|M.Sc Student||Gaizman Ron|
|Subject||Blind Source Separation in Varying Mixing Systems|
|Department||Department of Electrical Engineering||Supervisor||Professor Emeritus Yehoshua Zeevi|
|Full Thesis text|
The problem of blind source separation (BSS) is concerned with recovering M sources from N mixtures with only limited knowledge of the mixing system (thus, "blindly"). The “cocktail party effect” is a useful illustration of the BSS problem, whereby our auditory system and brain manage to separate a single auditory source from a mixture of conversations, music, and background noise. The human brain does it naturally and effortlessly, and many researchers are looking to emulate the human brain’s ability to separate a single auditory and even surmount it. The BSS problem is also common when photographing a semi-reflectance surface such as a display window. In this example, a mixture of the light transmitted from the other side of the glass (i.e. where the photographed object usually lies) and the light that is reflected from the direction of the observer, is created. It goes without saying that many photographers would like to have the ability to eliminate the reflected image.
Most research has focused on invariant time/position (instantaneous/convolutive) mixing systems using both Independent Component Analysis (ICA) and Sparse Component Analysis (SCA). Additionally, a growing body of research is now focusing on variant time/position systems. The use of variant time/position systems is required, for example, when people are in motion (say, in the “cocktail party problem”) or when the reflected image is distorted or faded in a non-uniformly way. Therefore, this thesis will focus on single-path position varying BSS problem wherein the mixing system is comprised of attenuation and/or delay/shift that is changing over time/position. The selected framework is based on a relatively new approach for solving the time/position variant problem known as the Staged Sparse Component Analysis (SSCA) developed by Kaftory & Zeevi (2009). The underlying assumption of the aforementioned approach is that the sources are sparse, or rather, can be sparsified. In the first stage, we use the sparseness quality in order to estimate the system, whereas in the second stage we estimate the sources.
The approach is strongly dependent on an exact estimation of the mixing system and is very sensitive to inherent errors. We further explore several methods for multi-model estimation and provide evidence for the significance of the mixing models estimation for the successful solution of the problem. We also explore the possibility of estimating the success of the inversion using different methods. We compare known methods and propose a new success estimation method. Using the success estimation, we can optimize the mixing system estimation in order to achieve superior results.
Due to recurring errors in estimation and system inversion, recent studies suggested using a regularization factor when inverting the system and estimating the sources. This term takes into consideration prior knowledge about our sources in the system inversion stage. We explore the right strength of this factor in comparison to the system estimation model and suggest using strength that is space varying in accordance to the model’s sensitivity. The results are demonstrated on spatially varying instantaneous and single-path mixtures used mainly on natural images.