While neural network approaches have made significant strides in resolving classical signal processing problems, it is often the case that hybrid approaches that draw insight from both signal processing and neural networks produce more complete solutions. In this paper, we present a hybrid classical digital signal processing/deep neural network (DSP/DNN) approach to source separation (SS) highlighting the theoretical link between variational autoencoder and classical approaches to SS. We propose a system that transforms the single channel under-determined SS task to an equivalent multichannel over-determined SS problem in a properly designed latent space. The separation task in the latent space is treated as finding a variational block-wise disentangled representation of the mixture. We show empirically, that the design choices and the variational formulation of the task at hand motivated by the classical signal processing theoretical results lead to robustness to unseen out-of-distribution data and reduction of the overfitting risk. To address the resulting permutation issue we explicitly incorporate a novel differentiable permutation loss function and augment the model with a memory mechanism to keep track of the statistics of the individual sources.

翻译：尽管神经网络方法在解决经典信号处理问题上取得了显著进展，但结合信号处理与神经网络洞察的混合方法往往能产生更完整的解决方案。本文提出了一种混合经典数字信号处理/深度神经网络（DSP/DNN）的源分离（SS）方法，凸显了变分自编码器与经典SS方法之间的理论联系。我们设计了一个系统，将单通道欠定SS任务转化为在适当设计的潜在空间中等价的多通道过定SS问题。潜在空间中的分离任务被视为寻找混合信号的变分块状解耦表示。实验表明，受经典信号处理理论结果启发而采用的设计选择与变分公式化，能够提升对未见过分布外数据的鲁棒性并降低过拟合风险。为解决由此产生的排列问题，我们显式引入了一种新颖的可微排列损失函数，并通过记忆机制增强模型以追踪各个源的统计特征。