# Training Adaptive Reconstruction Networks for Blind Inverse Problems

arXiv: https://arxiv.org/abs/2202.11342 · HTML: https://mlsanity.com/paper/2202.11342/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 107 references that are in the map.
- First posted on arXiv 23 Feb 2022.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Blind Super-Resolution With Iterative Kernel Correction](https://mlsanity.com/paper/1904.03377/) (2019)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Learning a Convolutional Neural Network for Non-uniform Motion Blur Removal](https://mlsanity.com/paper/1503.00593/) (2015)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [A Neural Approach to Blind Motion Deblurring](https://mlsanity.com/paper/1603.04771/) (2016)
- [Learning to Deblur](https://mlsanity.com/paper/1406.7444/) (2014)
- [Solving Inverse Problems With Deep Neural Networks -- Robustness Included?](https://mlsanity.com/paper/2011.04268/) (2020)
- [TorchRadon: Fast Differentiable Routines for Computed Tomography](https://mlsanity.com/paper/2009.14788/) (2020)
- [Unrolled Optimization with Deep Priors](https://mlsanity.com/paper/1705.08041/) (2017)
- [Blind Image Deconvolution using Deep Generative Priors](https://mlsanity.com/paper/1802.04073/) (2018)
- [Learning The Invisible: A Hybrid Deep Learning-Shearlet Framework for Limited Angle Computed Tomography](https://mlsanity.com/paper/1811.04602/) (2018)
- [B-spline Parameterized Joint Optimization of Reconstruction and K-space Trajectories (BJORK) for Accelerated 2D MRI](https://mlsanity.com/paper/2101.11369/) (2021)
- [Graph-Based Blind Image Deblurring From a Single Photograph](https://mlsanity.com/paper/1802.07929/) (2018)
- [PILOT: Physics-Informed Learned Optimized Trajectories for Accelerated MRI](https://mlsanity.com/paper/1909.05773/) (2019)
- [Deep Phase Decoder: Self-calibrating phase microscopy with an untrained deep neural network](https://mlsanity.com/paper/2001.09803/) (2020)

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

- [Block Coordinate Plug-and-Play Methods for Blind Inverse Problems](https://mlsanity.com/paper/2305.12672/) (2023)
- [Reconstruct Anything Model: a lightweight general model for computational imaging](https://mlsanity.com/paper/2503.08915/) (2025)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)

## Abstract (arXiv)

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly.Second, we illustrate that this training procedure allows tackling challenging blind inverse problems.Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging (MRI) with sensitivity estimation and off-resonance effects, computerized tomography (CT) with a tilted geometry and image deblurring with Fresnel diffraction kernels.