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3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

Nuobei Xie, Yunmei Chen, Huafeng Liu
2019 Sensors  
In this paper, we develop a novel tensor based nonlocal low-rank framework for dynamic PET reconstruction.  ...  Spatial structures are effectively enhanced not only by nonlocal and sparse features, but momentarily by tensor-formed low-rank approximations in the temporal realm.  ...  Nonlocal Low Rank Tensor Approximation The nonlocal tensor regularization consists of two parts: forming the nonlocal tensor within the recovered frames and formulating the low-rank property in the formed  ... 
doi:10.3390/s19235299 pmid:31805743 pmcid:PMC6928938 fatcat:yslvbcnle5d27kjzt7lyj2fjd4

Low-Rank Tensor Approximation with Laplacian Scale Mixture Modeling for Multiframe Image Denoising

Weisheng Dong, Guangyu Li, Guangming Shi, Xin Li, Yi Ma
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
In this work, we propose a novel low-rank tensor approximation framework with Laplacian Scale Mixture (LSM) modeling for multi-frame image denoising.  ...  Patch-based low-rank models have shown effective in exploiting spatial redundancy of natural images especially for the application of image denoising.  ...  Nonlocal low-rank tensor approximation Low-rank tensor approximation consists of two steps: patch grouping and low-rank approximation.  ... 
doi:10.1109/iccv.2015.58 dblp:conf/iccv/DongLSLM15 fatcat:ughpcgu3abduvn6vshcraxgjie

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Dong Zeng, Qi Xie, Wenfei Cao, Jiahui Lin, Hao Zhang, Shanli Zhang, Jing Huang, Zhaoying Bian, Deyu Meng, Zongben Xu, Zhengrong Liang, Wufan Chen (+1 others)
2017 IEEE Transactions on Medical Imaging  
low-rankness extent of a tensor.  ...  a new DCPCT image reconstruction algorithm to improve low dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basisrepresentation tensor sparsity regularization, for measuring  ...  low-rank essence of a tensor.  ... 
doi:10.1109/tmi.2017.2749212 pmid:28880164 pmcid:PMC5711606 fatcat:goxfi22akbgwvow24oqte6sfdi

Hyperspectral Image Denoising Using Global Weighted Tensor Norm Minimum and Nonlocal Low-Rank Approximation

Xiangyang Kong, Yongqiang Zhao, Jize Xue, Jonathan Cheung-Wai Chan
2019 Remote Sensing  
The weighted multilinear rank is utilized to depict the GC information. To preserve structural information with NSS, a patch-group-based low-rank-tensor-approximation (LRTA) model is designed.  ...  To keep the integrity of the global structure and improve the details of the restored HSI, we propose a global and nonlocal weighted tensor norm minimum denoising method which jointly utilizes GC and NSS  ...  Conclusions In this paper, we proposed an HSI denoising method by jointly utilizing nonlocal and global low-rankness of HSI. Global low-rankness was exploited via three modes unfolding matrices.  ... 
doi:10.3390/rs11192281 fatcat:fbdkpbphjfhepdqe5atmzg56oe

Tensor train rank minimization with nonlocal self-similarity for tensor completion [article]

Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma
2020 arXiv   pre-print
To tackle this issue, we suggest the TT rank minimization with nonlocal self-similarity for tensor completion by simultaneously exploring the spatial, temporal/spectral, and nonlocal redundancy in visual  ...  The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors (order >3).  ...  Tensor completion via nonlocal TT rank minimization The proposed method, called tensor completion via nonlocal TT rank minimization (NL-TT), involves three main steps: grouping, completion, and aggregation  ... 
arXiv:2004.14273v1 fatcat:qx2ovjbvm5cd3mvhk6p7jt72hm

Multi-energy CT reconstruction using tensor nonlocal similarity and spatial sparsity regularization

Wenkun Zhang, Ningning Liang, Zhe Wang, Ailong Cai, Linyuan Wang, Chao Tang, Zhizhong Zheng, Lei Li, Bin Yan, Guoen Hu
2020 Quantitative Imaging in Medicine and Surgery  
Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor.  ...  A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images.  ...  The nonlocal tensor similarity of interchannel images is exploited by the intrinsic tensor sparsity regularization that combines the Tucker (48) and canonical polyadic (CP) (49) low-rank tensor decomposition  ... 
doi:10.21037/qims-20-594 pmid:33014727 pmcid:PMC7495318 fatcat:3s77ijzpzrbfvceshsibn76snm

Weighted Low-rank Tensor Recovery for Hyperspectral Image Restoration [article]

Yi Chang, Luxin Yan, Houzhang Fang, Sheng Zhong, Zhijun Zhang
2017 arXiv   pre-print
To overcome these limitations, in this work, we propose a unified low-rank tensor recovery model for comprehensive HSI restoration tasks, in which non-local similarity between spectral-spatial cubic and  ...  Further, to improve the capability and flexibility, we formulate it as a weighted low-rank tensor recovery (WLRTR) model by treating the singular values differently, and study its analytical solution.  ...  Figure 4 (b) shows the result of 2-D spatial low-rank recovery result, where the low-rank matrix is formed via spatial nonlocal similar patches. spectral low-rank recovery result, where the low-rank matrix  ... 
arXiv:1709.00192v1 fatcat:ueremc3lzvhlna42pgngpgb3ka

Joint Weighted Tensor Schatten $p$ -Norm and Tensor $l_p$ -Norm Minimization for Image Denoising

