This paper revisits two prominent adaptive filtering algorithms through the lens of algorithm unrolling, namely recursive least squares (RLS) and equivariant adaptive source separation (EASI), in the context of source estimation and separation. Building upon the unrolling methodology, we introduce novel task-based deep learning frameworks, denoted as Deep RLS and Deep EASI. These architectures transform the iterations of the original algorithms into layers of a deep neural network, thereby enabling efficient source signal estimation by taking advantage of a training process. To further enhance performance, we propose training these deep unrolled networks utilizing a loss function grounded on a Stein's unbiased risk estimator (SURE). Our empirical evaluations demonstrate the efficacy of this SURE-based approach for enhanced source signal estimation.

翻译：本文从算法展开的视角重新审视了两种著名的自适应滤波算法——递归最小二乘（RLS）和等变自适应源分离（EASI），并将其应用于源估计与分离问题。基于展开方法，我们提出了新颖的基于任务的深度学习框架，分别称为Deep RLS和Deep EASI。这些架构将原始算法的迭代过程转化为深度神经网络的层结构，从而通过利用训练过程实现高效的源信号估计。为了进一步提升性能，我们提出基于斯坦因无偏风险估计（SURE）的损失函数来训练这些深度展开网络。我们的实验评估证明了这种基于SURE的方法在增强源信号估计方面的有效性。