Image Denoising Based On Sparse Representation

Multiplicative noise arises in many image applications, such as ultrasound(US) images and synthetic aperture radar(SAR) images. It is signal dependent. Therefore, multiplicative noise removal becomes a very challenging problem. However, traditional methods for multiplicative noise removal often cannot keep structural details well.Focusing on the above problem, the variation model and sparse representation are applied to multiplicative noise removal in this paper. Sparse representation can learn an adaptive dictionary from the degraded image, which can capture the distinctive characteristic of the original image. The main works include the following aspects:(1) A nonlocal total variation(TV) model based on nonlocal TV norm for Rayleigh multiplicative noise removal was proposed. By introducing an auxiliary variable, this paper constructed an approximation functional, and designed a fast Split-Bregman algorithm with high computational efficiency. Experiments show that the proposed model has a superior performance than traditional ones in terms of Peak Signal-to-Noise Ratio(PSNR) ? Structural Similarity(SSIM) and subjective visual quality, and enhances capability of preserving features, such as textures and edges.(2) An image restoration model that combines the advantages of sparse representation over dictionary learning and TV regularization method was proposed to solve the multiplicative noise removal problem. An adaptive dictionary is learned from the degraded image by K-SVD algorithm, which contributes to recover textures and preserve more geometrical structures. TV regularization term is efficient to keep sharp edges and reduce the artifacts caused by dictionary learning. To effectively solve this complex model functional, we introduced two auxiliary variables to construct an approximation functional, and designed Split-Bregman algorithm to minimize the energy functional. Bregman variables make the algorithm stable and regularization parameters do not need to be updated in Bregman iteration process. This method achieves higher PSNRs?MSSIMs, and lower MAEs(Mean Absolute-deviation Errors), preserving more meaningful structural details, such as textures, and showing a better visual effect.(3) A sparse representation model over dictionary learning was presented for speckle reduction in US images. This model contained three terms: a sparse representation prior, a TV regularization term, and a data-fidelity term capturing the statistics of Rayleigh noise. To solve the optimization problem, the functional was decomposed into several subproblems by the Split-Bregman algorithm. Experimental results on real US images validate that the proposed method is not only able to remove noise effectively, but also able to preserve reliably edges and structural details of tissues, and to delineate accurately the regions of interest.