Multiplicative noise removal with a sparsity-aware optimization model
Jian Lu Lixin Shen Chen Xu Yuesheng Xu
Inverse Problems & Imaging 2017, 11(6): 949-974 doi: 10.3934/ipi.2017044

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.

keywords: Multiplicative noise proximity operator nonconvex variational model image restoration
Translating solutions to mean curvature flow with a forcing term in Minkowski space
Hongjie Ju Jian Lu Huaiyu Jian
Communications on Pure & Applied Analysis 2010, 9(4): 963-973 doi: 10.3934/cpaa.2010.9.963
We study the existence, uniqueness and asymptotic behavior of rotationally symmetric translating solutions to mean curvature flow with a forcing term in Minkowski space. As a result, a part of conjectures in [1] is proved.
keywords: elliptic equation asymptotic behavior. symmetric solution Spacelike hypersurface

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