Spatially dependent regularization parameter selection for total generalized variation-based image denoising
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Spatially dependent regularization parameter selection for total generalized variation-based image denoising Tian-Hui Ma1 · Ting-Zhu Huang1 · Xi-Le Zhao1
Received: 11 July 2015 / Revised: 31 March 2016 / Accepted: 6 April 2016 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016
Abstract We propose a novel image denoising model based on the total generalized variation (TGV) regularization. In the model, a spatially dependent regularization parameter is utilized to adaptively fit the local image features, resulting in further exploitation of the denoising potential of the TGV regularization. The proposed model is formulated under a joint optimization framework, by which the estimations of the restored image and the regularization parameter are achieved simultaneously. Furthermore, the model is general purpose that can handle various types of noise occurring in image processing. An alternating minimizationbased numerical scheme is especially developed, which leads to an efficient algorithmic solution to the nonconvex optimization problem. Numerical experiments are reported to illustrate the effectiveness of our model in terms of both peak signal-to-noise ratio and visual perception. Keywords Alternating minimization · Image denoising · Total generalized variation (TGV) · Spatially dependent regularization parameter selection Mathematics Subject Classification programming)
68U10 (Image processing) · 90C26 (Nonconvex
1 Introduction One of the most fundamental problems in image processing and computer vision is image denoising, which plays a significant role in a wide range of real-world applications, such as image segmentation, astronomical imaging, and object recognition. In image denoising, a
Communicated by Joerg Fliege.
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Tian-Hui Ma [email protected] School of Mathematical Sciences/Research Center for Image and Vision Computing, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
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noisy image f is modeled as f = N (u org ),
(1)
where u org denotes the underlying true image and N (·) represents the degradation process regarding the type of the noise. To obtain a reasonable estimate of u org from f (denoted by u), a popular and effective strategy is to use some regularization techniques, which tackles the original problem by solving an optimization model of the following form: min : F(u) + α R(u), u
(2)
where F(u) is the fidelity term for measuring the closeness of u to f , the function R(u) represents the regularization term which encourages u to exhibit some expected properties, and the parameter α is called the regularization parameter for the trade-off between the two terms. One central issue for the effectiveness of regularization techniques is the appropriate choice of the regularizer. Most regularizers characterize the solution based on some form of a priori assumption about the true image. The total variation regularization (Rudin et al. 1992) (termed as TV) assumes that the true image is piecewise constant, so tha
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