# Harnessing Sparsity over the Continuum: Atomic Norm Minimization for Super Resolution

## TL;DR

This paper explains how atomic norm minimization, a convex optimization method, can be used for super resolution tasks, providing mathematical foundations, performance guarantees, and applications in microscopy.

## Contribution

It offers a comprehensive exposition of atomic norm minimization for super resolution, including theoretical guarantees and practical application insights.

## Key findings

- Atomic norm minimization provides effective super resolution solutions.
- The approach has proven performance guarantees.
- Application demonstrated in fluorescence microscopy image reconstruction.

## Abstract

Convex optimization recently emerges as a compelling framework for performing super resolution, garnering significant attention from multiple communities spanning signal processing, applied mathematics, and optimization. This article offers a friendly exposition to atomic norm minimization as a canonical convex approach to solve super resolution problems. The mathematical foundations and performances guarantees of this approach are presented, and its application in super resolution image reconstruction for single-molecule fluorescence microscopy are highlighted.