# Deconvolution of Point Sources: A Sampling Theorem and Robustness Guarantees

arXiv: https://arxiv.org/abs/1707.00808 · HTML: https://mlsanity.com/paper/1707.00808/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2017.

## Built on by (most cited first, 2 of 2)

- [Off-the-grid learning of mixtures from a continuous dictionary](https://mlsanity.com/paper/2207.00171/) (2022)
- [Straight-Through meets Sparse Recovery: the Support Exploration Algorithm](https://mlsanity.com/paper/2301.13584/) (2023)

## Abstract (arXiv)

In this work we analyze a convex-programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one-dimensional model where the kernel is either a Gaussian function or a Ricker wavelet, inspired by applications in geophysics and imaging. Our analysis establishes that minimizing a continuous counterpart of the ℓ1 norm achieves exact recovery of the original spikes as long as (1) the signal support satisfies a minimum-separation condition and (2) there are at least two samples close to every spike. In addition, we derive theoretical guarantees on the robustness of the approach to both dense and sparse additive noise.