# Blind inverse problems with isolated spikes

arXiv: https://arxiv.org/abs/2111.02093 · HTML: https://mlsanity.com/paper/2111.02093/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2021.

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

- [A Morse-Bott Framework for Blind Inverse Problems: Local Recovery Guarantees and the Failure of the MAP](https://mlsanity.com/paper/2508.02923/) (2025)

## Abstract (arXiv)

Assume that an unknown integral operator living in some known subspace is observed indirectly, by evaluating its action on a few Dirac masses at unknown locations. Is this information enough to recover the operator and the impulse responses locations stably? We study this question and answer positively under realistic technical assumptions. We illustrate the well-foundedness of this theory on two challenging optical imaging problems: blind super-resolution and deconvolution. This provides a simple, practical and theoretically grounded approach to solve these long resisting problems.