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.

翻译：盲信号分离（BSS）是一项重要且具有挑战性的信号处理任务。给定一个观测信号，该信号是多个未知（隐藏/潜在）信号的叠加，BSS的目标是仅从观测到的混合信号中恢复出独立的底层信号。作为一个欠定问题，BSS通常难以求解，而现代深度学习为工程师提供了一套有效的工具来解决此问题。例如，自编码器学习输入数据的低维隐藏编码，随后可用于执行信号分离。在实时系统中，常见的瓶颈在于将数据传输（通信）至中央控制端以等待决策。带宽限制决定了传输数据的频率与分辨率。为克服此限制，压缩感知（CS）技术允许直接采集压缩数据，并具备近乎最优的重构保证。本文探讨以下问题：能否将压缩采集与深度学习相结合用于BSS，以构建完整的“采集-分离-预测”流程？换言之，目标是在从未解压信号的情况下，直接对压缩采集的信号执行BSS。我们以图像数据（MNIST与E-MNIST）为例，展示了所提出的压缩自编码器方法如何解决压缩BSS问题，并提供了相关理论见解。