New bounds on image denoising: Viewpoint of sparse representation and non-local averaging

Image denoising plays a fundamental role in many image processing applications. Utilizing sparse representation and nonlocal averaging together is such a successful framework that leads to considerable progress in denoising. Almost all the newly proposed denoising algorithms are built base on it, different in detailed implementation, and the denoising performance seems converging. What is the denoising bound of this framework turns into a key question. In this paper, we assume all the possible algorithms under the framework can be approximated by a fixed two steps denoising process with different parameters. Step one cluster geometric similar image patches into groups so that patches within each group could be sparse represented under the basis of the group. Step two use the atoms of the group basis and radiometric similar patches of each patch for non-local averaging. The parameters of the process are the cluster number, the atoms and the number of radiometric similar patches for estimating each patch. Finally, the bound is derived as the minimum denoising error of all the possible parameters. Comparing with previous bounds, the new one is image specific and more practical. Experiment results show that there still exists room to improve the denoising performance for natural images.