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