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A fast minimization method for blur and multiplicative noise removal. (English) Zbl 1278.94013
Summary: Multiplicative noise and blur removal problems have attracted much attention in recent years. In this paper, we propose an efficient minimization method to recover images from input blurred and multiplicative noisy images. In the proposed algorithm, we make use of the logarithm to transform blurring and multiplicative noise problems into additive image degradation problems, and then employ \(l_{1}\)-norm to measure in the data-fitting term and the total variation to measure the regularization term. The alternating direction method of multipliers (ADMM) is used to solve the corresponding minimization problem. In order to guarantee the convergence of the ADMM algorithm, we approximate the associated nonconvex domain of the minimization problem by a convex domain. Experimental results are given to demonstrate that the proposed algorithm performs better than the other existing methods in terms of speed and peak signal noise ratio.

MSC:
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65F22 Ill-posedness and regularization problems in numerical linear algebra
65K10 Numerical optimization and variational techniques
65J22 Numerical solution to inverse problems in abstract spaces
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
68U10 Computing methodologies for image processing
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