Wavelet and Linear Algebra

ACCELERATED ALGORITHMS FOR SILRTC ALGORITHM BY FAST TRI-FACTORIZATION METHOD AND TOTAL VARIATION REGULARIZATION

Document Type : Research Paper

Authors

Ali Tavakoli 1
Rasool Ebrahimi 2

1 Department of Mathematics, University of Mazandaran, Babolsar, Iran

2 Mathematics department, University of Mazandaran, Babolsar, Iran

https://doi.org/10.22072/wala.2024.2016583.1439
Abstract
Tensor completion is one of the ecient methods for restoring data
such that minimizing the rank of the tensor leads to an appropriate solution.
However, it gives a non-convex objective function, which generates an NPhard
problem. To overcome this problem, instead of using the rank function,
the trace norm is applied. To solve this problem, Simple Low Rank Tensor
Completion (SiLRTC) can be used. In the methods based on trace norm, the
Singular Value Decomposition (SVD) is used, which increases computational
complexity of these methods with increasing dimensions. In order to reduce
the computational complexity of SVD, the approximate SVD can be utilized.
In this paper, to accelerate the convergence speed of SiLRTC Algorithm, the
new combined method FTF-SiLRTC is presented. On the other hand, the
images recovered using the mentioned algorithms are generally accompanied
by horizontal and vertical noise lines and have low accuracy. To solve this
diculty, the total variation (TV) regularization is added to the problem and
the FTF-SiLRTC-TV Algorithm is introduced to solve it with higher accuracy.

Keywords

Image processing
Low rank matrix completion
Low rank tensor completion
Fast tri-factorization method
Wavelet and Linear Algebra
Volume 11, Issue 2
October 2024
Pages 32-51

Home

Guide for Authors

Submit Manuscript

Reviewers

Contact Us