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

arXiv: https://arxiv.org/abs/2307.16708 · HTML: https://mlsanity.com/paper/2307.16708/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [Uncertainty Quantification in Deep MRI Reconstruction](https://mlsanity.com/paper/1901.11228/) (2019)
- [Unsupervised Learning with Stein's Unbiased Risk Estimator](https://mlsanity.com/paper/1805.10531/) (2018)
- [LoRD-Net: Unfolded Deep Detection Network with Low-Resolution Receivers](https://mlsanity.com/paper/2102.02993/) (2021)
- [Degrees of Freedom Analysis of Unrolled Neural Networks](https://mlsanity.com/paper/1906.03742/) (2019)
- [A Machine Learning Pipeline Stage for Adaptive Frequency Adjustment](https://mlsanity.com/paper/2007.01820/) (2020)
- [Leveraging Deep Stein's Unbiased Risk Estimator for Unsupervised X-ray Denoising](https://mlsanity.com/paper/1811.12488/) (2018)
- [Tractable Evaluation of Stein's Unbiased Risk Estimate with Convex Regularizers](https://mlsanity.com/paper/2211.05947/) (2022)
- [Deep-RLS: A Model-Inspired Deep Learning Approach to Nonlinear PCA](https://mlsanity.com/paper/2011.07458/) (2020)
- [One-Bit Compressive Sensing: Can We Go Deep and Blind?](https://mlsanity.com/paper/2203.11278/) (2022)

## Abstract (arXiv)

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.