Error Estimations for Total Variation Type Regularization

Kuan Li, Chun Huang and Ziyang Yuan
Additional contact information
Kuan Li: School of Cyberspace Security, Dongguan University of Technology, Dongguan 523808, China
Chun Huang: College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
Ziyang Yuan: Department of Mathematics, National University of Defense Technology, Changsha 410073, China

Mathematics, 2021, vol. 9, issue 12, 1-14

Abstract: This paper provides several error estimations for total variation (TV) type regularization, which arises in a series of areas, for instance, signal and imaging processing, machine learning, etc. In this paper, some basic properties of the minimizer for the TV regularization problem such as stability, consistency and convergence rate are fully investigated. Both a priori and a posteriori rules are considered in this paper. Furthermore, an improved convergence rate is given based on the sparsity assumption. The problem under the condition of non-sparsity, which is common in practice, is also discussed; the results of the corresponding convergence rate are also presented under certain mild conditions.

Keywords: total variation; regularization; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/12/1373/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/12/1373/ (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:9:y:2021:i:12:p:1373-:d:574477

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 ().