Spectrum-blind sampling and compressive sensing for continuous-index signals

Spectrum-blind sampling (SBS), proposed in the mid-90psilas, is a sensing technique enabling minimum-rate sampling and reconstruction of signals with unknown but sparse spectra. SBS is applicable to continuous or discrete-index signals, finite or infinite length, in one or more dimensions. We revisit SBS and explore its relationship to compressive sensing (CS). On the one hand, recent results in CS provide efficient reconstruction techniques for SBS. On the other hand, SBS provides efficient structured designs for blind, non-adaptive sensing of spectrum-sparse signals with minimal sampling requirements, and formulation leading to reconstruction cost only linear in the amount of data, and robustness against noise.