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

## TL;DR

This paper introduces a new constrained optimization approach for single molecule localization microscopy, reformulating the sparse approximation problem to improve high-density molecule localization accuracy.

## Contribution

It presents a novel $ ext{l}_2- ext{l}_0$ constrained optimization method for SMLM, offering an alternative to existing high-density localization algorithms.

## Key findings

- Achieves comparable results to state-of-the-art methods on simulated datasets.
- Uses a reformulation of the $ ext{l}_0$ pseudo-norm for better sparse approximation.
- Demonstrates potential for high-density molecule localization improvements.

## Abstract

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.