| Sparse representation models have been of central interest in recent years due to important achievements in computational harmonic analysis, such as wavelet transformations, and the most recent sampling theory, compressed sensing. Numerous applications based on sparse models have been studied in the last decade leading to promising results. These applications include areas in seismology, image processing, wireless sensor networks, computed tomography and magnetic resonance imaging just to mention a few.;In this work, we propose to extend such applications in the area of image processing, particularly for the image segmentation problem, and examine algorithms involved in sparse modeling from both theoretical and numerical perspectives. In particular, we focus on the Path Following Signal Recovery (PFSR) algorithm introduced by Argaez et al. in 2010, and the Fixed-Point Least-Squares Preconditioned Conjugate Gradient (FPLS PCG) algorithm, presented for the first time in this thesis.;Numerical results are presented supporting our ideas in sparse modeling, specifically for solving the image denoising, image deblurring, image separation, and image inpainting problem. |
