Compressive Sampling of Ensembles of Correlated Signals

TL;DR

This paper introduces novel sampling architectures for efficiently acquiring correlated signal ensembles at sub-Nyquist rates, leveraging structured randomness and low-rank matrix recovery techniques.

Contribution

It presents new sampling methods that do not require prior correlation knowledge, enabling low-rank matrix recovery from fewer samples in correlated signal ensembles.

Findings

Ensembles can be sampled below Nyquist rate using proposed architectures.

Low-rank matrix recovery enables reconstruction from fewer samples.

More correlation in signals reduces the number of samples needed.

Abstract

We propose several sampling architectures for the efficient acquisition of an ensemble of correlated signals. We show that without prior knowledge of the correlation structure, each of our architectures (under different sets of assumptions) can acquire the ensemble at a sub-Nyquist rate. Prior to sampling, the analog signals are diversified using simple, implementable components. The diversification is achieved by injecting types of "structured randomness" into the ensemble, the result of which is subsampled. For reconstruction, the ensemble is modeled as a low-rank matrix that we have observed through an (undetermined) set of linear equations. Our main results show that this matrix can be recovered using standard convex programming techniques when the total number of samples is on the order of the intrinsic degree of freedom of the ensemble --- the more heavily correlated the ensemble, the fewer samples are needed. To motivate this study, we discuss how such ensembles arise in the context of array processing.