# Super-Resolution of Point Sources via Convex Programming

arXiv: https://arxiv.org/abs/1507.07034 · HTML: https://mlsanity.com/paper/1507.07034/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2015.

## Built on by (most cited first, 1 of 1)

- [Penalising the biases in norm regularisation enforces sparsity](https://mlsanity.com/paper/2303.01353/) (2023)

## Abstract (arXiv)

We consider the problem of recovering a signal consisting of a superposition of point sources from low-resolution data with a cut-off frequency f. If the distance between the sources is under 1/f, this problem is not well posed in the sense that the low-pass data corresponding to two different signals may be practically the same. We show that minimizing a continuous version of the l1 norm achieves exact recovery as long as the sources are separated by at least 1.26/f. The proof is based on the construction of a dual certificate for the optimization problem, which can be used to establish that the procedure is stable to noise. Finally, we illustrate the flexibility of our optimization-based framework by describing extensions to the demixing of sines and spikes and to the estimation of point sources that share a common support.