A Novel Iterative Thresholding Algorithm Based on Plug-and-Play Priors for Compressive Sampling

We propose a novel fast iterative thresholding algorithm for image compressive sampling (CS) recovery using three existing denoisers—i.e., TV (total variation), wavelet, and BM3D (block-matching and 3D filtering) denoisers. Through the use of the recently introduced plug-and-play prior approach, we turn these denoisers into CS solvers. Thus, our method can jointly utilize the global and nonlocal sparsity of images. The former is captured by TV and wavelet denoisers for maintaining the entire consistency; while the latter is characterized by the BM3D denoiser to preserve details by exploiting image self-similarity. This composite constraint problem is then solved with the fast composite splitting technique. Experimental results show that our algorithm outperforms several excellent CS techniques.