無歪の条件から導かれた式を学習に加味するという手法がすでに提案されている.本稿では周波数領域におけるFF-BSSにおいてその手法を適用し, 様々な信号源に対しての信号歪み抑制法の性能をシミュレーションにより解析する. In the blind source separation (BSS), a separation block is trained so as to make its output signals to be statistically independent. Since the frequency domain BSS has some degree of freedom, the wave form and frequency response of the separated signals may be changed from the originals, resulting in signal distortion. In this paper, a learning algorithm, suppressing the signal distortion, for the feedforward BSS, implemented in the frequency domain, is proposed. A condition on both complete separation and signal distortion free has been proposed. This condition is included in the learning process as constraint. Usefulness of the proposed learning algorithm is analyzed by using several kinds of the signal sources