Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees

Mei, Jin; Dong, Yiqiu; Huang, Ting; Yin, Wotao

doi:10.1007/s10915-017-0460-5

Cited by 70 publications

(51 citation statements)

References 47 publications

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“…The symmetric alternating direction method with multipliers (symmetric ADMM) is an acceleration method of ADMM, which can be used to solve the constraint optimization formulation in image processing [34][35][36][37][38][39][40][41][42][43].…”

Section: Symmetric Admmmentioning

confidence: 99%

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Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

et al. 2018

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Hyperspectral unmixing, aiming to estimate the fractional abundances of pure spectral signatures in each mixed pixel, has attracted considerable attention in analyzing hyperspectral images. Plenty of sparse unmixing methods have been proposed in the literature that achieved promising performance. However, many of these methods overlook the latent geometrical structure of the hyperspectral data which limit their performance to some extent. To address this issue, a double reweighted sparse and graph regularized unmixing method is proposed in this paper. Specifically, a graph regularizer is employed to capture the correlation information between abundance vectors, which makes use of the property that similar pixels in a spectral neighborhood have higher probability to share similar abundances. In this way, the latent geometrical structure of the hyperspectral data can be transferred to the abundance space. In addition, a double weighted sparse regularizer is used to enhance the sparsity of endmembers and the fractional abundance maps, where one weight is introduced to promote the sparsity of endmembers as a hyperspectral image typically contains fewer endmembers compared to the overcomplete spectral library and the other weight is exploited to improve the sparsity of the abundance matrix. The weights of the double weighted sparse regularizer used for the next iteration are adaptively computed from the current abundance matrix. The experimental results on synthetic and real hyperspectral data demonstrate the superiority of our method compared with some state-of-the-art approaches.

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Section: Symmetric Admmmentioning

confidence: 99%

“…Many optimization methods can be applied to solve the proposed formulation (P2), such as the split Bregman method, alternating direction method with multipliers [35][36][37][38][39][40]42,43,49,50]. Here, we employ symmetric ADMM to solve (P2) due to its simplicity and efficiency [34].…”

Section: Optimization Algorithmmentioning

confidence: 99%

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

et al. 2018

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“…Ill-posed inverse problems arise in many important applications, including astronomy, medical tomography, geophysics, sound source detection, and image deblurring (refer, e.g., to [1][2][3][4][5][6] and references therein). In this paper, we consider linear discrete ill-posed problems of the form…”

Section: Introductionmentioning

confidence: 99%

Vector Extrapolation Based Landweber Method for Discrete Ill-Posed Problems

Zhao

Huang

et al. 2017

Mathematical Problems in Engineering

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Landweber method is one of the classical iterative methods for solving linear discrete ill-posed problems. However, Landweber method generally converges very slowly. In this paper, we present the vector extrapolation based Landweber method, which exhibits fast and stable convergence behavior. Moreover, a restarted version of the vector extrapolation based Landweber method is proposed for practical considerations. Numerical results are given to illustrate the benefits of the vector extrapolation based Landweber method.

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“…In their model the piecewise constant assumption of the reflection component is not considered. Total Variation (TV) had been widely used in image processing [19][20][21][22][23]. Ma and Osher [24] applied TV and nonlocal TV regularization to Retinex theory.…”

Section: Introductionmentioning

confidence: 99%

A Convex Optimization Model and Algorithm for Retinex

Zhao

Huang

Zhao

et al. 2017

Mathematical Problems in Engineering

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Retinex is a theory on simulating and explaining how human visual system perceives colors under different illumination conditions. The main contribution of this paper is to put forward a new convex optimization model for Retinex. Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain. The resulting objective function involves three terms including the Tikhonov regularization of the illumination component, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers (ADMM) to solve the convex optimization model. Numerical experiments demonstrate the advantages of the proposed model which can decompose an image into the illumination and the reflection components.

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Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees

Cited by 70 publications

References 47 publications

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

Vector Extrapolation Based Landweber Method for Discrete Ill-Posed Problems

A Convex Optimization Model and Algorithm for Retinex

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