Weighted-Celo Sparse Regularisation For Molecule Localisation In Super-Resolution Microscopy With Poisson Data

We consider a variational model for Single Molecule Localisation Microscopy (SMLM) super-resolution. More specifically, we study a generalization of the Continuous Exact l
₀
penalty, recently introduced to relax the l
₂
-l
₀
problem, where a weighted-l
₂
data fidelity now models signal-dependent Poisson noise. For the numerical solution of the associated non-convex minimisation problem, we propose an iterative reweighted l
₁
(IRL1) algorithm, for which efficient parameter computation strategies are detailed. Both qualitative and quantitative molecule localisation results are reported, showing that the proposed weighted-CEL0 (wCEL0) model for Poisson noisy data improves the results obtained by CEL0 and state-of-the art deep-learning approaches for the high-density SMLM ISBI 2013 dataset.