M.Sc Student | Michael Yotam |
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Subject | Blind Source Separation by Underdetermined Time/Position Varying Mixtures |

Department | Department of Electrical Engineering |

Supervisor | Professor Emeritus Yehoshua Zeevi |

Full Thesis text |

Blind Source Separation (BSS) is a well studied problem. Yet, application to many real-life Multiple Input Multiple Output (MIMO) scenarios poses both theoretical and practical challenges. Most studies of the BSS problem assume that the mixing system is time/position invariant. Whereas this assumption simplifies the problem considerably, in most cases it is invalid. For example, "sources" and "receivers" in the familiar "cocktail party effect" scenario move in most cases and the mixing system is therefore time/position varying. In other real life scenarios, physical constraints limit the number of sensors to be smaller than the number of sources. For these reasons, we devote this study to the challenging case of BSS encountered in the context of underdetermined time/position varying mixing systems, wherein the number of observed mixtures is smaller than the number of sources, and the mixing system is varying in time/position according to a parametric model.

In general, when data is missing or there is some uncertainty regarding
system and processed signals, one must compensate for these limitations and constraints
by better understanding the statistical properties of the problem. In the
context of the underdetermined time/position varying BSS problem, two levels of
difficulties are encountered. First, the mixing system has to be estimated, and
second, even for the case of fully known (or estimated) system, the
underdetermined nature of the problem introduces ambiguities. We utilize the
Staged Sparse Component Analysis (SSCA), introduced by Kaftory and Zeevi (2009,
2012). This batch algorithm, applicable to parametric time/position varying
mixing systems, exploits signal sparseness to estimate the mixing system. The
application of an inverse process then allows estimation of the source signals.
A variant of the SSCA approach - Underdetermined SSCA (UDSSCA) - is defined. It
utilizes the signal sparseness in the estimation of the signals, instead of
using the mixing system inversion stage. The process of signal estimation is
performed in a sparse domain by implementing the winner-takes-all heuristic
strategy, inspired by minimization of the *l*1 norm.

We provide insight into this solution through a comparison with a sparse “local” stochastic MMSE solution and quasi-inversion of the system, using geometric inspection tools, and by analyzing algorithm-deduced data as random variables. We conclude by showing the robustness of this strategy to small system estimation errors and its computational efficiency. Results are illustrated for 1D (Audio) and 2D (Image) signals using simulation on real and synthetic signals.