Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data
Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to extract the princi- pal components of the multi-way data based on tensor singular value decomposition. The tensor is split into a number of blocks of the same size. The low rank component of each block tensor is extracted using iterative tensor singular value thresholding method. The prin- cipal components of the multi-way data are the concatenation of all the low rank components of all the block tensors. We give the block tensor incoherence conditions to guarantee the successful decom- position. This factorization has similar optimality properties to that of low rank matrix derived from singular value decomposition. Ex- perimentally, we demonstrate its effectiveness in two applications, including motion separation for surveillance videos and illumination normalization for face images.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Auto Tensor Singular Value Thresholding: A Non-Iterative and Rank-Free Framework for Tensor Denoising
In modern data-driven tasks such as classification, optimization, and forecasting, mitigating the effects of intrinsic noise is crucial for improving predictive accuracy. While numerous denoising techniques have been dev…
Computational EfficiencyDenoisingTensor DecompositionOptimal Sparse Singular Value Decomposition for High-dimensional High-order Data
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternatin…
Dimensionality ReductionVocal Bursts Intensity PredictionFast Singular Value Shrinkage with Chebyshev Polynomial Approximation Based on Signal Sparsity
We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) f…
A Fast Algorithm for Cosine Transform Based Tensor Singular Value Decomposition
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value dec…
Nonconvex Nonsmooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm
The nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing. However, solving the nuclear n…
Compressive Sensing