# MRI Reconstruction Using Deep Bayesian Estimation

arXiv: https://arxiv.org/abs/1909.01127 · HTML: https://mlsanity.com/paper/1909.01127/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2019.

## Built on by (most cited first, 29 of 29)

- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [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)
- [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)
- [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)
- [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)
- [Physics-Driven Autoregressive State Space Models for Medical Image Reconstruction](https://mlsanity.com/paper/2412.09331/) (2024)
- [BlindHarmony: "Blind" Harmonization for MR Images via Flow model](https://mlsanity.com/paper/2305.10732/) (2023)
- [Generative Autoregressive Transformers for Model-Agnostic Federated MRI Reconstruction](https://mlsanity.com/paper/2502.04521/) (2025)
- [Deep, Deep Learning with BART](https://mlsanity.com/paper/2202.14005/) (2022)
- [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)
- [Generative Priors for MRI Reconstruction Trained from Magnitude-Only Images Using Phase Augmentation](https://mlsanity.com/paper/2308.02340/) (2023)
- [Universal Generative Modeling for Calibration-free Parallel Mr Imaging](https://mlsanity.com/paper/2201.10210/) (2022)
- [Unsupervised Radar Point Cloud Enhancement via Arbitrary LiDAR Guided Diffusion Prior](https://mlsanity.com/paper/2505.09887/) (2025)
- [Generalized Deep Learning-based Proximal Gradient Descent for MR Reconstruction](https://mlsanity.com/paper/2211.16881/) (2022)
- [Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2212.05503/) (2022)
- [Diffusion Probabilistic Generative Models for Accelerated, in-NICU Permanent Magnet Neonatal MRI](https://mlsanity.com/paper/2505.15984/) (2025)
- [Conditional Denoising Diffusion Model-Based Robust MR Image Reconstruction from Highly Undersampled Data](https://mlsanity.com/paper/2510.06335/) (2025)
- [Accelerating Stroke MRI with Diffusion Probabilistic Models through Large-Scale Pre-training and Target-Specific Fine-Tuning](https://mlsanity.com/paper/2603.13007/) (2026)
- [Trustworthy MRI Reconstruction via Bayesian Uncertainty Quantification with Sparsity Prior Models](https://mlsanity.com/paper/2606.17343/) (2026)
- [Stochastic Finite-Transition Learning and Exploration for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2610.13095/) (2026)

## Abstract (arXiv)

Purpose: To develop a deep learning-based Bayesian inference for MRI reconstruction. Methods: We modeled the MRI reconstruction problem with Bayes's theorem, following the recently proposed PixelCNN++ method. The image reconstruction from incomplete k-space measurement was obtained by maximizing the posterior possibility. A generative network was utilized as the image prior, which was computationally tractable, and the k-space data fidelity was enforced by using an equality constraint. The stochastic backpropagation was utilized to calculate the descent gradient in the process of maximum a posterior, and a projected subgradient method was used to impose the equality constraint. In contrast to the other deep learning reconstruction methods, the proposed one used the likelihood of prior as the training loss and the objective function in reconstruction to improve the image quality. Results: The proposed method showed an improved performance in preserving image details and reducing aliasing artifacts, compared with GRAPPA, ℓ1-ESPRiT, and MODL, a state-of-the-art deep learning reconstruction method. The proposed method generally achieved more than 5 dB peak signal-to-noise ratio improvement for compressed sensing and parallel imaging reconstructions compared with the other methods. Conclusion: The Bayesian inference significantly improved the reconstruction performance, compared with the conventional ℓ1-sparsity prior in compressed sensing reconstruction tasks. More importantly, the proposed reconstruction framework can be generalized for most MRI reconstruction scenarios.