Reconstruction for block-based compressive sensing of image with reweighted double sparse constraint

Block compressive sensing reduces the computational complexity by dividing the image into multiple patches for processing, but the performance of the reconstruction algorithm is decreased. Generally, the reconstruction algorithm improves the quality of reconstructed image by adding various constraints and regularization terms, namely prior information. In this paper, a reweighted double sparse constraint reconstruction model which combines the residual sparsity and 1 regularization term is proposed. The residual sparsity aims to exploit the nonlocal similarity of image patches, and the 1 regularization term is used to utilize the local sparsity of image patches. The resulting model is solved under the frame of split Bregman iteration (SBI). A large number of experiments show that the algorithm in this paper can reconstruct the original image efficiently and is comparable to the current representative compressive sensing reconstruction algorithm.