Convergent prediction–correction-based ADMM for multi-block separable convex programming

Chang, Xiaokai; Liu, Sanyang; Zhao, Pengjun; Xu, Li

doi:10.1016/j.cam.2017.11.033

Cited by 33 publications

(15 citation statements)

References 25 publications

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“…• Low-level imaging and analysis: image restoration and denoising [105], [149], [261], [280], [281], texture image denoising [166], hyperspectral image denoising [50], [100], [285], image completion and inpainting [39], [299], image composition for high-dynamic range imaging [21], image decomposition for intrinsic image computation [151], [313] and for structural image decomposition [43], image alignment and rectification [219], [231], [259], [293], [328], image stitching and mosaicking [163], image colorization [306], multi-focus image [277], [278], [325], [326], [327], pansharpening [322], change detection [51], face recognition [185], [289], [320], partial-duplicate image search [302], image saliency detection [147], [160], [161], [222], [228] and image analysis [343], [173]. • Medical imaging: RPCA has become a powerful tool to increase the performance of data acquisition [89], [90], [210],…”

Section: A Image Processingmentioning

confidence: 99%

On the Applications of Robust PCA in Image and Video Processing

et al. 2018

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Robust PCA (RPCA) via decomposition into lowrank plus sparse matrices offers a powerful framework for a large variety of applications such as image processing, video processing and 3D computer vision. Indeed, most of the time these applications require to detect sparse outliers from the observed imagery data that can be approximated by a lowrank matrix. Moreover, most of the time experiments show that RPCA with additional spatial and/or temporal constraints often outperforms the state-of-the-art algorithms in these applications. Thus, the aim of this paper is to survey the applications of RPCA in computer vision. In the first part of this paper, we review representative image processing applications as follows: (1) lowlevel imaging such as image recovery and denoising, image composition, image colorization, image alignment and rectification, multi-focus image and face recognition, (2) medical imaging like dynamic Magnetic Resonance Imaging (MRI) for acceleration of data acquisition, background suppression and learning of inter-frame motion fields, and (3) imaging for 3D computer vision with additional depth information like in Structure from Motion (SfM) and 3D motion recovery. In the second part, we present the applications of RPCA in video processing which utilize additional spatial and temporal information compared to image processing. Specifically, we investigate video denoising and restoration, hyperspectral video and background/foreground separation. Finally, we provide perspectives on possible future research directions and algorithmic frameworks that are suitable for these applications.

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Section: A Image Processingmentioning

confidence: 99%

On the Applications of Robust PCA in Image and Video Processing

et al. 2018

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“…similar to the method in [1], and by using the Valiron-Knopp-Bohr formula, then it yields σ F u � +∞, that is, F(s) is an entire function in the whole plane. We denote L β to be a class of all the functions F(s) of form (1) which are analytic in the half plane Rs < β(− ∞ < β < ∞), and the sequence λ n satisfies (3) and (5), and denote L ∞ to be the class of all the functions F(s) of form (1) which are analytic in the whole plane Rs < +∞, and the sequence λ n satisfies (3), (5), and (4). us, if − ∞ < β <+∞ and F(s) ∈ L ∞ , then F(s) ∈ L β .…”

Section: Introductionmentioning

confidence: 99%

The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

Tang

Chen

2020

Journal of Function Spaces

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In this article, we discuss the growth of entire functions represented by Laplace–Stieltjes transform converges on the whole complex plane and obtain some equivalence conditions about proximate growth of Laplace–Stieltjes transforms with finite order and infinite order. In addition, we also investigate the approximation of Laplace–Stieltjes transform with the proximate order and obtain some results containing the proximate growth order, the error, An∗, and λn, which are the extension and improvement of the previous theorems given by Luo and Kong and Singhal and Srivastava.

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“…Moreover, Yu [1] introduced the concepts of the order of G(s) and estimated the growth of the maximal molecule M u (σ, G), the maximal term μ(σ, G), the Borel line, and the order of entire functions represented by LaplaceStieltjes transform convergent in the whole complex plane. After his works, considerable attention has been paid to the growth and the value distribution of the functions represented by Lap-laceStieltjes transform convergent in the half plane or whole complex plane in the field of complex analysis (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

Cui

2020

Journal of Function Spaces

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One purpose of this paper is to study the growth of entire functions defined by Laplace-Stieltjes transform converges on the whole complex plane, by introducing the concept of p,q-proximate order, and one equivalence theorem of the p,q-proximate order of Laplace-Stieltjes transforms is obtained. Besides, the second purpose of this paper is to investigate the approximation of entire functions defined by Laplace-Stieltjes transforms with p,q-proximate order, and some results about the p,q-proximate order, the error, and the coefficients of Laplace-Stieltjes transforms are obtained, which are generalization and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.

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Convergent prediction–correction-based ADMM for multi-block separable convex programming

Cited by 33 publications

References 25 publications

On the Applications of Robust PCA in Image and Video Processing

On the Applications of Robust PCA in Image and Video Processing

The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

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