Marrying Compressed Sensing and Deep Signal Separation

TL;DR

This paper explores integrating compressed sensing with deep autoencoders to perform blind signal separation directly on compressed data, enabling efficient, real-time signal processing without decompression.

Contribution

It introduces a novel compressive autoencoder framework for blind signal separation directly on compressed signals, combining CS and deep learning in a unified pipeline.

Findings

Successfully separates signals from compressed measurements of MNIST and E-MNIST datasets

Provides theoretical insights into the compressive BSS problem

Demonstrates potential for real-time, bandwidth-efficient signal processing

Abstract

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.