# MR image reconstruction using deep density priors

arXiv: https://arxiv.org/abs/1711.11386 · HTML: https://mlsanity.com/paper/1711.11386/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 30 of 37)

- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Federated Learning of Generative Image Priors for MRI Reconstruction](https://mlsanity.com/paper/2202.04175/) (2022)
- [Explicitly Minimizing the Blur Error of Variational Autoencoders](https://mlsanity.com/paper/2304.05939/) (2023)
- [Generative Modeling in Sinogram Domain for Sparse-view CT Reconstruction](https://mlsanity.com/paper/2211.13926/) (2022)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Joint Motion Correction and Super Resolution for Cardiac Segmentation via Latent Optimisation](https://mlsanity.com/paper/2107.03887/) (2021)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [Accelerated Motion Correction with Deep Generative Diffusion Models](https://mlsanity.com/paper/2211.00199/) (2022)
- [Adversarial Robustness of MR Image Reconstruction under Realistic Perturbations](https://mlsanity.com/paper/2208.03161/) (2022)
- [Self-Supervised Adversarial Diffusion Models for Fast MRI Reconstruction](https://mlsanity.com/paper/2406.15656/) (2024)
- [MRI Reconstruction Using Deep Energy-Based Model](https://mlsanity.com/paper/2109.03237/) (2021)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRI](https://mlsanity.com/paper/2403.05245/) (2024)
- [K-space and Image Domain Collaborative Energy based Model for Parallel MRI Reconstruction](https://mlsanity.com/paper/2203.10776/) (2022)
- [NPB-REC: A Non-parametric Bayesian Deep-learning Approach for Undersampled MRI Reconstruction with Uncertainty Estimation](https://mlsanity.com/paper/2404.04550/) (2024)
- [Autoregressive Image Diffusion: Generation of Image Sequence and Application in MRI](https://mlsanity.com/paper/2405.14327/) (2024)
- [Robust multi-coil MRI reconstruction via self-supervised denoising](https://mlsanity.com/paper/2411.12919/) (2024)
- [Posterior temperature optimized Bayesian models for inverse problems in medical imaging](https://mlsanity.com/paper/2202.00986/) (2022)
- [Generative Priors for MRI Reconstruction Trained from Magnitude-Only Images Using Phase Augmentation](https://mlsanity.com/paper/2308.02340/) (2023)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [Cine cardiac MRI reconstruction using a convolutional recurrent network with refinement](https://mlsanity.com/paper/2309.13385/) (2023)
- [Diffusion Probabilistic Generative Models for Accelerated, in-NICU Permanent Magnet Neonatal MRI](https://mlsanity.com/paper/2505.15984/) (2025)
- [PRO: Projection Domain Synthesis for CT Imaging](https://mlsanity.com/paper/2506.13443/) (2025)
- [UPMRI: Unsupervised Parallel MRI Reconstruction via Projected Conditional Flow Matching](https://mlsanity.com/paper/2512.17493/) (2025)

## Abstract (arXiv)

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimation