A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration

Yang, Junfeng; Yin, Wotao; Zhang, Yin; Wang, Yilun

doi:10.1137/080730421

Cited by 474 publications

(224 citation statements)

References 37 publications

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“…For years, these restoration models are usually solved by gradient descent method, which is quite slow due to the non-smoothness of the objective functionals. Recently, various convex optimization techniques have been proposed to efficiently solve these models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], some of which are closely related to iterative shrinkage-thresholding algorithms [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Wu¹,

Zhang

Duan

et al. 2011

J Sci Comput

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Recently total variation (TV) regularization has been proven very successful in image restoration and segmentation. In image restoration, TV based models offer a good edge preservation property. In image segmentation, TV (or vectorial TV) helps to obtain convex formulations of the problems and thus provides global minimizations. Due to these advantages, TV based models have been extended to image restoration and data segmentation on manifolds. However, TV based restoration and segmentation models are difficult to solve, due to the nonlinearity and non-differentiability of the TV term. Inspired by the success of operator splitting and the augmented Lagrangian method (ALM) in 2D planar image processing, we extend the method to TV and vectorial TV based image restoration and segmentation on triangulated surfaces, which are widely used in computer graphics and computer vision. In particular, we will focus on the following problems. First, several Hilbert spaces will be given to describe TV and vectorial TV based variational models in the discrete setting. Second, we present ALM applied to TV and vectorial TV image restoration on mesh surfaces, leading to efficient algorithms for both gray and color image restoration. Third, we discuss ALM for vectorial TV based multi-region image segmentation, which also works for both gray and color images. The proposed method benefits from fast solvers for

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Section: Introductionmentioning

confidence: 99%

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Wu¹,

Zhang

Duan

et al. 2011

J Sci Comput

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show abstract

“…This result can be found as Lemma 3.3 in [29]. When g is a characteristic function χ C (x) of a convex set C:…”

Section: Solving the Subproblem In Apgmentioning

confidence: 94%

“…Moreover, the problem reformulation is more suitable for improving the efficiency of GAPG, and we can also avoid solving the image denoising subproblem. Finally the GAPG framework is combined with the continuation technique [22] [24][27] [29][30] to solve the resulting optimization problem. Our method works for both anisotropic and isotropic discrete TV-based image restoration.…”

mentioning

confidence: 99%

A Generalized Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration

Zuo

Lin

2011

IEEE Trans. on Image Process.

106

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Abstract-This paper proposes a generalized accelerated proximal gradient (GAPG) approach for solving total variation (TV) based image restoration problems. The GAPG algorithm generalizes the original APG algorithm by replacing the Lipschitz constant with an appropriate positive definite matrix, resulting in faster convergence. For TV-based image restoration problems, we further introduce two auxiliary variables that approximate the partial derivatives. Constraints on the variables can be easily imposed without modifying the algorithm much, and the TV regularization can be either isotropic or anisotropic. Compared with the recently developed APG-based methods for TV-based image restoration, i.e., monotone version of the twostep iterative shrinkage/thresholding algorithm (MTwIST) and monotone version of the fast iterative shrinkage/thresholding algorithm (MFISTA), our GAPG is much simpler as it does not require to solve an image denoising subproblem. Moreover, the convergence rate of O(k −2 ) is maintained by our GAPG, where k is the number of iterations; the cost of each iteration in GAPG is also lower. As a result, in our experiments our GAPG approach can be much faster than MTwIST and MFISTA. The experiments also verify that our GAPG converges faster than the original APG and MTwIST when they solve identical problems.

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“…This advantage of total variation regularization was first discovered in [6] for image denoising and deblurring, and has been generalized to multichannel problems in [7], the TV-L1 model in [8], TV-based compressed sensing in [9,10], and an edge-guided compressive sensing reconstruction approach for recovering images of higher qualities from fewer measurements in [11].…”

Section: Introductionmentioning

confidence: 99%

Enhanced Resolution of Microwave Sounder Imagery through Fusion with Infrared Sensor Data

et al. 2017

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Abstract:The images acquired by microwave sensors are blurry and have low resolution. On the other hand, the images obtained using infrared/visible sensors are often of higher resolution. In this paper, we develop a data fusion methodology and apply it to enhance the resolution of a microwave image using the data from a collocated infrared/visible sensor. Such an approach takes advantage of the spatial resolution of the infrared instrument and the sensing accuracy of the microwave instrument. The model leverages sparsity in signals and is based on current research in sparse optimization and compressed sensing. We tested our method using a precipitation scene captured with the Advanced Microwave Sounding Unit (AMSU-B) microwave instrument and the Advanced Very High Resolution Radiometer (AVHRR) infrared instrument and compared the results to simultaneous radar observations. We show that the data fusion product is better than the original AMSU-B and AVHRR observations across all statistical indicators.

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A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration

Cited by 474 publications

References 37 publications

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces

A Generalized Accelerated Proximal Gradient Approach for Total-Variation-Based Image Restoration

Enhanced Resolution of Microwave Sounder Imagery through Fusion with Infrared Sensor Data

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