Novel techniques for sparse representation problems

Abstract

Sparse representations have been used in solving many problems in computer science. Two issues that need to be addressed in formulating such a representation are: the problem design; and the optimization technique. Many optimization problems contain one/multiple non-smooth terms in the objective function. Besides, the feasibility of an optimization problem depends on the availability of adequate computational resources. In this thesis, a new parallelizable optimization technique that uses more information and has better convergence than state-of-the-art counterparts is presented. Theoretical derivation of the bound of the recovery probability of using sparse representation based on a L_1-minimization is also shown. A clustering-based technique for dictionary and signal dimension reduction to replace the traditional naïve downsampling technique is introduced to address computational resource constraints. Finally, an anomaly detection and localization technique using a sparse representation problem and used in a case study for an important and challenging field; namely automated visual inspection (AVI) is presented. The experimental results are encouraging.