Deep Learning Meets Adaptive Filtering: A Stein's Unbiased Risk Estimator Approach

TL;DR

This paper introduces deep unrolled versions of RLS and EASI adaptive filtering algorithms trained with Stein's unbiased risk estimator, leading to improved source signal estimation performance.

Contribution

It presents novel deep learning frameworks for RLS and EASI algorithms using unrolling and SURE-based training, advancing adaptive filtering methods.

Findings

Deep RLS and Deep EASI outperform original algorithms.

SURE-based training surpasses mean squared error loss.

Sets a benchmark for future SURE-based neural network training.

Abstract

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.