# What's in a Prior? Learned Proximal Networks for Inverse Problems

**Authors:** Zhenghan Fang, Sam Buchanan, Jeremias Sulam  
**arXiv:** [2310.14344](https://arxiv.org/abs/2310.14344)  
**Date:** 2023-10-22  
**Summary page:** https://www.summarizepaper.com/en/paper/2310.14344v2/

## Key points

- Authors Zhenghan Fang, Sam Buchanan, and Jeremias Sulam explore proximal operators in inverse problems and apply modern deep learning models.
- They introduce learned proximal networks (LPN) for data-driven nonconvex regularizers.
- The authors propose a training strategy called proximal matching to recover the log-prior of the true data distribution.
- LPNs offer unsupervised and expressive proximal operators with convergence guarantees for general inverse problems.
- The effectiveness of LPNs is demonstrated in solving realistic inverse problems using datasets like CelebA.
- LPNs are employed in tasks such as deblurring with PnP-ADMM methodology, comparing favorably with state-of-the-art methods like PnP-BM3D and PnP-DnCNN.
- Results show that LPNs achieve state-of-the-art performance and provide insights into learned priors from data.

## Summary

In the paper "What's in a Prior? Learned Proximal Networks for Inverse Problems," authors Zhenghan Fang, Sam Buchanan, and Jeremias Sulam explore the use of proximal operators in inverse problems and the application of modern deep learning models to address these challenges. The authors introduce a framework for developing learned proximal networks (LPN) that provide exact proximal operators for data-driven nonconvex regularizers. They also propose a new training strategy called proximal matching, which promotes the recovery of the log-prior of the true data distribution. These LPNs offer unsupervised and expressive proximal operators that can be used for general inverse problems with convergence guarantees. To demonstrate the effectiveness of LPNs, the authors showcase their capabilities in solving realistic inverse problems using datasets like CelebA. By employing LPNs in tasks such as deblurring with PnP-ADMM methodology, they compare their approach with state-of-the-art methods like PnP-BM3D and PnP-DnCNN. The results show that LPNs not only achieve state-of-the-art performance but also provide insights into the resulting priors learned from data. Overall, this research highlights the importance of incorporating learned proximal networks in addressing inverse problems and showcases their potential to improve performance and provide valuable insights into data priors.