A new approach to image sparse decomposition based on MP

One of main problems in image sparse decomposition is the contradiction between the quality of the image and the algorithm's speed. To overcome this key problem, a new fast algorithm is presented. At first the number of atoms is decreased by making use of the atom energy property; then this algorithm converts very time-consuming inner product calculations in sparse decomposition into correlations that are fast done by FFT. Experimental results show that the performance of the proposed algorithm is effective.