M.Sc Thesis

M.Sc StudentCarasso David
SubjectRobust Blind Source Separation on MIMO Systems
Algorithms and Analysis
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Yehoshua Zeevi
Full Thesis textFull thesis text - English Version


The geometrical approach to Blind Source Separation (BSS), based on Sparse Component Analysis (SCA) is studied with emphasis on the effects of noise and distortions on the recovery of the source signals (mostly images). The geometrical approach is based on the projection of mixtures of sources onto a space in which the sources (and hence the mixtures) are sparse, constituting a scatter plot of the projections versus each other. The data points are clustered around axes whose orientations are the estimators of the columns of A, a matrix constructed by the mixing coefficients.  The BSS scheme implies the distribution around several cardinal orientations, thus linear estimation methods should be combined with methods that distribute the data into separate clusters.

Since sparsity is always partial the data points are not simply separated into the orientation subsets. We propose the use of robust regression methods in the orientation estimation algorithm. Robust regression is based on limiting the effect of outliers on regression estimators. In this work we show that the combination of clustering and linear estimation requires a gradual application of robust regression. The proposed algorithm Gradual Waited Least Squares (GWLTS), in the case of 3x3 BSS achieved improvement of at least one order of magnitude in the error of the reconstructed sources.

To confront effects to orientation estimation caused by noise we propose the application of “wavelets denoising" to BSS, to reduce noise level of the mixtures. We show that denoising the mixtures can be applied before performing SCA and retain the original orientations. Representing the mixtures in a wavelet domain, we define an effective measure of the sparsity of a selected node. A node selection rule for SCA can be constructed from this measure.

We propose a geometrical approach to BSS that does not exercise SCA for the 2x2 case. The scatter plot of two mixtures, generated by mixing two positive sources, is bounded by a parallelogram, the orientations of which are defined by two ratios of the four mixing coefficients. Based on these observations a robust geometrical method for BSS is presented with reference to the scatter plot of the mixtures.

The effect of additive errors to the mixing matrix coefficients is studied, by the development of the Cross-talk Error (CTE). Bounds on the performance are developed, and considered in the context of the design of Multiple Input Multiple Output (MIMO) system.