# Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameters

arXiv: https://arxiv.org/abs/2405.02944 · HTML: https://mlsanity.com/paper/2405.02944/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 45 references that are in the map.
- First posted on arXiv 5 May 2024.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest](https://mlsanity.com/paper/1603.00275/) (2016)
- ["Double-DIP": Unsupervised Image Decomposition via Coupled Deep-Image-Priors](https://mlsanity.com/paper/1812.00467/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [Solving Linear Inverse Problems Using GAN Priors: An Algorithm with Provable Guarantees](https://mlsanity.com/paper/1802.08406/) (2018)
- [Compressed Sensing with Deep Image Prior and Learned Regularization](https://mlsanity.com/paper/1806.06438/) (2018)
- [Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation](https://mlsanity.com/paper/2005.03991/) (2020)
- [Algorithmic Guarantees for Inverse Imaging with Untrained Network Priors](https://mlsanity.com/paper/1906.08763/) (2019)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [Untrained networks for compressive lensless photography](https://mlsanity.com/paper/2103.07609/) (2021)
- [Algorithmic Aspects of Inverse Problems Using Generative Models](https://mlsanity.com/paper/1810.03587/) (2018)
- [Deep DIH : Statistically Inferred Reconstruction of Digital In-Line Holography by Deep Learning](https://mlsanity.com/paper/2004.12231/) (2020)
- [Scan-specific Self-supervised Bayesian Deep Non-linear Inversion for Undersampled MRI Reconstruction](https://mlsanity.com/paper/2203.00361/) (2022)

## Abstract (arXiv)

Inverse imaging problems (IIPs) arise in various applications, with the main objective of reconstructing an image from its compressed measurements. This problem is often ill-posed for being under-determined with multiple interchangeably consistent solutions. The best solution inherently depends on prior knowledge or assumptions, such as the sparsity of the image. Furthermore, the reconstruction process for most IIPs relies significantly on the imaging (i.e. forward model) parameters, which might not be fully known, or the measurement device may undergo calibration drifts. These uncertainties in the forward model create substantial challenges, where inaccurate reconstructions usually happen when the postulated parameters of the forward model do not fully match the actual ones. In this work, we devoted to tackling accurate reconstruction under the context of a set of possible forward model parameters that exist. Here, we propose a novel Moment-Aggregation (MA) framework that is compatible with the popular IIP solution by using a neural network prior. Specifically, our method can reconstruct the signal by considering all candidate parameters of the forward model simultaneously during the update of the neural network. We theoretically demonstrate the convergence of the MA framework, which has a similar complexity with reconstruction under the known forward model parameters. Proof-of-concept experiments demonstrate that the proposed MA achieves performance comparable to the forward model with the known precise parameter in reconstruction across both compressive sensing and phase retrieval applications, with a PSNR gap of 0.17 to 1.94 over various datasets, including MNIST, X-ray, Glas, and MoNuseg. This highlights our method's significant potential in reconstruction under an uncertain forward model.