Residual Correlation Regularization Based Image Denoising

Patch-based denoising algorithms aim to reconstruct the clean image patch leaving behind the residual as contaminating noise. The residual should possess statistical properties of contaminating noise. However, it is very likely that the residual patch contains remnants from the clean image patch. In this letter, we propose a new residual correlation based regularization for image denoising. The regularization can effectively render residual patches as uncorrelated as possible. It allows us to derive an analytical solution for sparse coding (atom selection and coefficient calculation). It also leads to a new online dictionary learning update. The clean image is obtained through alternating between the two stages of sparse coding and dictionary updating. The performance of the proposed algorithm is compared with state-of-the-art denoising algorithms in terms of peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and feature similarity index (FSIM), as well as through visual comparison. Experimental results show that the proposed algorithm is highly competitive and often better than leading denoising algorithms. The proposed algorithm is also shown to offer an efficient complement to the benchmark algorithm of block-matching and 3D filtering (BM3D) especially.