Abstract
The multiplicative noise removal problem for a corrupted image has recently been considered under the framework of regularization based approaches, where the regularizations are typically de ned on sparse dictionaries and/or total va- riation (TV). This framework was demonstrated to be e ective. However, the sparse regularizers used so far are based overwhelmingly on the synthesis model, and the TV based regularizer may induce the stair-casing e ect in the recon- structed image. In this paper, we propose a new method using a sparse analysis model. Our formulation contains a data delity term derived from the distri- bution of the noise and two regularizers. One regularizer employs a learned analysis dictionary, and the other regularizer is an enhanced TV by introducing a parameter to control the smoothness constraint de ned on pixel-wise di er- ences. To address the resulting optimization problem, we adapt the alternating direction method of multipliers (ADMM) framework, and present a new method where a relaxation technique is developed to update the variables exibly with either image patches or the whole image, as required by the learned dictionary and the enhanced TV regularizers, respectively. Experimental results demon- strate the improved performance of the proposed method as compared with several recent baseline methods, especially for relatively high noise levels.