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.

2012 Visual Communications and Image Processing
Li Song
Li Song
Professor, IEEE Senior Member

Professor, Doctoral Supervisor, the Deputy Director of the Institute of Image Communication and Network Engineering of Shanghai Jiao Tong University, the Double-Appointed Professor of the Institute of Artificial Intelligence and the Collaborative Innovation Center of Future Media Network, the Deputy Secretary-General of the China Video User Experience Alliance and head of the standards group.