# Robust and tractable multidimensional exponential analysis

arXiv: https://arxiv.org/abs/2404.11004 · HTML: https://mlsanity.com/paper/2404.11004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2024.

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

- [Active Learning Classification from a Signal Separation Perspective](https://mlsanity.com/paper/2502.16425/) (2025)

## Abstract (arXiv)

Motivated by a number of applications in signal processing, we study the following question. Given samples of a multidimensional signal of the form  f(boldsymbolℓ)=sumk=1K akexp(-ilangle boldsymbolℓ, wkrangle), quad w1,cdots,wk∈ℝq,  boldsymbolℓ∈ mathbbZq,  |boldsymbolℓ| <n,  determine the values of the number K of components, and the parameters ak and wk's. We note that the the number of samples of f in the above equation is (2n-1)q. We develop an algorithm to recuperate these quantities accurately using only a subsample of size O(qn) of this data. For this purpose, we use a novel localized kernel method to identify the parameters, including the number K of signals. Our method is easy to implement, and is shown to be stable under a very low SNR range. We demonstrate the effectiveness of our resulting algorithm using 2 and 3 dimensional examples from the literature, and show substantial improvements over state-of-the-art techniques including Prony based, MUSIC and ESPRIT approaches.