Sparse Representation Theory And Its Application In Image Reconstruction And Denoising

Image reconstruction and de-noising are fundamental problems in image processing, with information continuous increases, which become hot issues in engineering application to solve it effective and fastness on massive data image. Recent Compressed Sensing(CS) theoretical proved that sampling far less information than traditional sample method can precisely reconstruct the original signal while robust to noise, which indicates that sparse representation theory image reconstruction and de-noising.This paper mainly focus on a family of matching pursuit algorithms which is based on the sparse representation theory. Begin with the background of image reconstruction and de-noising, and induced mainly noising models, and enumerate some classical de-noising method. With review of Compressed Sensing (CS) and quest to solve the Po problem, we introduced Matching Pursuit(MP) algorithm and Orthogonal Matching Pursuit(OMP) algorithm, and further variants algorithm like Weak Matching Pursuit (WMP) and Stage-wise Orthogonal Matching Pursuit(StOMP), still we’ll compare with another Basic Pursuit(BP) algorithm base on different idea but in fact doing the same performance. In the examples, we’ll compare their work performance and time-consume on image reconstruction.This paper also introduced the K times singular value decomposition(K-SVD) theory and its algorithm on image de-noising. We chose StOMP instead of OMP in the K-SVD reconstruction aiming to overcome OMP’s time-consuming problem in sparse representation iterations. From the examples, we tested and verified StOMP’s performance in K-SVD de-noising and less time-consuming compare to OMP.