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We propose a continuous non-convex variational model for Single MoleculeLocalisation Microscopy (SMLM) super-resolution in order to overcome lightdiffraction 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 modelsignal-dependent Poisson noise. For the numerical solution of the associatedminimisation problem, we consider an iterative reweighted $\ell_1$ (IRL1)strategy for which we detail efficient parameter computation strategies. Wereport qualitative and quantitative molecule localisation results showing thatthe proposed weighted-CEL0 (wCEL0) model improves the results obtained by CEL0and state-of-the art deep-learning approaches for the high-density SMLM ISBI2013 dataset.

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