Novel methods for multilinear data completion and de-noising based on tensor-SVD

07/07/2014
by   Zemin Zhang, et al.
0

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data and as an application consider 3-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4].

READ FULL TEXT

page 4

page 6

page 7

page 8

research
07/02/2013

Novel Factorization Strategies for Higher Order Tensors: Implications for Compression and Recovery of Multi-linear Data

In this paper we propose novel methods for compression and recovery of m...
research
02/16/2015

Exact tensor completion using t-SVD

In this paper we focus on the problem of completion of multidimensional ...
research
12/15/2017

A novel nonconvex approach to recover the low-tubal-rank tensor data: when t-SVD meets PSSV

In this paper we fix attention on a recently developed tensor decomposit...
research
01/30/2020

Grassmannian Optimization for Online Tensor Completion and Tracking in the t-SVD Algebra

We propose a new streaming algorithm, called TOUCAN, for the tensor comp...
research
09/06/2019

Recovery of Future Data via Convolution Nuclear Norm Minimization

This paper is about recovering the unseen future data from a given seque...
research
05/22/2019

Sparse Equisigned PCA: Algorithms and Performance Bounds in the Noisy Rank-1 Setting

Singular value decomposition (SVD) based principal component analysis (P...
research
12/04/2018

Sturm: Sparse Tubal-Regularized Multilinear Regression for fMRI

While functional magnetic resonance imaging (fMRI) is important for heal...

Please sign up or login with your details

Forgot password? Click here to reset