Cauchy noise removal using groupbased lowrank prior Abstract   Although the extensive research on Gaussian noise removal, few works consider the Cauchy noise removal problem. In this paper, we propose a novel groupbased lowrank method for Cauchy noise removal. By exploiting the nonlocal selfsimilarity of natural images, we consider a group of similar patches as an approximate lowrank matrix, and formulate the denoising of each group as a lowrank matrix recovery problem. Meanwhile, we develop the alternating direction method of multipliers algorithm to solve the proposed nonconvex model with guaranteed convergence. Experiments illustrate that our method has superior performance over the stateoftheart methods in terms of both visual and quantitative measures.

Image Denoising Using Local Tangent Space Alignment We propose a novel image denoising approach, which is based on exploring an underlying (nonlinear) lowdimensional manifold. Using local tangent space alignment (LTSA), we u0027learnu0027 such a manifold, which approximates the image content effectively. The denoising is performed by minimizing a newly defined objective function, which is a sum of two terms: (a) the difference between the noisy image and the denoised image, (b) the distance from the image patch to the manifold. We extend the LTSA method from manifold learning to denoising. We introduce the local dimension concept that leads to adaptivity to different kind of image patches, e.g. flat patches having lower dimension. We also plug in a basic denoising stage to estimate the local coordinate more accurately. It is found that the proposed method is competitive: its performance surpasses the KSVD denoising method.