Off-the-grid regularisation for Poisson inverse problems

Marta Lazzaretti (), Claudio Estatico (), Alejandro Melero () and Luca Calatroni ()
Additional contact information
Marta Lazzaretti: Universitá di Genova
Claudio Estatico: Universitá di Genova
Alejandro Melero: Achucarro Basque Center for Neuroscience
Luca Calatroni: CNRS-UniCA-Inria

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 16, 827-860

Abstract: Abstract Off-the-grid regularisation has been extensively employed over the last decade in the context of ill-posed inverse problems formulated in the continuous setting of the space of Radon measures $${{\mathcal {M}}(\Omega )}$$ M ( Ω ) . These approaches enjoy convexity and counteract the discretisation biases as well the numerical instabilities typical of their discrete counterparts. In the framework of sparse reconstruction of discrete point measures (sum of weighted Diracs), a Total Variation regularisation norm in $${{\mathcal {M}}(\Omega )}$$ M ( Ω ) is typically combined with an $$L^2$$ L 2 data term modelling additive Gaussian noise. To assess the framework of off-the-grid regularisation in the presence of signal-dependent Poisson noise, we consider in this work a variational model where Total Variation regularisation is coupled with a Kullback–Leibler data term under a non-negativity constraint. Analytically, we study the optimality conditions of the composite functional and analyse its dual problem. Then, we consider an homotopy strategy to select an optimal regularisation parameter and use it within a Sliding Frank-Wolfe algorithm. Several numerical experiments on both 1D/2D/3D simulated and real 3D fluorescent microscopy data are reported.

Keywords: Off-the-grid sparse regularisation; Poisson noise; Sliding Frank-Wolfe; Fluorescence microscopy imaging (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-025-00688-7 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_s10589-025-00688-7

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

DOI: 10.1007/s10589-025-00688-7

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 ().