Image compressive recovery based on dictionary learning from under-sampled measurement

Compressive sensing(CS) has attracted many attentions in recent years, which assumes that the signal can be exactly reconstruction from its only a few measurements when it is sparsity enough under a certain domain. In this paper, we address the image compressive recovery problem. Firstly, a specific adaptive dictionary learning method is adopted to represent the image more sparsely, which learns atoms in dictionary from the under-sampled measurement directly and shows some good performance in adapting to the compressed sensing framework. Secondly, by utilizing the nonlocal self-similarity in image, we also propose a novel nonlocal CS model with multiple regularizations to preserve the details in the reconstruction image, which are seen as the important information to human perception. In addition, to further improve the computational efficiency, an iterative algorithm is developed to solve the proposed model effectively. Extensive experiments on various benchmark images verify that, compared to the existing excellent methods, the proposed model shows superior and competitive performance.