Weighted-CEL0 sparse regularisation for molecule localisation in super-resolution microscopy with Poisson data

TL;DR

This paper introduces a novel weighted-CEL0 regularisation model for super-resolution microscopy that effectively localises molecules in Poisson noise conditions, outperforming existing methods including deep learning approaches.

Contribution

It develops a weighted-CEL0 variational model with an IRL1 algorithm for improved molecule localisation in SMLM, addressing Poisson noise challenges.

Findings

wCEL0 outperforms CEL0 in localisation accuracy

wCEL0 surpasses state-of-the-art deep learning methods

The IRL1 algorithm efficiently solves the minimisation problem

Abstract

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 $\ell_0$ (CEL0) penalty recently introduced to relax the $\ell_2-\ell_0$ problem where a weighted-$\ell_2$ data fidelity is considered to model signal-dependent Poisson noise. For the numerical solution of the associated minimisation problem, we consider an iterative reweighted $\ell_1$ (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.