Fixed-Point Proximity Minimization: A Theoretical Review and Numerical Study

Authors

Daniel Weddle, Department of Mathematics and Statistics, Old Dominion UniversityFollow
Jianfeng Guo, School of Computer Science and Engineering, Sun Yat-sen UniversityFollow

Disciplines

Applied Mathematics | Signal Processing

Publication Date

2021

Document Type

Article

DOI

10.25778/s7bd-z775

Abstract

This study examines the relatively recent development of a “fixed-point proximity” approach to one type of minimization problem, considers its application to image denoising, and explores convergence and divergence of the iterative algorithm beyond a (previously supplied) theoretically guaranteed convergence bound on one of the parameters (𝜆). While reviewing the fixed-point proximity approach and its application to image denoising, we aim to communicate the concepts and details in a way that will facilitate understanding for undergraduates and for scholars from other subfields. In the latter portion of our study, the numerical experiment provides thought-provoking data on the effects that parameters 𝜇 and 𝜆 have on convergence or divergence once 𝜆 exceeds the range known to guarantee convergence.

Recommended Citation

Weddle, Daniel and Guo, Jianfeng (2021) "Fixed-Point Proximity Minimization: A Theoretical Review and Numerical Study," OUR Journal: ODU Undergraduate Research Journal: Vol. 8, Article 10.
DOI: 10.25778/s7bd-z775
Available at: https://digitalcommons.odu.edu/ourj/vol8/iss1/10