Weighted tensor nuclear norm minimization for color image denoising

Hosono, Kaito; Ono, Shunsuke; Miyata, Takamichi

doi:10.1109/icip.2016.7532926

Cited by 27 publications

(22 citation statements)

References 16 publications

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“…The nonlocal tensor based methods have been used in image processing community [56,57]. Nonlocal similarity suggests that one patch may have many patches with similar structure within the same image.…”

Section: B Nonlocal Coupled Tensor Cp Decomposition Model For Hsi-msmentioning

confidence: 99%

Nonlocal Coupled Tensor CP Decomposition for Hyperspectral and Multispectral Image Fusion

Yang

Chanussot

et al. 2020

IEEE Trans. Geosci. Remote Sensing

124

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Hyperspectral super-resolution, which aims at enhancing the spatial resolution of hyperspectral images (HSIs), has recently attracted considerable attention. A common way of hyperspectral super-resolution is to fuse the HSI with a higher spatial resolution multispectral image (MSI). Various approaches have been proposed to solve this problem by establishing the degradation model of low spatial resolution HSIs and MSIs based on matrix factorization methods, e.g., unmixing and sparse representation. However, this category of approaches cannot well construct the relationship between the high spatial resolution HSI and MSI. In fact, since the HSI and the MSI capture the same scene, these two image sources must have common factors. In this paper, we propose a nonlocal tensor decomposition model for HSI-MSI fusion. Firstly, the nonlocal similar patch tensors of the HSI are constructed according to the MSI, for the purpose of calculating the smooth order of all the patches for clustering. Then, the relationship between the high spatial resolution HSI and the MSI is explored through a coupled tensor canonical polyadic (CP) decomposition. The fundamental idea of the proposed model is that the factor matrices in CP decomposition of the high spatial resolution HSI's nonlocal tensor can be shared with the matrices factorized by the MSI's nonlocal tensor. Alternating direction method of multipliers is used to solve the proposed model. Through this method, the spatial structure of the MSI can be successfully transferred to the HSI. Experimental results on three synthetic datasets and one real dataset suggest that the proposed method substantially outperforms existing state-of-the-art HSI-MSI fusion methods. Index Terms-e Hyperspectral images, multispectral images, data fusion, nonlocal tensor, coupled CP decomposition.

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Section: B Nonlocal Coupled Tensor Cp Decomposition Model For Hsi-msmentioning

confidence: 99%

Nonlocal Coupled Tensor CP Decomposition for Hyperspectral and Multispectral Image Fusion

Yang

Chanussot

et al. 2020

IEEE Trans. Geosci. Remote Sensing

124

View full text Add to dashboard Cite

show abstract

“…There have been a number of works in this field during the past few decades. And plenty of denoising methods arose due to various regularization models exploited in [1], [3], [4], [7], [11], [12], [14], [15], [17], [18], [29]- [35]. The classic total variation (TV) models in [3] and [29] utilizing local structure patterns were effective in recovering smooth regions while tending to smear out image details.…”

Section: Introductionmentioning

confidence: 99%

“…However, the transformed color images inevitably suffer from the information loss without fully considering cross-channel correlation. The third one was to jointly denoise the RGB channels by fully considering the cross-channel dependency [18], [19], [31]- [33]. References [31]- [33] concatenated the patches from RGB channels as a vector and utilized the weighted nuclear norm minimization (WNNM), dictionary learning and weighted sparse coding schemes respectively for real-world image denoising.…”

Section: Introductionmentioning

confidence: 99%

“…Directly unfolding or flattening a tensor would lead to information loss by destroying the multi-way structure of the data. Hosono et al proposed WTNNM for color image processing [18], [19]. The differences between WTNNM in [18], [19] and the proposed t-product based WTNNM lie in two aspects: the calculation of the tensor nuclear norm (TNN) and the assumption of noise for different color channels.…”

Section: Introductionmentioning

confidence: 99%

“…Hosono et al proposed WTNNM for color image processing [18], [19]. The differences between WTNNM in [18], [19] and the proposed t-product based WTNNM lie in two aspects: the calculation of the tensor nuclear norm (TNN) and the assumption of noise for different color channels. In [18] and [19], the TNN was calculated via tensor's matricization in [22] while the TNN in this paper is a new definition rigorously deduced from t-product [26].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Real Color Image Denoising Using t-Product- Based Weighted Tensor Nuclear Norm Minimization

2019

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Color images can be seen as third-order tensors with column, row and color modes. Considering two inherent characteristics of a color image including the non-local self-similarity (NSS) and the cross-channel correlation, we extract non-local similar patch groups from a color image and treat these groups as tensors with each color channel corresponding to the frontal slice of the tensor to exploit the information within and cross channel correlation. Inspired by recently proposed tensor-tensor product (t-product), t-SVD, tensor tubal rank and rigorously deduced tensor nuclear norm, a novel t-product based weighted tensor nuclear norm minimization (WTNNM) is proposed to model the extracted non-local similar patch group tensor (NPGT). Considering the NPGT is of low tubal rank, we formulate real color image denoising as a low tubal rank tensor recovery problem and solve it with the weighted tensor nuclear norm minimization. Experiments on both simulated and realistic noisy images verify the effectiveness of our method. INDEX TERMS Color image denoisinig, non-local self-similarity, cross-channel correlation, tensor tubal rank, t-SVD, tensor nuclear norm.

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The Fréchet derivative of the tensor t-function

Lund

Schweitzer

2023

Calcolo

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The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in Lund (Numer Linear Algebra Appl 27(3):e2288). In this work, we investigate properties of the Fréchet derivative of the tensor t-function and derive algorithms for its efficient numerical computation. Applications in condition number estimation and nuclear norm minimization are explored. Numerical experiments implemented by the toolbox hosted at https://gitlab.com/katlund/t-frechet illustrate properties of the t-function Fréchet derivative, as well as the efficiency and accuracy of the proposed algorithms.

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Weighted tensor nuclear norm minimization for color image denoising

Cited by 27 publications

References 16 publications

Nonlocal Coupled Tensor CP Decomposition for Hyperspectral and Multispectral Image Fusion

Nonlocal Coupled Tensor CP Decomposition for Hyperspectral and Multispectral Image Fusion

Real Color Image Denoising Using t-Product- Based Weighted Tensor Nuclear Norm Minimization

The Fréchet derivative of the tensor t-function

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