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

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.