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Single Molecule Localization Microscopy (SMLM) enables the acquisition ofhigh-resolution images by alternating between activation of a sparse subset offluorescent molecules present in a sample and localization. In this work, thelocalization problem is formulated as a constrained sparse approximationproblem which is resolved by rewriting the $\ell_0$ pseudo-norm using anauxiliary term. In the preliminary experiments with the simulated ISBI datasetsthe algorithm yields as good results as the state-of-the-art in high-densitymolecule localization algorithms.

Single molecule localization by $\ell_2-\ell_0$ constrained optimization