Spectral Compressive Sensing with Polar Interpolation

TL;DR

This paper introduces a novel greedy algorithm for spectral compressive sensing that improves frequency estimation accuracy and noise robustness by using band-exclusion and polar interpolation techniques.

Contribution

The paper presents a new spectral compressive sensing algorithm that overcomes dictionary coherence and discretization issues, enhancing spectral estimation performance.

Findings

Outperforms existing methods in fidelity.

Shows increased tolerance to noise.

Effective in line spectral estimation from compressive measurements.

Abstract

Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and by the discretization of the frequency parameter space. In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most existing approaches in fidelity and tolerance to noise.