A nonlocal low rank model for poisson noise removal

Zhao, Mingchao; Wen, Yi; Ng, Michael K.; Li, Hongwei

doi:10.3934/ipi.2021003

Cited by 10 publications

(2 citation statements)

References 49 publications

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“…For image restoration with Poisson observations, Le et al [26] proposed a variational model combined the TV for the underlying image and the KL divergence for the data-fitting term to denoise an image, where the TV can preserve good details of images and the KL divergence is suitable for Poisson noise by the maximum likelihood estimation. Zhao et al [56] proposed a nonlocal low-rank model for Poisson noise removal, while it only utilized the low-rankness of the underlying images. Besides, some fast first-order algorithms were proposed and studied to solve this kind of models efficiently, see [15,43,49,55] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Matrix Completion with Poisson Observations via Nuclear Norm and Total Variation Constraints

Qiu,

null,

Zhang

2024

JCM

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In this paper, we study the low-rank matrix completion problem with Poisson observations, where only partial entries are available and the observations are in the presence of Poisson noise. We propose a novel model composed of the Kullback-Leibler (KL) divergence by using the maximum likelihood estimation of Poisson noise, and total variation (TV) and nuclear norm constraints. Here the nuclear norm and TV constraints are utilized to explore the approximate low-rankness and piecewise smoothness of the underlying matrix, respectively. The advantage of these two constraints in the proposed model is that the low-rankness and piecewise smoothness of the underlying matrix can be exploited simultaneously, and they can be regularized for many real-world image data. An upper error bound of the estimator of the proposed model is established with high probability, which is not larger than that of only TV or nuclear norm constraint. To the best of our knowledge, this is the first work to utilize both low-rank and TV constraints with theoretical error bounds for matrix completion under Poisson observations. Extensive numerical examples on both synthetic data and real-world images are reported to corroborate the superiority of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Low-Rank Matrix Completion with Poisson Observations via Nuclear Norm and Total Variation Constraints

Qiu,

null,

Zhang

2024

JCM

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“…where B is the incomplete tensor, X is the underlying tensor, and P(•) is a linear projector. The choice of P relies on the specific application [39,64,67].…”

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confidence: 99%

A novel $ \ell_{0} $ minimization framework of tensor tubal rank and its multi-dimensional image completion application

Xiao,

Huang,

Deng

et al. 2024

IPI

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Recently, minimizing the tensor tubal rank based on the tensor singular value decomposition (t-SVD) has attracted significant attention in the tensor completion task. The widely-used solutions of tensor-tubal-rank minimization rely upon various convex and nonconvex surrogates of the tensor rank. However, these tensor rank surrogates usually lead to inaccurate descriptions of the tensor rank. To mitigate the limitation, we propose an innovative 0 minimization framework with guaranteed convergence to provide a novel paradigm for minimization of the tensor rank. To demonstrate the effectiveness of our framework, we develop a new tensor completion model employing a tensor adaptive sparsity-deduced rank (TASR). Subsequently, we formulate an algorithm rooted in the proposed 0 minimization framework to address this model effectively. Experimental results on multi-dimensional image data demonstrate that our method is superior to several state-of-the-art approaches. The code is accessible at https://github.com/Jin-liangXiao/L0-TC.

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