Low-Rank Combined Adaptive Sparsifying Transform for Blind Compressed Sensing Image Recovery

Compressed sensing (CS) exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undegraded images. Because the synthesis dictionary learning methods involves NP-hard sparse coding and expensive learning steps, sparsifying transform based blind compressed sending (BCS) has been shown to be effective and efficient in applications, while also enjoying good convergence guarantees. By minimizing the rank of an overlapped patch group matrix to efficiently exploit the nonlocal self-similarity features of the image, while the sparsifying transform model imposes the local features of the image. We propose a combined low-rank and adaptive sparsifying transform (LRAST) BCS method to better represent natural images. We utilized the patch coordinate (PCD) descent algorithm to optimize the method, and this enforced the intrinsic local sparsity and nonlocal self-similarity of the images simultaneously in a unified framework. The experimental results indicated a promising performance, even in comparison to state-of-theart methods.