
Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms
This work studies the Tensor Robust Principal Component Analysis (TRPCA)...
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Exact Tensor Completion from Sparsely Corrupted Observations via Convex Optimization
This paper conducts a rigorous analysis for provable estimation of multi...
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Tensor Ntubal rank and its convex relaxation for lowrank tensor recovery
As lowrank modeling has achieved great success in tensor recovery, many...
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Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data
Tensor principal component analysis (TPCA) is a multilinear extension o...
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RIPbased performance guarantee for lowtubalrank tensor recovery
The essential task of multidimensional data analysis focuses on the ten...
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Solving Principal Component Pursuit in Linear Time via l_1 Filtering
In the past decades, exactly recovering the intrinsic data structure fro...
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Robust PCA via Outlier Pursuit
Singular Value Decomposition (and Principal Component Analysis) is one o...
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Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted LowRank Tensors via Convex Optimization
This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA RPCA to the tensor case. Our model is based on a new tensor Singular Value Decomposition (tSVD) kilmer2011factorization and its induced tensor tubal rank and tensor nuclear norm. Consider that we have a 3way tensor X∈R^n_1× n_2× n_3 such that X=L_0+S_0, where L_0 has low tubal rank and S_0 is sparse. Is that possible to recover both components? In this work, we prove that under certain suitable assumptions, we can recover both the lowrank and the sparse components exactly by simply solving a convex program whose objective is a weighted combination of the tensor nuclear norm and the ℓ_1norm, i.e., _L,EL_*+λE_1, s.t.X=L+E, where λ= 1/√((n_1,n_2)n_3). Interestingly, TRPCA involves RPCA as a special case when n_3=1 and thus it is a simple and elegant tensor extension of RPCA. Also numerical experiments verify our theory and the application for the image denoising demonstrates the effectiveness of our method.
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