Non-local sparse regularization model with application to image denoising

We study problems related to denoising of natural images corrupted by Gaussian white noise. Important structures in natural images such as edges and textures are jointly characterized by local variation and nonlocal invariance. Both provide valuable schemes in the regularization of image denoising. In this paper, we propose a framework to explore two sets of ideas involving on the one hand, locally learning a dictionary and estimating the sparse regularization signal descriptions for each coefficient; and on the other hand, nonlocally enforcing the invariance constraint by introducing patch self-similarities of natural images into the cost functional. The minimization of this new cost functional leads to an iterative thresholding-based image denoising algorithm; its efficient implementation is discussed. Experimental results from image denoising tasks of synthetic and real noisy images show that the proposed method outperforms the state-of-the-art, making it possible to effectively restore raw images from digital cameras at a reasonable speed and memory cost.