TítuloCompression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics
Tipo de publicaciónJournal Article
Year of Publication2015
AutoresRomero, D, López-Valcarce, R, Leus, G
JournalIEEE Trans. Information Theory
Start Page1410
Date Published03/2015
Palabras clavecompass, compressed sensing
Resumen The class of complex random vectors whose covariancematrix is linearly parameterized by a basis of HermitianToeplitz (HT) matrices is considered, and the maximumcompression ratios that preserve all second-order informationare derived — the statistics of the uncompressed vector mustbe recoverable from a set of linearly compressed observations.This kind of vectors arises naturally when sampling widesensestationary random processes and features a number ofapplications in signal and array processing.Explicit guidelines to design optimal and nearly optimalschemes operating both in a periodic and non-periodic fashionare provided by considering two of the most common linearcompression schemes, which we classify as dense or sparse. Itis seen that the maximum compression ratios depend on thestructure of the HT subspace containing the covariance matrix ofthe uncompressed observations. Compression patterns attainingthese maximum ratios are found for the case without structure aswell as for the cases with circulant or banded structure. Universalsamplers are also proposed to compress unknown HT subspaces.