Low-rank tensor completion via smooth matrix factorization

Zheng, Yu‐Bang; Huang, Ting‐Zhu; Ji, Teng-Yu; Jiang, Tai-Xiang; Ma, Tianhui

doi:10.1016/j.apm.2019.02.001

Cited by 63 publications

(30 citation statements)

References 40 publications

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“…Bouali and Ladjal [20] used the unidirectional total variation (UTV) to exploit the direction features of stripes in Moderate-Resolution Imaging Spectroradiometer (MODIS) images. Subsequently, UTV [26,27] and its variants have been widely used for destriping [21,23,[28][29][30][31]. For example, Dou et al [28] proposed a non-convex destriping model by employing the 0 -norm variant of UTV and the global sparsity regularization, which is depicted by the 1 -norm to constrain the stripe noise.…”

Section: Existing Methodsmentioning

confidence: 99%

Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

Sun

Huang

et al. 2019

Remote Sensing

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Remote sensing images have been applied to a wide range of fields, but they are often degraded by various types of stripes, which affect the image visual quality and limit the subsequent processing tasks. Most existing destriping methods fail to exploit the stripe properties adequately, leading to suboptimal performance. Based on a full consideration of the stripe properties, we propose a new destriping model to achieve stripe detection and stripe removal simultaneously. In this model, we adopt the unidirectional total variation regularization to depict the directional property of stripes and the weighted ℓ 2 , 1 -norm regularization to depict the joint sparsity of stripes. Then, we combine the alternating direction method of multipliers and iterative support detection to solve the proposed model effectively. Comparison results on simulated and real data suggest that the proposed method can remove and detect stripes effectively while preserving image edges and details.

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Section: Existing Methodsmentioning

confidence: 99%

Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

Sun

Huang

et al. 2019

Remote Sensing

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“…Fig. 12 shows the relative change (RelCha) [53] in each iteration loop of the Washington DC Mall dataset under σ = 0.025 and the San Diego dataset under σ = 0.075. Here, the RelCha is defined as…”

Section: ) Comparison With Other Methodsmentioning

confidence: 99%

Local Low-Rank and Sparse Representation for Hyperspectral Image Denoising

Huang

et al. 2019

IEEE Access

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Hyperspectral image (HSI) denoising is a fundamental task in a plethora of HSI applications. Global low-rank property is widely adopted to exploit the spectral-spatial information of HSIs, providing satisfactory denoising results. In this paper, instead of adopting the global low-rank property, we propose to adopt a local low rankness for HSI denoising. We develop an HSI denoising method via local low-rank and sparse representation, under an alternative minimization framework. In addition, the weighted nuclear norm is used to enhance the sparsity on singular values. The experiments on widely used hyperspectral datasets demonstrate that the proposed method outperforms several state-of-the-art methods visually and quantitatively. INDEX TERMS Hyperspectral image denoising, local low rankness, sparse representation, weighted nuclear norm.

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“…M ATRIX and tensor completion have received much attention in recent years, which have many applications, such as in hyperspectral data recovery [1], image/video inpainting [2], [3], [4], [5], [6], [7], image classification [8], [9] and high dynamic range (HDR) imaging [10], [11], [12]. In general, such matrix and tensor data have low rank structures.…”

Section: Introductionmentioning

confidence: 99%

Tensor factorization based method for low rank matrix completion and its application on tensor completion

Yu¹,

Zhang²

2022

Preprint

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Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency. To this end, we first establish the relationship between matrix rank and tensor tubal rank, and then reformulate matrix completion problem as a tensor completion problem. For the reformulated tensor completion problem, we adopt a two-stage strategy based on tensor factorization algorithm. In this way, a matrix completion problem of big size can be solved via some matrix computations of smaller sizes. For a third order tensor completion problem, to fully exploit the low rank structures, we introduce the double tubal rank which combines the tubal rank and the rank of the mode-3 unfolding matrix. For the mode-3 unfolding matrix rank, we follow the idea of matrix completion. Based on this, we establish a novel model and modify the tensor factorization based algorithm for third order tensor completion. Extensive numerical experiments demonstrate that the proposed methods outperform state-of-the-art methods in terms of both accuracy and running time.

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Low-rank tensor completion via smooth matrix factorization

Cited by 63 publications

References 40 publications

Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

Local Low-Rank and Sparse Representation for Hyperspectral Image Denoising

Tensor factorization based method for low rank matrix completion and its application on tensor completion

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