  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.
