Sparse Representation Algorithms and their Applications

Abstract

Sparse representation is an active research topic in signal and image processing because of its vast amount of applications like sampling, MEG, super resolution, speech coding etc. In this thesis, we are dealing with sparse representation of a signal and its applications in different fields. To approximate the sparse vector, we used Matching Pursuit (MP) and Orthogonal Matching Pursuit (OMP) algorithm and to minimize the dictionary KSVD is used. We prefer sparse approximation and dictionary minimization to reduce the computational complexity, it takes less space to store that is for memory saving as well as to increase efficiency that means to reduce the execution time. Some sparse based applications are implemented like noise removal- Denoising and Inpainting, Dictionary Learning and Face Recognition. In face recognition, two methods sparse representation based classification (SRC) and Extended sparse representation based classification (ESRC) are implemented. SRC is suitable only for over-complete dictionary, it is invalid for under-determined dictionaries. To over come this problem we go through ESRC. To get the low dimensional image, extract features from the face using different techniques like Down-sampling and Local Binary Pattern (LBP).