M.Sc Thesis

M.Sc StudentAchtenberg Albert
SubjectBlind Source Separation of Mixtures of Images Mixed Using
Non-Uniform Medium
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Yehoshua Zeevi
Full Thesis textFull thesis text - English Version


In many real world applications, input signals to a system are mixtures of some more meaningful sources. The problem of recovering m sources from n mixtures with only limited knowledge of the mixing process is known as the Blind Source Separation (BSS) problem. Most research in the field of BSS has focused on instantaneous and time invariant cases. Convolutive mixtures are being currently extensively studied, using SCA as well as the popular independent component analysis (ICA) techniques.

We address the open problem of blindly separating single-path position varying image mixtures without having prior information about the sources. Unlike instantaneous or convolutive mixture modules, we assume that the mixing system's spatial distortion and attenuation changes with position. We propose a staged method to estimate the mixing models and recover source signals from such mixtures. Our method is based on a Staged Sparse Component Analysis (SSCA) of the mixtures. We assume that the sources are sparse, or can be 'sparsified'. In the first stage we align the sources to estimate the spatial distortion component of the mixing system. In the second stage we classify the sparse signal samples to their estimated sources and estimate the spatial attenuation component of the mixing system. In the third and last stage we invert the mixing system to recover the sources.

Along our experiments with the staged approach for single-path position varying signals we have found that the inversion step is very sensitive to the spatial distortion component of the mixing system. Small error in the spatial distortion component leads to a significant degradation in separation quality. This observation requires finding a very accurate estimate of the mixing system to provide good separation quality. In practice, the model estimation stage has a level of uncertainty, variance, due to: noisy samples; bad spatial spread of samples; mixed samples in sparse representation and more. Recent studies propose adding regularization terms to the inversion process. However, in most cases where the spatial distortion is of significant magnitude this would not suffice. We propose a solution by adding a model refinement step that is based on simple image quality measures that would allow us to improve separation results. We test some standard methods and propose a new approach based on Phase Congruency measure.

We tested our suggested methods on different image classes for various mixing systems. Synthetically generated mixtures were used to test the proposed separation processes yielding good results.