This paper revisits two prominent adaptive filtering algorithms, namely recursive least squares (RLS) and equivariant adaptive source separation (EASI), through the lens of algorithm unrolling. 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, enabling efficient source signal estimation by leveraging a training process. To further enhance performance, we propose training these deep unrolled networks utilizing a surrogate loss function grounded on Stein's unbiased risk estimator (SURE). Our empirical evaluations demonstrate that the Deep RLS and Deep EASI networks outperform their underlying algorithms. Moreover, the efficacy of SURE-based training in comparison to conventional mean squared error loss is highlighted by numerical experiments. The unleashed potential of SURE-based training in this paper sets a benchmark for future employment of SURE either for training purposes or as an evaluation metric for generalization performance of neural networks.

翻译：本文通过算法展开的视角，重新审视了两种经典的自适应滤波算法——递归最小二乘（RLS）和等变自适应源分离（EASI）。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级，通过利用训练过程实现高效的源信号估计。为进一步提升性能，我们提出利用基于斯坦因无偏风险估计器（SURE）的替代损失函数来训练这些深度展开网络。实验评估表明，Deep RLS和Deep EASI网络在性能上优于其基础算法。此外，数值实验凸显了基于SURE的训练相比传统均方误差损失的有效性。本文揭示了SURE训练的潜力，为未来将SURE用于训练目的或作为神经网络泛化性能评估指标奠定了基础。