# PixCUE: Joint Uncertainty Estimation and Image Reconstruction in MRI using Deep Pixel Classification

arXiv: https://arxiv.org/abs/2303.00111 · HTML: https://mlsanity.com/paper/2303.00111/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 79 references that are in the map.
- First posted on arXiv 28 Feb 2023.

## Builds on (most cited first, 30 of 34)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [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)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (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)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Compressed Sensing MRI Reconstruction using a Generative Adversarial Network with a Cyclic Loss](https://mlsanity.com/paper/1709.00753/) (2017)
- [Deep Learning Methods for Parallel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1904.01112/) (2019)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition](https://mlsanity.com/paper/1902.03051/) (2019)
- [Swin Transformer for Fast MRI](https://mlsanity.com/paper/2201.03230/) (2022)
- [Uncertainty Quantification in Deep MRI Reconstruction](https://mlsanity.com/paper/1901.11228/) (2019)
- [Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Models](https://mlsanity.com/paper/2202.01479/) (2022)
- [Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction](https://mlsanity.com/paper/2102.06665/) (2021)
- [Deep learning for fast MR imaging: a review for learning reconstruction from incomplete k-space data](https://mlsanity.com/paper/2012.08931/) (2020)
- [Conditional Invertible Neural Networks for Medical Imaging](https://mlsanity.com/paper/2110.14520/) (2021)
- [Towards Lower-Dose PET using Physics-Based Uncertainty-Aware Multimodal Learning with Robustness to Out-of-Distribution Data](https://mlsanity.com/paper/2107.09892/) (2021)
- [Dual-domain Cascade of U-nets for Multi-channel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1911.01458/) (2019)
- [Towards Understanding the Invertibility of Convolutional Neural Networks](https://mlsanity.com/paper/1705.08664/) (2017)
- [Accelerating Quantitative Susceptibility Mapping using Compressed Sensing and Deep Neural Network](https://mlsanity.com/paper/2103.09375/) (2021)

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

- [Pixelwise Uncertainty Quantification of Accelerated MRI Reconstruction](https://mlsanity.com/paper/2601.13236/) (2026)
- [Self-Auditing Residual Drifting for Pathology-Preserving Accelerated Knee MRI](https://mlsanity.com/paper/2607.02428/) (2026)
- [CUPA-T2*: Covariance-Aware Uncertainty Propagation and Alignment for T2* Mapping in Accelerated MRI](https://mlsanity.com/paper/2608.08693/) (2026)

## Abstract (arXiv)

Deep learning (DL) models are capable of successfully exploiting latent representations in MR data and have become state-of-the-art for accelerated MRI reconstruction. However, undersampling the measurements in k-space as well as the over- or under-parameterized and non-transparent nature of DL make these models exposed to uncertainty. Consequently, uncertainty estimation has become a major issue in DL MRI reconstruction. To estimate uncertainty, Monte Carlo (MC) inference techniques have become a common practice where multiple reconstructions are utilized to compute the variance in reconstruction as a measurement of uncertainty. However, these methods demand high computational costs as they require multiple inferences through the DL model. To this end, we introduce a method to estimate uncertainty during MRI reconstruction using a pixel classification framework. The proposed method, PixCUE (stands for Pixel Classification Uncertainty Estimation) produces the reconstructed image along with an uncertainty map during a single forward pass through the DL model. We demonstrate that this approach generates uncertainty maps that highly correlate with the reconstruction errors with respect to various MR imaging sequences and under numerous adversarial conditions. We also show that the estimated uncertainties are correlated to that of the conventional MC method. We further provide an empirical relationship between the uncertainty estimations using PixCUE and well-established reconstruction metrics such as NMSE, PSNR, and SSIM. We conclude that PixCUE is capable of reliably estimating the uncertainty in MRI reconstruction with a minimum additional computational cost.