Xiaoqin Zhang, Jingjing Zheng, Yufang Yan, Li Zhao, Runhua Jiang
2019 IEEE Access  
INDEX TERMS Image denoising, low-rank tensor recovery, tensor Schatten p-norm.  ...  To solve this problem, this paper treats the image patches as matrices and proposes a low-rank tensor recovery model for image denoising, and thus it makes full use of spatial information within the image  ...  [9] give a color image denoising method via Weighted Tensor Nuclear Norm Minimization (WTNN) which stacks the nonlocal similar patches into a matrix in each color channel and processes all color channels  ... 
doi:10.1109/access.2018.2890561 fatcat:4lqsbubixrewxhkqtqye5wqile

Tensor train rank minimization with nonlocal self-similarity for tensor completion

Meng Ding, ,School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma, ,Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong, ,School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China
2020 Inverse Problems and Imaging  
To tackle this issue, we suggest the TT rank minimization with nonlocal self-similarity for tensor completion by simultaneously exploring the spatial, temporal/spectral, and nonlocal redundancy in visual  ...  The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of highorder tensors (order > 3).  ...  Some optimization methods has been proposed for TT rank minimization, such as alternating minimization [20, 47] , simple low-rank tensor completion via tensor train (SiLRTC-TT), and tensor completion  ... 
doi:10.3934/ipi.2021001 fatcat:fcyubmsxfvazlcx7mz2tthhisa

Joint Spatial and Spectral Low-Rank Regularization for Hyperspectral Image Denoising

Jize Xue, Yongqiang Zhao, Wenzhi Liao, Seong G. Kong
2018 IEEE Transactions on Geoscience and Remote Sensing  
Index Terms-Hyperspectral image (HSI) denoising, low-rank (LR) dictionary, nonlocal self-similarity, sparse representation, spectrum correlation.  ...  In this paper, we propose a joint spectral and spatial low-rank (LR) regularized method for HSI denoising, based on the assumption that the free-noise component in an observed signal can exist in latent  ...  Then, this nonlocal low-rankness regularization parameter is also set λ = 11 · max( √ n1, √ n2)σ in all the simulated data experiments.  ... 
doi:10.1109/tgrs.2017.2771155 fatcat:ielwfj6mgzfg5pznx2o6zchehu

NSTMR: Super-Resolution of Sentinel-2 Images Using Nonlocal Non-convex Surrogate of Tensor Multi-Rank

Xuanqi Wang, Tengyu Ji
2021 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
Specifically, the model consists of the data fidelity term and the low-multi-rank regularizer tailored to thoroughly mining the inherent spatial-nonlocal and spectral redundancy.  ...  Since S2 images can be naturally represented by tensors, we reformulate the degradation processas the tensorbased form.  ...  CONCLUSION To enhance the resolution of S2 images, we proposed a tensor-based nonlocal low-multi-rank regularized model by taking full advantage of the nonlocal spatial-spectral redundancy of the S2 image  ... 
doi:10.1109/jstars.2021.3083495 fatcat:ezciikmjq5godomiqvax7skqgi

Hyperspectral Image Denoising Based on Nonlocal Low-rank and TV Regularization

Xiangyang Kong, Yongqiang Zhao, Jize Xue, Jonathan Cheung-Wai Chan, Zhigang Ren, HaiXia Huang, Jiyuan Zang
2020 Remote Sensing  
As this tensor shows a stronger low-rank property than the original degraded HSI, the tensor weighted nuclear norm minimization (TWNNM) on the constructed tensor can effectively separate the low-rank clean  ...  Specifically, the HSI is first divided into local overlapping full-band patches (FBPs), then the nonlocal similar patches in each group are unfolded and stacked into a new third order tensor.  ...  Based on the notations in Section 2, , , and at location (i, j, and k) are given by = , , − , = , , − , = , , − (5) Nonlocal Low-rank Tensor Construction When constructing the nonlocal low-rank tensor  ... 
doi:10.3390/rs12121956 fatcat:dns7jhinafckddevoyl4v7fzma

Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration

Xinyuan Zhang, Xin Yuan, Lawrence Carin
2018 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition  
We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches.  ...  An iterative algorithm based on this low-rank tensor factorization strategy, called NLR-TFA, is presented in detail.  ...  NLR-CS is currently a state-of-the-art method that uses a nonlocal low-rank regularization method along with ADMM to solve image CS problems.  ... 
doi:10.1109/cvpr.2018.00859 dblp:conf/cvpr/Zhang0C18 fatcat:vfhlfqhbj5fdri3pof5pzfg6me

Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration [article]

Xinyuan Zhang, Xin Yuan, Lawrence Carin
2018 arXiv   pre-print
We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches.  ...  An iterative algorithm based on this low-rank tensor factorization strategy, called NLR-TFA, is presented in detail.  ...  NLR-CS is currently a state-of-the-art method that uses a nonlocal low-rank regularization method along with ADMM to solve image CS problems.  ... 
arXiv:1803.06795v1 fatcat:uueaqywykrhs5hkxrxutlo2ycu

Snapshot Hyperspectral Imaging Based on Weighted High-order Singular Value Regularization [article]

Niankai Cheng, Hua Huang, Lei Zhang, Lizhi Wang
2021 arXiv   pre-print
Then, we propose a weight high-order singular value regularization (WHOSVR) based low-rank tensor recovery model to characterize the structure prior of HSI.  ...  We first build high-order tensors by exploiting the spatial-spectral correlation in HSI.  ...  We exploit the nonlocal similarity across spatial and spectral dimensions to reformulate a low-rank tensor.  ... 
arXiv:2101.08923v1 fatcat:24hakjsfvre7vaprllveih6gvu
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