A hybrid regularizers model for multiplicative noise removal

In this paper, we propose a variational method for restoring images corrupted by multiplicative noise. Computationally, we employ the alternating minimization method to solve our minimization problem. We also study the existence and uniqueness of the proposed problem. Finally, experimental results are provided to demonstrate the superiority of our proposed hybrid model and algorithm for image denoising in comparison with state-of-the-art methods.

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A Fast High-Order Total Variation Minimization Method for Multiplicative Noise Removal

Mathematical Problems in Engineering ◽

10.1155/2013/834035 ◽

2013 ◽

Vol 2013 ◽

pp. 1-13 ◽

Cited By ~ 6

Author(s):

Xiao-Guang Lv ◽

Jiang Le ◽

Jin Huang ◽

Liu Jun

Keyword(s):

Total Variation ◽

Multiplicative Noise ◽

Noise Removal ◽

High Order ◽

Alternating Minimization ◽

Minimization Method ◽

Total Variation Minimization ◽

Alternating Minimization Algorithm ◽

Staircase Effect ◽

Multiplicative Noise Removal

Multiplicative noise removal problem has received considerable attention in recent years. The total variation regularization method for the solution of the noise removal problem can preserve edges well but has the sometimes undesirable staircase effect. In this paper, we propose a fast high-order total variation minimization method to restore multiplicative noisy images. The proposed method is able to preserve edges and at the same time avoid the staircase effect in the smooth regions. An alternating minimization algorithm is employed to solve the proposed high-order total variation minimization problem. We discuss the convergence of the alternating minimization algorithm. Some numerical results show that the proposed method gives restored images of higher quality than some existing multiplicative noise removal methods.

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A Multi-Exposure Variational Method for Retinex

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.310816.161216a ◽

2017 ◽

Vol 7 (1) ◽

pp. 156-171

Author(s):

Xue Yang ◽

Yu-Mei Huang

Keyword(s):

Variational Method ◽

Existence And Uniqueness ◽

Variational Model ◽

Alternating Minimization ◽

Single Image ◽

Minimization Method ◽

Proposed Model ◽

Retinex Theory ◽

The Given ◽

Alternating Minimization Method

AbstractRetinex theory explains how the human visual system perceives colors. The goal of retinex is to decompose the reflectance and the illumination from the given images and thereby compensating for non-uniform lighting. The existing methods for retinex usually use a single image with a fixed exposure to restore the reflectance of the image. In this paper, we propose a variational model for retinex problem by utilizing multi-exposure images of a given scene. The existence and uniqueness of the solutions of the proposed model have been elaborated. An alternating minimization method is constructed to solve the proposed model and its convergence is also demonstrated. The experimental results show that the proposed method is effective for reflectance recovery in retinex problem.

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