Compressive Multiplexing of Correlated Signals

TL;DR

This paper introduces a compressive multiplexing architecture for efficiently acquiring correlated signal ensembles by exploiting their low-rank structure, enabling recovery from fewer samples than traditional methods.

Contribution

It proposes a novel multiplexing and sampling scheme that leverages the low-rank structure of correlated signals for efficient acquisition and reconstruction.

Findings

Sampling rate is within a logarithmic factor of the signal complexity

Ensemble recovery is formulated as a low-rank matrix recovery problem

The method exploits unknown correlation structure for efficient sampling

Abstract

We present a general architecture for the acquisition of ensembles of correlated signals. The signals are multiplexed onto a single line by mixing each one against a different code and then adding them together, and the resulting signal is sampled at a high rate. We show that if the $M$ signals, each bandlimited to $W/2$ Hz, can be approximated by a superposition of $R < M$ underlying signals, then the ensemble can be recovered by sampling at a rate within a logarithmic factor of $RW$ (as compared to the Nyquist rate of $MW$). This sampling theorem shows that the correlation structure of the signal ensemble can be exploited in the acquisition process even though it is unknown a priori. The reconstruction of the ensemble is recast as a low-rank matrix recovery problem from linear measurements. The architectures we are considering impose a certain type of structure on the linear operators. Although our results depend on the mixing forms being random, this imposed structure results in a very different type of random projection than those analyzed in the low-rank recovery literature to date.