# Mathematical Foundation of Sparsity-based Multi-snapshot Spectral Estimation

arXiv: https://arxiv.org/abs/2202.11189 · HTML: https://mlsanity.com/paper/2202.11189/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2022.

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

- [Coded Hankel Polynomial Chaos: Spectral Identification of Dominant Polynomial-Chaos Modes](https://mlsanity.com/paper/2608.16126/) (2026)

## Abstract (arXiv)

In this paper, we study the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements in a bounded domain. We aim to provide a mathematical foundation for sparsity-based super-resolution in such spectral estimation problems in both one- and multi-dimensional spaces. In particular, we estimate the resolution and stability of the location recovery when considering the sparsest solution under the measurement constraint, and characterize their dependence on the cut-off frequency, the noise level, the sparsity of point sources, and the incoherence of the amplitude vectors of point sources. Our estimate emphasizes the importance of the high incoherence of amplitude vectors in enhancing the resolution of multi-snapshot spectral estimation. Moreover, to the best of our knowledge, it also provides the first stability result in the super-resolution regime for the well-known sparse MMV problem in DOA estimation.