# Deformation-Compensated Learning for Image Reconstruction without Ground Truth

arXiv: https://arxiv.org/abs/2107.05533 · HTML: https://mlsanity.com/paper/2107.05533/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 89 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [A Deep Learning Framework for Unsupervised Affine and Deformable Image Registration](https://mlsanity.com/paper/1809.06130/) (2018)
- [Deep Plug-and-Play Super-Resolution for Arbitrary Blur Kernels](https://mlsanity.com/paper/1903.12529/) (2019)
- [Deep Learning in Medical Image Registration: A Review](https://mlsanity.com/paper/1912.12318/) (2019)
- [DeepRED: Deep Image Prior Powered by RED](https://mlsanity.com/paper/1903.10176/) (2019)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [Plug and play methods for magnetic resonance imaging (long version)](https://mlsanity.com/paper/1903.08616/) (2019)
- [Time-Dependent Deep Image Prior for Dynamic MRI](https://mlsanity.com/paper/1910.01684/) (2019)
- [Image Restoration using Total Variation Regularized Deep Image Prior](https://mlsanity.com/paper/1810.12864/) (2018)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [Probabilistic Noise2Void: Unsupervised Content-Aware Denoising](https://mlsanity.com/paper/1906.00651/) (2019)

## Built on by (most cited first, 9 of 9)

- [A theoretical framework for self-supervised MR image reconstruction using sub-sampling via variable density Noisier2Noise](https://mlsanity.com/paper/2205.10278/) (2022)
- [Deep Learning for Retrospective Motion Correction in MRI: A Comprehensive Review](https://mlsanity.com/paper/2305.06739/) (2023)
- [Benchmarking Self-Supervised Learning Methods for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2502.14009/) (2025)
- [Fully Unsupervised Dynamic MRI Reconstruction via Diffeo-Temporal Equivariance](https://mlsanity.com/paper/2410.08646/) (2024)
- [Efficient Model-Based Deep Learning via Network Pruning and Fine-Tuning](https://mlsanity.com/paper/2311.02003/) (2023)
- [Self-Supervised Deep Equilibrium Models for Inverse Problems with Theoretical Guarantees](https://mlsanity.com/paper/2210.03837/) (2022)
- [A Unified Framework for Multimodal Image Reconstruction and Synthesis using Denoising Diffusion Models](https://mlsanity.com/paper/2602.08249/) (2026)
- [Regularization by Neural Style Transfer for MRI Field-Transfer Reconstruction with Limited Data](https://mlsanity.com/paper/2308.10968/) (2023)
- [Investigating Self-Supervised Image Denoising with Denaturation](https://mlsanity.com/paper/2405.01124/) (2024)

## Abstract (arXiv)

Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work on Noise2Noise (N2N) has shown the potential of using multiple noisy measurements of the same object as an alternative to having a ground-truth. However, existing N2N-based methods are not suitable for learning from the measurements of an object undergoing nonrigid deformation. This paper addresses this issue by proposing the deformation-compensated learning (DeCoLearn) method for training deep reconstruction networks by compensating for object deformations. A key component of DeCoLearn is a deep registration module, which is jointly trained with the deep reconstruction network without any ground-truth supervision. We validate DeCoLearn on both simulated and experimentally collected magnetic resonance imaging (MRI) data and show that it significantly improves imaging quality.