A general framework for whiteness-based parameters selection in variational models

Francesca Bevilacqua (), Alessandro Lanza (), Monica Pragliola () and Fiorella Sgallari ()
Additional contact information
Francesca Bevilacqua: University of Bologna
Alessandro Lanza: University of Bologna
Monica Pragliola: University of Naples Federico II
Fiorella Sgallari: University of Bologna

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 5, 457-489

Abstract: Abstract In this work, we extend the residual whiteness principle, originally proposed in (Lanza et al. in Electron Trans Numer Anal 53:329–352 2020) for the selection of a single regularization parameter in variational models for inverse problems under additive white noise corruption, to much broader scenarios. More specifically, we address the problem of estimating multiple parameters for imaging inverse problems subject to both white and non-white but whitenable noise corruptions, thus covering most of the application cases. The proposed parameter selection criterion, referred to as generalized whiteness principle, is formulated as a bilevel optimization problem. To circumvent the non-smoothness of the variational models typically employed in imaging problems—the non-smoothness representing a bottleneck in the bilevel set-up—we propose to adopt a derivative-free minimization algorithm for the solution of the designed bilevel problem. We refer to this novel numerical solution paradigm as bilevel derivative-free approach. Numerical tests highlight both the ability of the proposed generalized whiteness principle to effectively select multiple parameters and the significant advantages, in terms of computational cost, of the bilevel derivative-free numerical solution framework.

Keywords: Variational models; Whiteness principle; Bilevel optimization; Derivative free methods (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-024-00615-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00615-2

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-024-00615-2

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().