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3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction
2019
Sensors
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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
2015
2015 IEEE International Conference on Computer Vision (ICCV)
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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
2017
IEEE Transactions on Medical Imaging
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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
2019
Remote Sensing
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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]
2020
arXiv
pre-print
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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
2020
Quantitative Imaging in Medicine and Surgery
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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]
2017
arXiv
pre-print
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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
2019
IEEE Access
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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
2020
Inverse Problems and Imaging
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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
2018
IEEE Transactions on Geoscience and Remote Sensing
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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
2021
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing
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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
2020
Remote Sensing
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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
2018
2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition
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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]
2018
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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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