Abstract: There arc two main problems in image sparse decomposition that the speed is timcconsuming and the visual effect of reconstructed image is not very good. This paper introduced a new algorithm based on MP and IDFI门in image sparse decomposition. Two-dimensional image to be decomposed is converted into ono-dimensional signal. Likewise, the atoms of the over-complete dictionary arc converted into oncdimensional atoms. Then, the inner product operation between image or residual image and atom is transformed into the cross-correlation operation of one-dimensional signals.Finally, the method of FF"T realizes the cross correlation operation between oncdimensional signal and oncdimensional atom. Experimental results show that, when the size of the image is 512 X 512，compared with the two-imensional FIST method, the proposed algorithm speeds up a little more than 2. 11 times without any loss of the reconstructed image quality.

Key words: Image processing, Sparse decomposition, MP, Over-complete dictionary, FIST