Compressed sensing deals with the reconstruction of signals

from sub-Nyquist samples by exploiting the sparsity of their

projections onto known subspaces. In contrast, the present

article is concerned with the reconstruction of second-order

statistics, such as covariance and power spectrum, even in

the absence of sparsity priors. The framework described here

leverages the statistical structure of random processes to

enable signal compression and offers an alternative perspective

at sparsity-agnostic inference. Capitalizing on parsimonious

representations, we illustrate how compression and reconstruction

tasks can be addressed in popular applications such

as power spectrum estimation, incoherent imaging, direction

of arrival estimation, frequency estimation, and wideband

spectrum sensing.

%B IEEE Signal Processing Magazine
%V 33
%P 78--93
%8 01/2016
%G eng
%N 1
%0 Journal Article
%J IEEE Trans. Information Theory
%D 2015
%T Compression Limits for Random Vectors with Linearly Parameterized Second-Order Statistics
%A Daniel Romero
%A R. López-Valcarce
%A Geert Leus
%K compass
%K compressed sensing
%X 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 — 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.

%B IEEE Trans. Information Theory
%V 61
%P 1410-1425
%8 03/2015
%G eng
%N 3
%& 1410
%R 10.1109/TIT.2015.2394784
%0 Conference Paper
%B IEEE Sensor Array Multichannel Signal Process. Workshop (SAM)
%D 2014
%T Cooperative compressive power spectrum estimation
%A Dyonisius D Ariananda
%A Daniel Romero
%A Geert Leus
%K cognitive radio
%K wsn
%B IEEE Sensor Array Multichannel Signal Process. Workshop (SAM)
%G eng
%0 Conference Paper
%B IEEE Int. Workshop Comput. Advances Multi-Sensor Adaptive Process (CAMSAP)
%D 2013
%T Compressive Angular and Frequency Periodogram Reconstruction for Multiband Signals
%A Ariananda, D. D.
%A Daniel Romero
%A Geert Leus
%K cognitive radio
%K dynacs
%B IEEE Int. Workshop Comput. Advances Multi-Sensor Adaptive Process (CAMSAP)
%C San Martin
%G eng
%R 10.1109/CAMSAP.2013.6714102
%0 Conference Paper
%B Inform. Theory Appl. Workshop
%D 2013
%T Compressive Covariance Sampling
%A Daniel Romero
%A Geert Leus
%K cognitive radio
%K dynacs
%B Inform. Theory Appl. Workshop
%P 1-8
%8 Feb.
%G eng
%R 10.1109/ITA.2013.6502949
%0 Conference Paper
%B Int. Conf. Acoust., Speech, Signal Process. (ICASSP)
%D 2013
%T Compressive wideband spectrum sensing with spectral prior information
%A Daniel Romero
%A R. López-Valcarce
%A Geert Leus
%K cognitive radio
%K dynacs
%K spectrum sensing
%X Wideband spectrum sensing provides a means to determine

the occupancy of channels spanning a broad range of frequencies.

Practical limitations impose that the acquisition should

be accomplished at a low rate, much below the Nyquist lower

bound. Dramatic rate reductions can be obtained by the observation

that only a few parameters need to be estimated in

typical spectrum sensing applications. This paper discusses

the joint estimation of the power of a number of channels,

whose power spectral density (PSD) is known up to a scale

factor, using compressive measurements. First, relying on

a Gaussian assumption, an efficient approximate maximum

likelihood (ML) technique is presented. Next, a least-squares

estimator is applied for the general non-Gaussian case.

%B Int. Conf. Acoust., Speech, Signal Process. (ICASSP)
%G eng
%R 10.1109/ICASSP.2013.6638505
%0 Journal Article
%J IEEE Trans. Signal Process.
%D 2013
%T Wideband Spectrum Sensing From Compressed Measurements Using Spectral Prior Information
%A Daniel Romero
%A Geert Leus
%K cognitive radio
%K compressed sensing
%K dynacs
%K spectrum sensing
%B IEEE Trans. Signal Process.
%V 61
%P 6232-6246
%G eng
%R 10.1109/TSP.2013.2283473
%0 Conference Paper
%B IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2012)
%D 2012
%T Generalized matched filter detector for fast fading channels
%A Daniel Romero
%A R. López-Valcarce
%A Geert Leus
%K cognitive radio
%K dynacs
%K spectrum sensing
%X We consider the problem of detecting a known signal with constant magnitude immersed in noise of unknown variance,

when the propagation channel is frequency-flat and randomly

time-varying within the observation window. A Basis Expansion

Model with random coefficients is used for the channel, and a Generalized Likelihood Ratio approach is adopted in order to cope with deterministic nuisance parameters. The resulting scheme can be seen as a generalization of the well-known

Matched Filter detector, to which it reduces for timeinvariant

channels. Closed-form analytical expressions are provided for the distribution of the test statistic under both hypotheses, which allow to assess the detection performance.

%B IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP 2012)
%I IEEE
%C Kyoto, Japan
%8 07/2012
%G eng
%R 10.1109/ICASSP.2012.6288587