# Recurrent Inference Machines for Solving Inverse Problems

arXiv: https://arxiv.org/abs/1706.04008 · HTML: https://mlsanity.com/paper/1706.04008/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2017.

## Built on by (most cited first, 30 of 33)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Recurrent Variational Network: A Deep Learning Inverse Problem Solver applied to the task of Accelerated MRI Reconstruction](https://mlsanity.com/paper/2111.09639/) (2021)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration](https://mlsanity.com/paper/2312.15701/) (2023)
- [Conditional Variational Autoencoder for Learned Image Reconstruction](https://mlsanity.com/paper/2110.11681/) (2021)
- [Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning](https://mlsanity.com/paper/2206.07050/) (2022)
- [On Retrospective k-space Subsampling schemes For Deep MRI Reconstruction](https://mlsanity.com/paper/2301.08365/) (2023)
- [Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems](https://mlsanity.com/paper/2103.15138/) (2021)
- [Rethinking Temporal Fusion with a Unified Gradient Descent View for 3D Semantic Occupancy Prediction](https://mlsanity.com/paper/2504.12959/) (2025)
- [Fixed points of nonnegative neural networks](https://mlsanity.com/paper/2106.16239/) (2021)
- [Equilibrium Aggregation: Encoding Sets via Optimization](https://mlsanity.com/paper/2202.12795/) (2022)
- [Unsupervised Knowledge-Transfer for Learned Image Reconstruction](https://mlsanity.com/paper/2107.02572/) (2021)
- [R3L: Connecting Deep Reinforcement Learning to Recurrent Neural Networks for Image Denoising via Residual Recovery](https://mlsanity.com/paper/2107.05318/) (2021)
- [Machine learning-enabled velocity model building with uncertainty quantification](https://mlsanity.com/paper/2411.06651/) (2024)
- [Recurrent Localization Networks applied to the Lippmann-Schwinger Equation](https://mlsanity.com/paper/2102.00063/) (2021)
- [AAPM DL-Sparse-View CT Challenge Submission Report: Designing an Iterative Network for Fanbeam-CT with Unknown Geometry](https://mlsanity.com/paper/2106.00280/) (2021)
- [Recurrent Inference Machines as inverse problem solvers for MR relaxometry](https://mlsanity.com/paper/2106.07379/) (2021)
- [Assessment of Data Consistency through Cascades of Independently Recurrent Inference Machines for fast and robust accelerated MRI reconstruction](https://mlsanity.com/paper/2111.15498/) (2021)
- [Robust partial Fourier reconstruction for diffusion-weighted imaging using a recurrent convolutional neural network](https://mlsanity.com/paper/2105.09378/) (2021)
- [Deep MRI Reconstruction with Radial Subsampling](https://mlsanity.com/paper/2108.07619/) (2021)
- [Recurrent Inference Machine for Medical Image Registration](https://mlsanity.com/paper/2406.13413/) (2024)
- [Foreground color prediction through inverse compositing](https://mlsanity.com/paper/2103.13423/) (2021)
- [Learned Interferometric Imaging for the SPIDER Instrument](https://mlsanity.com/paper/2301.10260/) (2023)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Relaxometry Guided Quantitative Cardiac Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/2403.00549/) (2024)
- [ReQuestNet: A Foundational Learning model for Channel Estimation](https://mlsanity.com/paper/2508.08790/) (2025)
- [An inversion problem for optical spectrum data via physics-guided machine learning](https://mlsanity.com/paper/2404.02387/) (2024)
- [Evaluating structural uncertainty in accelerated MRI: are voxelwise measures useful surrogates?](https://mlsanity.com/paper/2503.10527/) (2025)
- [Optimal transport unlocks end-to-end learning for single-molecule localization](https://mlsanity.com/paper/2512.10683/) (2025)

## Abstract (arXiv)

Much of the recent research on solving iterative inference problems focuses on moving away from hand-chosen inference algorithms and towards learned inference. In the latter, the inference process is unrolled in time and interpreted as a recurrent neural network (RNN) which allows for joint learning of model and inference parameters with back-propagation through time. In this framework, the RNN architecture is directly derived from a hand-chosen inference algorithm, effectively limiting its capabilities. We propose a learning framework, called Recurrent Inference Machines (RIM), in which we turn algorithm construction the other way round: Given data and a task, train an RNN to learn an inference algorithm. Because RNNs are Turing complete [1, 2] they are capable to implement any inference algorithm. The framework allows for an abstraction which removes the need for domain knowledge. We demonstrate in several image restoration experiments that this abstraction is effective, allowing us to achieve state-of-the-art performance on image denoising and super-resolution tasks and superior across-task generalization.