# Compressive Multidimensional Harmonic Retrieval with Prior Knowledge

## TL;DR

This paper introduces a method for multidimensional harmonic retrieval that leverages prior spectral knowledge to improve frequency estimation accuracy using atomic norm minimization and Vandermonde decomposition.

## Contribution

It proposes a novel approach to incorporate prior spectral interval information into MD frequency estimation via semidefinite programming.

## Key findings

- Enhanced frequency estimation accuracy with prior knowledge
- Effective MD Vandermonde decomposition for block Toeplitz matrices
- Numerical results demonstrate improved performance over existing methods

## Abstract

This paper concerns the problem of estimating multidimensional (MD) frequencies using prior knowledge of the signal spectral sparsity from partial time samples. In many applications, such as radar, wireless communications, and super-resolution imaging, some structural information about the signal spectrum might be known beforehand. Suppose that the frequencies lie in given intervals, the goal is to improve the frequency estimation performance by using the prior information. We study the MD Vandermonde decomposition of block Toeplitz matrices in which the frequencies are restricted to given intervals. We then propose to solve the frequency-selective atomic norm minimization by converting them into semidefinite program based on the MD Vandermonde decomposition. Numerical simulation results are presented to illustrate the good performance of the proposed method.