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

摘要

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, the previous methods focus more on single measurement vector and default to using impractical random sampling. In this paper, we employ a deterministic and simple sampling scheme, that is, using three sub-Nyquist channels with pairwise coprime undersampling ratios. A multi-task model is utilized to unite the three-channel samples and address the multiple measurement vector problem. The model is solved by the proposed complex-valued multi-task algorithm based on variational Bayesian inference. Simulations show that this method is feasible and robust at quite low sampling rates.