Line Spectral Estimation Based on Compressed Sensing with Deterministic Sub-Nyquist Sampling

TL;DR

This paper introduces a deterministic sub-Nyquist sampling scheme using coprime ratios and a Bayesian inference algorithm for accurate spectral estimation of frequency-sparse signals, avoiding random sampling complexities.

Contribution

It proposes a simple, deterministic sampling method with coprime ratios and a Bayesian-based spectral estimation algorithm, advancing compressed sensing applications.

Findings

Sampling at three coprime sub-Nyquist rates is effective.

The Bayesian algorithm accurately estimates spectra at low sampling rates.

The method demonstrates robustness and feasibility through simulations.

Abstract

As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random sampling in data acquisition, which is difficult to implement in hardware. In this paper, we propose a deterministic and simple sampling scheme, that is, sampling at three sub-Nyquist rates which have coprime undersampled ratios. This sampling method turns out to be valid through numerical experiments. A complex-valued multitask algorithm based on variational Bayesian inference is proposed to estimate the spectra of frequency-sparse signals after sampling. Simulations show that this method is feasible and robust at quite low sampling rates.