A new compressive sensing based image denoising method using block-matching and sparse representations over learned dictionaries

Suppressing noise and preserving detail information such as edges and textures are two key challenges in image denoising. In this paper, a new method for eliminating noise from images is presented which is based on not only compressive sensing but also sparse and redundant representations over trained dictionaries. The objective function of the proposed technique consists of two terms. The first term processes the noisy image by the hard thresholding operator in the bandelet domain to provide the noise-free image as well as guaranteeing the similarity between the denoised image and the noisy image, while the second term ensures that the image admits a sparse decomposition in a dictionary. In addition, the proposed method takes advantage of the block-matching technique for representing the dictionary elements such that the noisy image is firstly grouped by the block-matching technique, and then an identical sparse vector is used for all patches in a group. Simulations using images contaminated by additive white Gaussian noise demonstrate that the performance of the proposed method considerably surpasses that of state-of-the-art methods, both visually and in terms of quantitative criteria, namely peak signal to noise ratio and structural similarity.