@article {770, title = {Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics}, journal = {IEEE Trans. Information Theory}, volume = {61}, year = {2015}, month = {03/2015}, pages = {1410-1425}, chapter = {1410}, abstract = {
The class of complex random vectors whose covariance
matrix is linearly parameterized by a basis of Hermitian
Toeplitz (HT) matrices is considered, and the maximum
compression ratios that preserve all second-order information
are derived {\textemdash} the statistics of the uncompressed vector must
be recoverable from a set of linearly compressed observations.
This kind of vectors arises naturally when sampling widesense
stationary random processes and features a number of
applications in signal and array processing.
Explicit guidelines to design optimal and nearly optimal
schemes operating both in a periodic and non-periodic fashion
are provided by considering two of the most common linear
compression schemes, which we classify as dense or sparse. It
is seen that the maximum compression ratios depend on the
structure of the HT subspace containing the covariance matrix of
the uncompressed observations. Compression patterns attaining
these maximum ratios are found for the case without structure as
well as for the cases with circulant or banded structure. Universal
samplers are also proposed to compress unknown HT subspaces.
}, keywords = {compass, compressed sensing}, doi = {10.1109/TIT.2015.2394784}, author = {Daniel Romero and R. L{\'o}pez-Valcarce and Geert Leus} }