Multi-dimensional Spectral Super-Resolution with Prior Knowledge via Frequency-Selective Vandermonde Decomposition and ADMM

TL;DR

This paper introduces a novel super-resolution method for multi-dimensional frequency estimation from incomplete or noisy data, leveraging prior interval knowledge and advanced optimization techniques.

Contribution

It develops a frequency-selective atomic norm minimization framework using MD Vandermonde decomposition and ADMM for efficient low-rank tensor recovery.

Findings

High accuracy in frequency estimation demonstrated through simulations

Effective incorporation of prior frequency interval knowledge

Fast convergence of the proposed ADMM-based algorithms

Abstract

This paper is concerned with estimation of multiple frequencies from incomplete and/or noisy samples based on a low-CP-rank tensor data model where each CP vector is an array response vector of one frequency. Suppose that it is known a priori that the frequencies lie in some given intervals, we develop efficient super-resolution estimators by exploiting such prior knowledge based on frequency-selective (FS) atomic norm minimization. We study the MD Vandermonde decomposition of block Toeplitz matrices in which the frequencies are restricted to lie in given intervals. We then propose to solve the FS atomic norm minimization problems for the low-rank spectral tensor recovery by converting them into semidefinite programs based on the MD Vandermonde decomposition. We also develop fast solvers for solving these semidefinite programs via the alternating direction method of multipliers (ADMM), where each iteration involves a number of refinement steps to utilize the prior knowledge. Extensive simulation results are presented to illustrate the high performance of the proposed methods.