  Blind signal separation (BSS) is an important and challenging signal
processing task. Given an observed signal which is a superposition of a
collection of unknown (hidden/latent) signals, BSS aims at recovering the
separate, underlying signals from only the observed mixed signal. As an
underdetermined problem, BSS is notoriously difficult to solve in general, and
modern deep learning has provided engineers with an effective set of tools to
solve this problem. For example, autoencoders learn a low-dimensional hidden
encoding of the input data which can then be used to perform signal separation.
In real-time systems, a common bottleneck is the transmission of data
(communications) to a central command in order to await decisions. Bandwidth
limits dictate the frequency and resolution of the data being transmitted. To
overcome this, compressed sensing (CS) technology allows for the direct
acquisition of compressed data with a near optimal reconstruction guarantee.
This paper addresses the question: can compressive acquisition be combined with
deep learning for BSS to provide a complete acquire-separate-predict pipeline?
In other words, the aim is to perform BSS on a compressively acquired signal
directly without ever having to decompress the signal. We consider image data
(MNIST and E-MNIST) and show how our compressive autoencoder approach solves
the problem of compressive BSS. We also provide some theoretical insights into
the problem.
