# LWGNet: Learned Wirtinger Gradients for Fourier Ptychographic Phase Retrieval

arXiv: https://arxiv.org/abs/2208.04283 · HTML: https://mlsanity.com/paper/2208.04283/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 8 Aug 2022.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Data-Driven Design for Fourier Ptychographic Microscopy](https://mlsanity.com/paper/1904.04175/) (2019)
- [Solving Fourier ptychographic imaging problems via neural network modeling and TensorFlow](https://mlsanity.com/paper/1803.03434/) (2018)
- [Phase retrieval for Fourier Ptychography under varying amount of measurements](https://mlsanity.com/paper/1805.03593/) (2018)
- [Accelerated Wirtinger Flow for Multiplexed Fourier Ptychographic Microscopy](https://mlsanity.com/paper/1803.03714/) (2018)
- [Full-field Fourier ptychography (FFP): spatially varying pupil modeling and its application for rapid field-dependent aberration metrology](https://mlsanity.com/paper/1905.00162/) (2019)

## Built on by (most cited first, 2 of 2)

- [PtychoDV: Vision Transformer-Based Deep Unrolling Network for Ptychographic Image Reconstruction](https://mlsanity.com/paper/2310.07504/) (2023)
- [Complex-valued Retrievals From Noisy Images Using Diffusion Models](https://mlsanity.com/paper/2212.03235/) (2022)

## Abstract (arXiv)

Fourier Ptychographic Microscopy (FPM) is an imaging procedure that overcomes the traditional limit on Space-Bandwidth Product (SBP) of conventional microscopes through computational means. It utilizes multiple images captured using a low numerical aperture (NA) objective and enables high-resolution phase imaging through frequency domain stitching. Existing FPM reconstruction methods can be broadly categorized into two approaches: iterative optimization based methods, which are based on the physics of the forward imaging model, and data-driven methods which commonly employ a feed-forward deep learning framework. We propose a hybrid model-driven residual network that combines the knowledge of the forward imaging system with a deep data-driven network. Our proposed architecture, LWGNet, unrolls traditional Wirtinger flow optimization algorithm into a novel neural network design that enhances the gradient images through complex convolutional blocks. Unlike other conventional unrolling techniques, LWGNet uses fewer stages while performing at par or even better than existing traditional and deep learning techniques, particularly, for low-cost and low dynamic range CMOS sensors. This improvement in performance for low-bit depth and low-cost sensors has the potential to bring down the cost of FPM imaging setup significantly. Finally, we show consistently improved performance on our collected real data.