In order to reconstruct natural images from compressive sensing (CS) measurements accurately and effectively

a novel structured approximate message passing algorithm using a Laplacian scale mixture (LSM) prior is proposed. The higher-order statistical constraint of the AMP algorithm is created by the LSM model

turning the CS recovery problem into a prior information estimation problem and a singular value minimization problem. Firstly

we use the LSM distribution to model the sparsity of the singular values of the matrices built by similar patches

which denotes the similarity of image patches

and thus utilize the LSM model to describe the nonlocal similarity of images. Secondly

to obtain reliable prior information

the scale parameters of the LSM model are estimated through the use of the expectation-maximization (EM) algorithm. Finally

the singular value minimization problem is solved by the AMP algorithm to achieve the accurate image reconstruction. Experimental results show that the reconstruction quality of our structured AMP algorithm is superior to the state of art CS reconstruction algorithms.