We propose a continuous non-convex variational model for Single Molecule Localisation Microscopy (SMLM) super-resolution in order to overcome light diffraction barriers. Namely, we consider a variation of the Continuous Exact ℓ0 (CEL0) penalty recently introduced to relax the ℓ2−ℓ0 problem where a weighted-ℓ2 data fidelity is considered to model signal-dependent Poisson noise. For the numerical solution of the associated minimisation problem, we consider an iterative reweighted ℓ1 (IRL1) strategy for which we detail efficient parameter computation strategies. We report qualitative and quantitative molecule localisation results showing that the proposed weighted-CEL0 (wCEL0) model improves the results obtained by CEL0 and state-of-the art deep-learning approaches for the high-density SMLM ISBI 2013 dataset.
@article{arxiv.2010.13173,
title = {Weighted-CEL0 sparse regularisation for molecule localisation in super-resolution microscopy with Poisson data},
author = {Marta Lazzaretti and Luca Calatroni and Claudio Estatico},
journal= {arXiv preprint arXiv:2010.13173},
year = {2020}
}