Residual based Compressed Sensing Recovery using Sparse Representations over a Trained Dictionary

A novel image compressed sensing (CS) reconstruction technique is proposed, wherein the local sparsity and nonlocal similarities among the image patches are implicitly exploited to improve the performance of CS recovery. The proposed algorithm starts by an initial reconstruction of the image via a well-known straightforward CS reconstruction method. By partitioning this initial image recovery into overlapping blocks, the concept of group sparse representation is exploited to generate an optimal prediction of the image. Then, the prediction image is used to generate a residual in the domain of compressed sensing random projections. The obtained residual being typically more compressible than the original image, resulting in the higher CS recovery performance. Experimental results manifest that the proposed algorithm shows a significant distortion performance improvement as compared to the straightforward CS reconstruction algorithm, as well as shows a superior performance compared to recovery driven by existing residual based recovery in both peak signal-to-noise ration and visual perception.