Hyperspectral Image Denoising via Combined Non-Local Self-Similarity and Local Low-Rank Regularization

Zeng, Haijin; Xie, Xiaozhen; Kong, Wenfeng; Cui, Shuang; Ning, Jifeng

doi:10.1109/access.2020.2979809

Cited by 23 publications

(14 citation statements)

References 42 publications

(94 reference statements)

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“…Similarly, the j -th singular value of the optimal solution of Equation ( 9 ) has the same attribute, and then the larger the value of

, the smaller the value that should be reduced. Therefore, an intuitive way to set the weight is that the weight should be inversely proportional to

[ 20 ]:

where n is the number of similar patches in

sets to

to avoid division by zero, and

. Because

is not available before estimating

, it can be initialized as:

…”

Section: Principle and Methods Of Wsnlecmentioning

confidence: 99%

“…Recently, the image prior method based on nonlocal self-similarity [ 13 , 14 ] and low rank matrix approximating [ 15 , 16 , 17 , 18 ] can better preserve image edge details while denoising, which has achieved some success in image denoising [ 19 , 20 ]. Low rank matrix approximation aims to recover the underlying low rank matrix from degraded observations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Weighted Schatten p-Norm Low Rank Error Constraint for Image Denoising

Cheng

2021

Entropy

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Traditional image denoising algorithms obtain prior information from noisy images that are directly based on low rank matrix restoration, which pays little attention to the nonlocal self-similarity errors between clear images and noisy images. This paper proposes a new image denoising algorithm based on low rank matrix restoration in order to solve this problem. The proposed algorithm introduces the non-local self-similarity error between the clear image and noisy image into the weighted Schatten p-norm minimization model using the non-local self-similarity of the image. In addition, the low rank error is constrained by using Schatten p-norm to obtain a better low rank matrix in order to improve the performance of the image denoising algorithm. The results demonstrate that, on the classic data set, when comparing with block matching 3D filtering (BM3D), weighted nuclear norm minimization (WNNM), weighted Schatten p-norm minimization (WSNM), and FFDNet, the proposed algorithm achieves a higher peak signal-to-noise ratio, better denoising effect, and visual effects with improved robustness and generalization.

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“…Similarly, the j -th singular value of the optimal solution of Equation ( 9 ) has the same attribute, and then the larger the value of

, the smaller the value that should be reduced. Therefore, an intuitive way to set the weight is that the weight should be inversely proportional to

[ 20 ]:

where n is the number of similar patches in

sets to

to avoid division by zero, and

. Because

is not available before estimating

, it can be initialized as:

…”

Section: Principle and Methods Of Wsnlecmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Weighted Schatten p-Norm Low Rank Error Constraint for Image Denoising

Cheng

2021

Entropy

View full text Add to dashboard Cite

show abstract

“…He et al [10] propose a noise-adjusted iterative denosiing model based on LRMA (NAILRMA). In addition, based on the plugand-play framework, Zeng et al [11] proposed the NLRPnP model, which can simultaneously represent the local low-rank structure and non-local self-similarity of HSI.…”

Section: Related Workmentioning

confidence: 99%

Low-rank Meets Sparseness: An Integrated Spatial-Spectral Total Variation Approach to Hyperspectral Denoising

Zeng¹,

Huang²,

Chen³

et al. 2022

Preprint

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Spatial-Spectral Total Variation (SSTV) can quantify local smoothness of image structures, so it is widely used in hyperspectral image (HSI) processing tasks. Essentially, SSTV assumes a sparse structure of gradient maps calculated along the spatial and spectral directions. In fact, these gradient tensors are not only sparse, but also (approximately) low-rank under FFT, which we have verified by numerical tests and theoretical analysis. Based on this fact, we propose a novel TV regularization to simultaneously characterize the sparsity and low-rank priors of the gradient map (LRSTV). The new regularization not only imposes sparsity on the gradient map itself, but also penalize the rank on the gradient map after Fourier transform along the spectral dimension. It naturally encodes the sparsity and lowrank priors of the gradient map, and thus is expected to reflect the inherent structure of the original image more faithfully. Further, we use LRSTV to replace conventional SSTV and embed it in the HSI processing model to improve its performance. Experimental results on multiple public data-sets with heavy mixed noise show that the proposed model can get 1.5dB improvement of PSNR.

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“…Tensors, as a generalization of vectors and matrices, arise in many data processing applications and have attracted great interests. For instance, video inpainting [1], magnetic resonance imaging (MRI) data recovery [2,3], 3D image reconstruction [4,5], high-order web link analysis [16], hyperspectral image (HSI) or multispectral image recovery [6,7], personalized web search [8], and seismic data reconstruction [9].…”

Section: Introductionmentioning

confidence: 99%

Enhanced nonconvex low-rank approximation of tensor multi-modes for tensor completion

Zeng¹,

Xie²,

Ning³

2020

Preprint

Self Cite

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Higher-order low-rank tensor arises in many data processing applications and has attracted great interests. Inspired by low-rank approximation theory, researchers have proposed a series of effective tensor completion methods. However, most of these methods directly consider the global low-rankness of underlying tensors, which is not sufficient for a low sampling rate; in addition, the single nuclear norm or its relaxation is usually adopted to approximate the rank function, which would lead to suboptimal solution deviated from the original one. To alleviate the above problems, in this paper, we propose a novel low-rank approximation of tensor multi-modes (LRATM), in which a double nonconvex Lγ norm is designed to represent the underlying joint-manifold drawn from the modal factorization factors of the underlying tensor. A block successive upper-bound minimization method-based algorithm is designed to efficiently solve the proposed model, and it can be demonstrated that our numerical scheme converges to the coordinatewise minimizers. Numerical results on three types of public multi-dimensional datasets have tested and shown that our algorithm can recover a variety of low-rank tensors with significantly fewer samples than the compared methods.

show abstract

Hyperspectral Image Denoising via Combined Non-Local Self-Similarity and Local Low-Rank Regularization

Cited by 23 publications

References 42 publications

Weighted Schatten p-Norm Low Rank Error Constraint for Image Denoising

Weighted Schatten p-Norm Low Rank Error Constraint for Image Denoising

Low-rank Meets Sparseness: An Integrated Spatial-Spectral Total Variation Approach to Hyperspectral Denoising

Enhanced nonconvex low-rank approximation of tensor multi-modes for tensor completion

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