A fast algorithm for image reconstruction based on sparse decomposition

Abstract

It is very slow at present to reconstruct an image from its sparse decomposition results. To overcome this one of the main drawbacks in image sparse decomposition, the property of the energy distribution of atoms is studied in this paper. Based on the property that energy of most atoms is highly concentrated, an algorithm is proposed to fast reconstruct an image from atoms  parameters by limiting atom reconstruction calculating within the atom energy concentrating area. Moreover, methods for fast calculating atom energy and normalization are also put forward. The fast algorithm presented in this paper improves the speed of the image reconstructing by approximately 32 times without degrading the reconstructed image quality.