Compressed sensing by collaborative reconstruction on overcomplete dictionary

• Nonlocal similarity is introduced to CS by collaborative models for the first time.
• A novel structured Ridgelet overcomplete dictionary is constructed for image blocks.
• Two collaborative models based on the overcomplete dictionary are established.
• A greedy pursuit algorithm of the collaborative reconstruction model is established.

In this paper, we propose a novel collaborative compressed sensing (CS) reconstruction method for natural images. The method is designed to enhance the accuracy and stability when recovering the sparse representations of image blocks on an overcomplete dictionary from the random measurements by introducing nonlocal self-similarity information. The main idea of collaborative reconstruction is to reconstruct an image block by the collaboration of a group of other blocks sharing similar structures to it, therefore more information is made use for individual blocks than their own measurements. The proposed reconstruction method is composed of two collaborative processes which are derived from two nonlocal self-similarity models: the jointly sparse model and the autoregressive model. By the experimental results, the method is shown to outperform the reconstruction methods without collaborations.