Abstract: It is very slow at present to reconstruct an image from its sparse decomposition results. To overcome this one of main drawbacks in image sparse decomposition, the energy distribution property of the atoms is studied in this paper. Based on the property that energy of most atoms is very 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 proposed. The fast algorithm presented in this paper improves the speed of the image reconstructing by about 32 times and at the same time doesn't degrade the reconstructed image quality at all.