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

arXiv: https://arxiv.org/abs/1904.04283 · HTML: https://mlsanity.com/paper/1904.04283/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2019.

## Built on by (most cited first, 3 of 3)

- [Spectral gap-based deterministic tensor completion](https://mlsanity.com/paper/2306.06262/) (2023)
- [Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude](https://mlsanity.com/paper/2510.16948/) (2025)
- [Characterization of the Basin of Convexity for Multi-Snapshot Spike Deconvolution via Variable Projection](https://mlsanity.com/paper/2607.09593/) (2026)

## Abstract (arXiv)

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.