Image Denoising Using Low Rank Minimization With Modified Noise Estimation

Recently, the application of low rank minimization to image denoising has shown remarkable denoising results which are equivalent or better than those of the existing state-of-the-art algorithms. However, due to iterative nature of low rank optimization, estimation of residual noise is an essential requirement after each iteration. Currently, this noise is estimated by using the filtered noise in the previous iteration without considering the geometric structure of the given image. This estimate may be affected in the presence of moderate and severe levels of noise. To obtain a more reliable estimate of residual noise, we propose a modified algorithm (GWNNM) which includes the contribution of the geometric structure of an image to the existing noise estimation. Furthermore, the proposed algorithm exploits the difference of large and small singular values to enhance the edges and textures during the denoising process. Consequently, the proposed modifications achieve significant improvements in the denoising results of the existing low rank optimization algorithms.

Multiscale Hybrid Non-local Means Filtering Using Modified Similarity Measure

A new multiscale implementation of non-local means filtering for image denoising is proposed. The proposed algorithm also introduces a modification of similarity measure for patch comparison. The standard Euclidean norm is replaced by weighted Euclidean norm for patch based comparison. Assuming the patch as an oriented surface, notion of normal vector patch is being associated with each patch. The inner product of these normal vector patches is then used in weighted Euclidean distance of photometric patches as the weight factor. The algorithm involves two steps: The first step is multiscale implementation of an accelerated non-local means filtering in the stationary wavelet domain to obtain a refined version of the noisy patches for later comparison. This step is inspired by a preselection phase of finding similar patches in various non-local means approaches. The next step is to apply the modified non-local means filtering to the noisy image using the reference patches obtained in the first step. These refined patches contain less noise, and consequently the computation of normal vectors and partial derivatives is more accurate. Experimental results indicate equivalent or better performance of proposed algorithm as compared to various state of the art algorithms.