Image Compressed Sensing Recovery based on Multi-scale Group Sparse Representation

Compressed Sensing (CS) is intended to recover a high-dimensional but sparse vector by a small number of linear sampling. Seeking an appropriate domain is of great importance to achieve a high enough degree of sparsity. In this paper, we propose a new scheme for image Compressed Sensing using multiscale strategy and structural group sparse representation, which efficiently characterizes the sparsity and multi-scale self-similarity of natural images in an adaptive group domain. Then, the group sparsity constraint and multi-scale self-similarity are exploited simultaneously under a unified framework. A multi-scale image pyramid is generated to construct the group during reconstruction. Meanwhile, effective dictionaries for each group are trained from the recovery image itself by a group-adaptive dictionary learning algorithm. Experimental results demonstrate that the proposed algorithm increases image CS recovery quality significantly and outperforms the state-of-the-art methods.