Blind Source Separation and Deconvolution of Fast Sampled Signals

In real world implementations of blind source separation and deconvolution, the mixing takes place in continuous time. In the models normally considered, discrete time sampling is implicitly assumed to provide a mixing filter matrix from a suitable demixing filter matrix which can be learned given an appropriate algorithm. In this paper, we consider the implications of trying to separate and deconvo lve signals which may include some signals which are low frequency compared to the sample rate. It is shown that if a fast sampling rate is u sed to obtain the discrete time observed data, learning to solve bl ind source separation and deconvolution tasks can be very difficult. Th is is due to the data covariance matrix becoming almost singular. We propose a discrete time model based on alternative discrete time operators which is capable of overcoming the problems and giving significant ly improved performance under the conditions described.

[1]  Åke Björck,et al.  Numerical Methods , 2020, Markov Renewal and Piecewise Deterministic Processes.

[2]  Ramesh C. Agarwal,et al.  New recursive digital filter structures having very low sensitivity and roundoff noise , 1975 .

[3]  K. Åström,et al.  Zeros of sampled systems , 1980 .

[4]  John C. Platt,et al.  Networks for the Separation of Sources that Are Superimposed and Delayed , 1991, NIPS.

[5]  Marimuthu Palaniswami,et al.  Digital estimation and control with a new discrete time operator , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[6]  G. Goodwin,et al.  High-speed digital signal processing and control , 1992, Proc. IEEE.

[7]  José Carlos Príncipe,et al.  The gamma model--A new neural model for temporal processing , 1992, Neural Networks.

[8]  Andrzej Cichocki,et al.  Neural networks for optimization and signal processing , 1993 .

[9]  M. Gevers,et al.  Parametrizations in control problems , 1993 .

[10]  José Carlos Príncipe,et al.  The gamma-filter-a new class of adaptive IIR filters with restricted feedback , 1993, IEEE Trans. Signal Process..

[11]  Qiang Li,et al.  A delta -operator recursive gradient algorithm for adaptive signal processing , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[12]  Juha Karhunen,et al.  Representation and separation of signals using nonlinear PCA type learning , 1994, Neural Networks.

[13]  Ah Chung Tsoi,et al.  A Comparison of Discrete-Time Operator Models and for Nonlinear System Identification , 1994, NIPS.

[14]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[15]  Christian Jutten,et al.  Blind source separation for convolutive mixtures , 1995, Signal Process..

[16]  Shun-ichi Amari,et al.  Recurrent Neural Networks For Blind Separation of Sources , 1995 .

[17]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[18]  Andrzej Cichocki,et al.  Convergence Analysis of Local Algorithms for Blind Decorrelation , 1996, NIPS 1996.

[19]  Kari Torkkola,et al.  Blind separation of delayed sources based on information maximization , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.