Thesis

Nonlinear non-Gaussian algorithms for signal and image processing

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Awarding institution
  • University of Strathclyde
Date of award
  • 2007
Thesis identifier
  • T12169
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • This thesis is initially concerned with solving the Blind Source Separation (BSS) problem. The BSS problem has been found to occur frequently in problems existing in various Scientific and Engineering application areas. The basic idea of the BSS problem is to separate a collection of mixed data into its underlying information components. To tackle the BSS problem two related methodologies have been utilized extensively throughout the literature. The first approach is by utilizing the statistical technique Independent Component Analysis (ICA). This method utilizes a transformation that maximizes the statistical independence of the mixed data components. The second approach is based on the Approximate Joint Diagonalization (AJD) of a set of target matrices, either the time delayed correlation matrices or matrix slices of the fourth order cumulant tensor. This approximate diagonalization results in matrices which are maximally diagonal. Within this thesis both of the above approaches are utilized within an adaptive gradient descent setting to tackle the BSS problem. The first contribution within this thesis is the novel application of the Matrix Momentum optimization framework to perform ICA, via the optimization of a Mutual Information based cost function. The algorithm is shown to give Newton like performance with low computational cost. The second contribution within this thesis is the first application of the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm to jointly diagonalize a set of time delayed correlation matrices. As a result of the above work it was also found that the SPSA algorithm could also be applied to the problem of Image Registration. Currently one of the most popular methods of solving the Image Registration problem is based on the maximization of the Mutual Information between the images. The final contribution within this thesis is the application of the SPSA algorithm to other novel Information Theoretic cost functions to perform Image Registration.
Advisor / supervisor
  • Durrani, Tariq S.
Resource Type
DOI
EThOS ID
  • uk.bl.ethos.501874
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