# Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork

arXiv: https://arxiv.org/abs/2101.04348 · HTML: https://mlsanity.com/paper/2101.04348/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 71 references that are in the map.
- First posted on arXiv 12 Jan 2021.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Phase Retrieval using Alternating Minimization](https://mlsanity.com/paper/1306.0160/) (2013)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Model-Driven Deep Learning for Physical Layer Communications](https://mlsanity.com/paper/1809.06059/) (2018)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Neural Proximal Gradient Descent for Compressive Imaging](https://mlsanity.com/paper/1806.03963/) (2018)
- [Unrolled Optimization with Deep Priors](https://mlsanity.com/paper/1705.08041/) (2017)
- [Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problems](https://mlsanity.com/paper/2002.09611/) (2020)
- [Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow](https://mlsanity.com/paper/1605.08285/) (2016)
- [Deep MIMO Detection](https://mlsanity.com/paper/1706.01151/) (2017)
- [PhaseMax: Convex Phase Retrieval via Basis Pursuit](https://mlsanity.com/paper/1610.07531/) (2016)
- [Deep HyperNetwork-Based MIMO Detection](https://mlsanity.com/paper/2002.02750/) (2020)
- [Inverse Problems, Deep Learning, and Symmetry Breaking](https://mlsanity.com/paper/2003.09077/) (2020)
- [Solving Phase Retrieval with a Learned Reference](https://mlsanity.com/paper/2007.14621/) (2020)
- [Expectation Consistent Approximate Inference: Generalizations and Convergence](https://mlsanity.com/paper/1602.07795/) (2016)
- [UPR: A Model-Driven Architecture for Deep Phase Retrieval](https://mlsanity.com/paper/2003.04396/) (2020)

## Built on by (most cited first, 3 of 3)

- [Unfolding-Aided Bootstrapped Phase Retrieval in Optical Imaging](https://mlsanity.com/paper/2203.01695/) (2022)
- [Towards Practical Single-shot Phase Retrieval with Physics-Driven Deep Neural Network](https://mlsanity.com/paper/2208.08604/) (2022)
- [Res-U2Net: Untrained Deep Learning for Phase Retrieval and Image Reconstruction](https://mlsanity.com/paper/2404.06657/) (2024)

## Abstract (arXiv)

Phase retrieval (PR) is an important component in modern computational imaging systems. Many algorithms have been developed over the past half-century. Recent advances in deep learning have introduced new possibilities for a robust and fast PR. An emerging technique called deep unfolding provides a systematic connection between conventional model-based iterative algorithms and modern data-based deep learning. Unfolded algorithms, which are powered by data learning, have shown remarkable performance and convergence speed improvement over original algorithms. Despite their potential, most existing unfolded algorithms are strictly confined to a fixed number of iterations when layer-dependent parameters are used. In this study, we develop a novel framework for deep unfolding to overcome existing limitations. Our development is based on an unfolded generalized expectation consistent signal recovery (GEC-SR) algorithm, wherein damping factors are left for data-driven learning. In particular, we introduce a hypernetwork to generate the damping factors for GEC-SR. Instead of learning a set of optimal damping factors directly, the hypernetwork learns how to generate the optimal damping factors according to the clinical settings, thereby ensuring its adaptivity to different scenarios. To enable the hypernetwork to adapt to varying layer numbers, we use a recurrent architecture to develop a dynamic hypernetwork that generates a damping factor that can vary online across layers. We also exploit a self-attention mechanism to enhance the robustness of the hypernetwork. Extensive experiments show that the proposed algorithm outperforms existing ones in terms of convergence speed and accuracy and still works well under very harsh settings, even under which many classical PR algorithms are unstable.