Michael Shamis (EE, Technion)
Tuesday, 21.9.2010, 14:30
Blind source separation of images and voice signals is a well known and well studied subject. Solutions for this problem have various applications, such as separation of voices of multiple speakers in the same room, denoising, separation of reflections superimposed on images, and more.
Classical time/position invariant Blind Source Separation is usually solved using Independent Component Analysis (ICA), which tries to find statistically independent signals as a linear combination of the mixed signals, or by using Sparse Component Analysis (SCA) which estimates the mixing matrix by analyzing the geometry of the problem and uses scatter plots of the mixed signals to estimate co-linear centroids of the scattered data, where each centroid corresponds to a column in the mixing matrix.
Most of the studies in the field assume time/position invariant signal combinations, although many real problems are not such. Recently, in his PhD thesis, Ran Kaftory has proposed an extension of the SCA method to solve multiple families of the time/position varying problems. He has shown that for instantaneous time/position varying mixtures, the problem of lines estimation transforms to estimation of non linear curves. In this research we explore the separation of instantaneous time/position varying mixtures for which the parametric structure of the mixtures family is known a priori .We show that the geometric approach can also be viewed as Maximum Likelihood (ML) problem when spasification is applied to the mixed signals. We propose a multi-staged SCA algorithm for separation of time/position invariant mixtures and extend the solution to a subset of time/position varying mixtures where the reconstruction is performed by curve fitting techniques and nearest neighbor clustering.
In addition to the geometric approach, we extend the well known technique of ICA, through ML , to the case of time/position varying instantaneous mixtures. We show that ML approach to the time/position varying separation problem can be developed from an information theory perspective as a joint entropy minimization of the unmixed signals. We prove that although the problem is non-convex, and may need non-linear optimization techniques, under certain conditions the correct signals separation constitutes a global maximum of the ML optimization problem.
We conclude by showing that the ML approach provides promising results, but due to the non-linear nature of the problem, its optimization is challenging and SCA-based approach can be used as a complimentary technique to circumvent some of the difficulties originating from the non linearities of the problem.
*PhD thesis under the supervision of Prof. Yehoshua Y. Zeevi.