Deep Learning Meets Adaptive Filtering: A Stein's Unbiased Risk Estimator Approach
This work addresses the challenge of enhancing adaptive filtering for signal processing applications, though it is incremental as it builds on existing unrolling methods.
This paper tackled the problem of improving adaptive filtering algorithms like RLS and EASI by unrolling them into deep neural networks and training them with Stein's unbiased risk estimator (SURE), resulting in Deep RLS and Deep EASI networks that outperform the original algorithms in source signal estimation.
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.