中文摘要：

压缩感知（CS）重构中的近似消息传递（AMP）算法通过迭代执行小波阈值操作和残差更新来快速准确地实现稀疏信号重构,但它所采用的小波系数稀疏约束并不适用于非稀疏的自然图像,尤其CS观测过程存在噪声干扰时.为此,文中提出了一种基于复合稀疏约束和AMP框架的CS图像重构算法,使用相似图像块低秩约束和双边滤波约束作为自然图像的联合先验信息,以改善图像规则纹理和边缘的恢复效果,从而提升算法的重构性能.无噪CS观测的重构实验表明,文中算法的峰值信噪比（PSNR）比仅用低秩约束的AMP算法提高了0.45 d B,比原始AMP算法高6.19 d B;而在含噪CS观测的重构实验中,对应的PSNR增益则分别是0.25和4.60 d B;无论是无噪观测还是含噪观测,文中算法都获得了更佳的主观视觉效果.

英文摘要：

In CS reconstruction, approximate message passing （AMP） can realize the reconstruction of sparse sig-nals 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, a CS 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 0.25dB and 4.60dB. In conclusion, the proposed algorithm can achieve a better visual quality whether it is noiseless or not.