Block compressive sensing of images using l_p norm minimization

Wherein the framework of block compressive sensing sampling of images, an l_p norm minimization algorithm is proposed. The proposed algorithm is memory efficient as we just need to store a block diagonal sensing matrix for sampling the small blocks divided from an original image. The whole image is reconstructed with an l_p norm minimization. To improve the quality of the reconstructed images and reduce the computation time, we combine the penalty function method with revised Hesse sequence quadratic programming in the l_p norm minimization. The algorithm is employed to reconstruct images with different block sizes. From analysis of the visual quality, the peak signal-to-noise and computation time of reconstructed images with different block sizes in detail, we select 16*16 as the optimal block size. Finally, reconstructed images obtained with the proposed algorithm are compared with those obtained with orthogonal matching pursuit algorithm (OMP) and iteratively reweighted least square algorithm (IRLS), respectively. The comparisons show that the proposed algorithm can obtain superior visual quality and peak signal-to-noise ratio (PSNR) performance with less computation time.