Boosting of Image Denoising Algorithms

Abstract

In this paper we propose a generic recursive algorithm for improving image denoising methods. Given the initial denoised image, we suggest repeating the following "SOS" procedure: (i) (S)trengthen the signal by adding the previous denoised image to the degraded input image, (ii) (O)perate the denoising method on the strengthened image, and (iii) (S)ubtract the previous denoised image from the restored signal-strengthened outcome. The convergence of this process is studied for the K-SVD image denoising and related algorithms. Still in the context of K-SVD image denoising, we introduce an interesting interpretation of the SOS algorithm as a technique for closing the gap between the local patch-modeling and the global restoration task, thereby leading to improved performance. In a quest for the theoretical origin of the SOS algorithm, we provide a graph-based interpretation of our method, where the SOS recursive update effectively minimizes a penalty function that aims to denoise the image, while being regularized by the graph Laplacian. We demonstrate the SOS boosting algorithm for several leading denoising methods (K-SVD, NLM, BM3D, and EPLL), showing tendency to further improve denoising performance.Comment: 33 pages, 9 figures, 3 tables, submitted to SIAM Journal on Imaging Science