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A New Multiplicative Denoising Variational Model Based on <tex> $m$</tex>th Root Transformation
Sangwoon Yun,Hyenkyun Woo IEEE 2012 IEEE TRANSACTIONS ON IMAGE PROCESSING - Vol.21 No.5
<P>In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are contaminated by multiplicative noise. Due to the edge-preserving feature of the total variation (TV), variational models with TV regularization have attracted much interest in removing multiplicative noise. However, the fidelity term of the variational model, based on maximum a posteriori estimation, is not convex, and so, it is usually difficult to find a global solution. Hence, the logarithmic function is used to transform the nonconvex variational model to the convex one. In this paper, instead of using the log, we exploit the th root function to relax the nonconvexity of the variational model. An algorithm based on the augmented Lagrangian function, which has been applied to solve the log transformed convex variational model, can be applied to solve our proposed model. However, this algorithm requires solving a subproblem, which does not have a closed-form solution, at each iteration. Hence, we propose to adapt the linearized proximal alternating minimization algorithm, which does not require inner iterations for solving the subproblems. In addition, the proposed method is very simple and highly parallelizable; thus, it is efficient to remove multiplicative noise in huge SAR images. The proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation.</P>
Alternating Minimization Algorithm for Speckle Reduction With a Shifting Technique
Hyenkyun Woo,Sangwoon Yun IEEE 2012 IEEE TRANSACTIONS ON IMAGE PROCESSING - Vol.21 No.4
<P>Speckles (multiplicative noise) in synthetic aperture radar (SAR) make it difficult to interpret the observed image. Due to the edge-preserving feature of total variation (TV), variational models with TV regularization have attracted much interest in reducing speckles. Algorithms based on the augmented Lagrangian function have been proposed to efficiently solve speckle-reduction variational models with TV regularization. However, these algorithms require inner iterations or inverses involving the Laplacian operator at each iteration. In this paper, we adapt Tseng's alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the Laplacian operator. The proposed method is very simple and highly parallelizable; therefore, it is very efficient to despeckle huge-size SAR images. Numerical results show that our proposed method outperforms the state-of-the-art algorithms for speckle-reduction variational models with a TV regularizer in terms of central-processing-unit time.</P>
FAST NONLOCAL REGULARIZATION METHOD FOR IMAGE RESTORATION
Hyenkyun Woo,Sangwoon Yun 한국산업응용수학회 2010 한국산업응용수학회 학술대회 논문집 Vol.5 No.1
In this paper, we propose an alternating minimization algorithm to solve nonlocal total variation based minimization problems. Because nonlocal total variation are designed based on self-similarity of images, it is very useful for various image restoration problems. Recently, several efficient optimization methods are developed to solve the Nonlocal TV minimization problem[4,6]. These methods are efficient but slow to handle deblurring problem. In this paper, we show how to efficiently enhance blurred image with alternating minimization algorithm[7] and Bregman operator splitting method[6].