Weighted-CEL0 sparse regularisation for molecule localisation in super-resolution microscopy with Poisson data
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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 ℓ_0 (CEL0) penalty recently introduced to relax the ℓ_2-ℓ_0 problem where a weighted-ℓ_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 ℓ_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.
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