Multi-scale image denoising while preserving edges in sparse domain

Image denoising is a classical and fundamental problem in image processing community. An important challenge in image denoising is to preserve image details while removing noise. However, most of the approaches depend on smoothness assumption of natural images to produce results with smeared edges, hence, degrading the quality. To address this concern, we propose two constraints to better preserve the edges while denoising the image via the sparse representation framework. The first constraint attempts to preserve the edges at the coarser scales of the image as the level of noise drop dramatically at coarser scales. Different levels of scales are considered to account different strength of noise. The second constraint prevents transitional smoothing by preserving the edges of intermediate image estimates across iterations. Experimental results demonstrate the ability of the proposed approach in removing noise while preserving edges in comparison to the state-of-the art approaches.