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Recently, total variation (TV) based minimization algorithms have achievedgreat success in compressive sensing (CS) recovery for natural images due toits virtue of preserving edges. However, the use of TV is not able to recoverthe fine details and textures, and often suffers from undesirable staircaseartifact. To reduce these effects, this letter presents an improved TV basedimage CS recovery algorithm by introducing a new nonlocal regularizationconstraint into CS optimization problem. The nonlocal regularization is builton the well known nonlocal means (NLM) filtering and takes advantage ofself-similarity in images, which helps to suppress the staircase effect andrestore the fine details. Furthermore, an efficient augmented Lagrangian basedalgorithm is developed to solve the above combined TV and nonlocalregularization constrained problem. Experimental results demonstrate that theproposed algorithm achieves significant performance improvements over thestate-of-the-art TV based algorithm in both PSNR and visual perception.

Improved Total Variation based Image Compressive Sensing Recovery by Nonlocal Regularization