Mixed Noise Removal in Hyperspectral Image via Low-Fibered-Rank Regularization

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

doi:10.1109/tgrs.2019.2940534

Cited by 189 publications

(107 citation statements)

References 65 publications

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“…We perform the simulated and real experiments to illustrate the efficiency and performance of our NLBTD method to restore HSI in this section. There are six methods are used to compare the performance of remove noise, consist of the lowrank matrix factorization with TV [22] (denoted as LRTV), a method combining with HyRes and sparse noise removal technique [54] (denoted as HyMiNoR), three-directional tensor nuclear norm method [23] (denoted as 3DTNN), a subspacebased method [52] (denoted as L1HyMixDe), low-rank tucker decomposition with spatial-spectral TV [55] (denoted as LRT-DTV), and block terms decomposition with spatial-spectral TV [41] (denoted as LRTFL0). According to the author's suggestions, we tune the parameters of these state-of-the-art methods to achieve optimal performance.…”

Section: Methodsmentioning

confidence: 99%

“…Furthermore, He et al [22] integrated a unified framework to simultaneously consider the spectral and spatial low-rankness, where the nuclear norm to explore the low-rank property and the total variation (TV) regularization to capture smooth information of HSI. However, the 3-D HSI will be reshaped into 2-D if using the matrix-based approaches, which destroys the spatial correlation [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Zeng

Huang

Chen

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Since the facility restrictions and weather conditions, hyperspectral image (HSI) is generally seriously polluted by a variety of noises. Recently, the method based on block term decomposition with rank-(L, L, 1) (BTD) has attracted wide attention in HSI mixed noise removal. BTD factorizes thirdorder HSI data into the sum of a series of component tensors, where each of the component tensors is represented by the outer product of a rank-L matrix ArB T r and a column vector cr. BTD has clear physical interpretation because its latent factors ArB T r and cr can be interpreted abundance map and spectral signature respectively. The essential uniqueness of BTD is under the lowrank assumption of ArB T r . However, the low-rank assumption is not always held in real scenarios. The BTD-based method usually sets L to full rank to achieve satisfactory results. In this paper, we suggest a novel model based on nonlocal block term decomposition (NLBTD) for HSI mixed noise removal. More specifically, for each grouped similar image block, BTD is introduced to capture nonlocal self-similarity and global spectral lowrankness, the unidirectional total variation (TV) is introduced to preserve local spectral smoothness. By faithfully exploring nonlocal self-similarity, global spectral low-rankness, and local spectral smoothness, the proposed method is expected to produce promising results with guarantee the essential uniqueness of BTD. To tackle the resulting model, we design an efficient algorithm based on the proximal alternating minimization with the theoretical guarantees. Extensive numerical experiments in HSI mixed noise removal demonstrate that the proposed NLBTD method achieves satisfactory performance compared with stateof-the-art methods.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Zeng

Huang

Chen

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since there exists correlations in the practical datasets such as images and user ratings, the resulting tensor data is often low-rank. The low-rank property has been exploited in problems like low-rank tensor completion [25,26,27,28,29,30] and low-rank tensor recovery [31,32,33,34,35]. Leveraging the low-rank property, a convex relaxation of the Tucker rank can be applied to robust tensor recovery [31,32] and tensor completion [25,26].…”

Section: Introductionmentioning

confidence: 99%

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Ren

Wang

Xiong

2020

Preprint

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Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

show abstract

“…Since there exist correlations in the practical datasets such as images and user ratings, the resulting tensor data is often low-rank. The low-rank property has been exploited in problems like low-rank tensor completion [25][26][27][28][29][30] and low-rank tensor recovery [31][32][33][34][35]. Leveraging the low-rank property, a convex relaxation of the Tucker rank can be applied to robust tensor recovery [31,32] and tensor completion [25,26].…”

Section: Introductionmentioning

confidence: 99%

“…To solve the unbalanced matricization scheme in the Tucker rank, tensor train rank is proposed to solve the tensor recovery and completion problem [29,33]. Some works also leverage another rank form called tubal multi-rank and its convex surrogate tensor nuclear norm as tools for tensor-related tasks [34,35]. This paper concerns only the recovery under the CP rank.…”

Section: Introductionmentioning

confidence: 99%

Tensor recovery from noisy and multi-level quantized measurements

Ren

Wang

Xiong

2020

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD-based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

show abstract

Mixed Noise Removal in Hyperspectral Image via Low-Fibered-Rank Regularization

Cited by 189 publications

References 65 publications

Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Tensor Recovery from Noisy and Multi-Level Quantized Measurements

Tensor recovery from noisy and multi-level quantized measurements

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