Nonconvex Tensor Relative Total Variation for Image Completion

Yunqing Bai, Jihong Pei and Min Li ()
Additional contact information
Yunqing Bai: ATR National Key Laboratory of Defense Technology, Shenzhen University, Shenzhen 518060, China
Jihong Pei: ATR National Key Laboratory of Defense Technology, Shenzhen University, Shenzhen 518060, China
Min Li: College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

Mathematics, 2023, vol. 11, issue 7, 1-17

Abstract: Image completion, which falls to a special type of inverse problems, is an important but challenging task. The difficulties lie in that (i) the datasets usually appear to be multi-dimensional; (ii) the unavailable or corrupted data entries are randomly distributed. Recently, low-rank priors have gained importance in matrix completion problems and signal separation; however, due to the complexity of multi-dimensional data, using a low-rank prior by itself is often insufficient to achieve desirable completion, which requires a more comprehensive approach. In this paper, different from current available approaches, we develop a new approach, called relative total variation (TRTV), under the tensor framework, to effectively integrate the local and global image information for data processing. Based on our proposed framework, a completion model embedded with TRTV and tensor p -shrinkage nuclear norm minimization with suitable regularization is established. An alternating direction method of multiplier (ADMM)-based algorithm under our framework is presented. Extensive experiments in terms of denoising and completion tasks demonstrate our proposed method are not only effective but also superior to existing approaches in the literature.

Keywords: tensor completion; tensor relative total variation; tensor p-shrinkage nuclear norm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/7/1682/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/7/1682/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:7:p:1682-:d:1113022

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().