Fast Algorithm For OMP-Based Image Sparse Decomposition And Its Primary Application

Sparse decomposition becomes very popular in the study of signal processing in recent years, because it can transform signal into a sparse formation. Sparse decomposition is therefore applied to image processing quickly.The Matching Pursuit (MP) algorithm is in common used in signal sparse decomposition. Orthogonal Matching Pursuit (OMP) is an improved algorithm of MP. Its method of selecting optimal atom is as same as MP, which selects the most matching atom with the image residual. The difference of MP and OMP is that OMP orthogonalizes the atoms, and then projects the signal residual onto the orthogonal atoms to get the signal component and residual component, and decomposes the residual repeatedly. The convergence rate of OMP is much faster than MP. Its disadvantage is that the computational burden is very huge. In this paper, signal sparse decomposition and image sparse decomposition based on Particle Swarm Optimization (PSO) algorithm are proposed. PSO is used to effectively search in the dictionary of atoms for the best atom at each step in OMP. It can reduce the computational burden considerably.In this paper, the image compression based on the OMP image sparse decomposition is studied. Image compression is one of key steps in image processing and it has been widely applied to many fields of modern sciences and technologies. A lot of image compression methods have been proposed after many years study, and obtain favorable application in many fields. However, for image compression at low bit rate, these methods usually don't perform as good as at high-bits. So it is necessary to develop a new method for image compression at low bit rate. Based on the image sparse decomposition, the distribution of image sparse decomposition results is analyzed. And then a coding scheme is proposed based on the image sparse decomposition results. In this coding scheme, the order of results is adjusted according to the value of projection, which is one of the parameters of image sparse decomposition, and then the projection is processed by pre-difference. After that, the range of projection value decreased largely. And then an image coding and quantization scheme is proposed. Based on the coding and quantization scheme, the image compression on the sparse decomposition is achieved.