# PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval

arXiv: https://arxiv.org/abs/2309.04171 · HTML: https://mlsanity.com/paper/2309.04171/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 62 references that are in the map.
- First posted on arXiv 8 Sep 2023.

## Builds on (most cited first, 25 of 25)

- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Intriguing Findings of Frequency Selection for Image Deblurring](https://mlsanity.com/paper/2111.11745/) (2021)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems](https://mlsanity.com/paper/1505.05114/) (2015)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [VS-Net: Variable splitting network for accelerated parallel MRI reconstruction](https://mlsanity.com/paper/1907.10033/) (2019)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [TFPnP: Tuning-free Plug-and-Play Proximal Algorithm with Applications to Inverse Imaging Problems](https://mlsanity.com/paper/2012.05703/) (2020)
- [Alternating Phase Projected Gradient Descent with Generative Priors for Solving Compressive Phase Retrieval](https://mlsanity.com/paper/1903.02707/) (2019)
- [Experimental robustness of Fourier Ptychography phase retrieval algorithms](https://mlsanity.com/paper/1511.02986/) (2015)
- [Deep Iterative Reconstruction for Phase Retrieval](https://mlsanity.com/paper/1904.11301/) (2019)
- [Holographic image reconstruction with phase recovery and autofocusing using recurrent neural networks](https://mlsanity.com/paper/2102.12281/) (2021)
- [DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval](https://mlsanity.com/paper/2011.10475/) (2020)
- [Deep Geometric Distillation Network for Compressive Sensing MRI](https://mlsanity.com/paper/2107.04943/) (2021)
- [An Interpretable MRI Reconstruction Network with Two-grid-cycle Correction and Geometric Prior Distillation](https://mlsanity.com/paper/2205.07062/) (2022)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [DOLPHIn - Dictionary Learning for Phase Retrieval](https://mlsanity.com/paper/1602.02263/) (2016)
- [FAS-UNet: A Novel FAS-driven Unet to Learn Variational Image Segmentation](https://mlsanity.com/paper/2210.15164/) (2022)

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

- [A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing](https://mlsanity.com/paper/2309.07524/) (2023)
- [prNet: Data-Driven Phase Retrieval via Stochastic Refinement](https://mlsanity.com/paper/2507.09608/) (2025)
- [DLMMPR:Deep Learning-based Measurement Matrix for Phase Retrieval](https://mlsanity.com/paper/2511.12556/) (2025)

## Abstract (arXiv)

The problem of phase retrieval (PR) involves recovering an unknown image from limited amplitude measurement data and is a challenge nonlinear inverse problem in computational imaging and image processing. However, many of the PR methods are based on black-box network models that lack interpretability and plug-and-play (PnP) frameworks that are computationally complex and require careful parameter tuning. To address this, we have developed PRISTA-Net, a deep unfolding network (DUN) based on the first-order iterative shrinkage thresholding algorithm (ISTA). This network utilizes a learnable nonlinear transformation to address the proximal-point mapping sub-problem associated with the sparse priors, and an attention mechanism to focus on phase information containing image edges, textures, and structures. Additionally, the fast Fourier transform (FFT) is used to learn global features to enhance local information, and the designed logarithmic-based loss function leads to significant improvements when the noise level is low. All parameters in the proposed PRISTA-Net framework, including the nonlinear transformation, threshold parameters, and step size, are learned end-to-end instead of being manually set. This method combines the interpretability of traditional methods with the fast inference ability of deep learning and is able to handle noise at each iteration during the unfolding stage, thus improving recovery quality. Experiments on Coded Diffraction Patterns (CDPs) measurements demonstrate that our approach outperforms the existing state-of-the-art methods in terms of qualitative and quantitative evaluations. Our source codes are available at https://github.com/liuaxou/PRISTA-Net.