Inverse Problems and Imaging
Restoration of images contaminated by multiplicative noise (also known as speckle noise) is a key issue in coherent image processing. Notice that images under consideration are often highly compressible in certain suitably chosen transform domains. By exploring this intrinsic feature embedded in images, this paper introduces a variational restoration model for multiplicative noise reduction that consists of a term reflecting the observed image and multiplicative noise, a quadratic term measuring the closeness of the underlying image in a transform domain to a sparse vector, and a sparse regularizer for removing multiplicative noise. Being different from popular existing models which focus on pursuing convexity, the proposed sparsity-aware model may be nonconvex depending on the conditions of the parameters of the model for achieving the optimal denoising performance. An algorithm for finding a critical point of the objective function of the model is developed based on coupled fixed-point equations expressed in terms of the proximity operator of functions that appear in the objective function. Convergence analysis of the algorithm is provided. Experimental results are shown to demonstrate that the proposed iterative algorithm is sensitive to some initializations for obtaining the best restoration results. We observe that the proposed method with SAR-BM3D filtering images as initial estimates can remarkably outperform several state of-art methods in terms of the quality of the restored images.
Original Publication Citation
Lu, J., Shen, L. X., Xu, C., & Xu, Y. S. (2017). Multiplicative noise removal with a sparsity-aware optimization model. Inverse Problems and Imaging, 11(6), 949-974. doi:10.3934/ipi.2017044
Lu, Jian; Shen, Lixin; Xu, Chen; and Xu, Yuesheng, "Multiplicative Noise Removal with a Sparsity-Aware Optimization Model" (2017). Mathematics & Statistics Faculty Publications. 44.