In CS reconstruction,approximate message passing ( AMP) can realize the reconstruction of sparse signals quickly and accurately by performing both wavelet de-noising and residual updating iteratively.However,the sparse constraints of the wavelet coefficients used in AMP are not suitable for non-sparse natural images,especially when the measuring process of CS is disturbed by noises.In order to solve this problem,aCS image reconstruction algorithm is proposed on the basis of composite sparse constraints and an AMP framework.This algorithm takes both the low-rank constraint of similar image patches and the bilateral filter constraint as the joint prior information of natural images to enhance the recovery effect of image textures and edges,thus improving the performance of the algorithm.The results of the reconstruction experiment with no noise in the measuring process of CS show that,the proposed algorithm averagely improves PSNR( Peak Signal to Noise Ratio) by 0.45dB and 6.19dB,respectively in comparison with the AMP algorithm that only uses low-rank constraint and the original AMP algorithm.While in the presence of noise,the corresponding average PSNR gains are respectively 0.25 dB and 4.60 dB.In conclusion,the proposed algorithm can achieve a better visual quality whether it is noiseless or not.