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Pixelwise Uncertainty Quantification of Accelerated MRI Reconstruction

Ilias I. Giannakopoulos, Lokesh B Gautham Muthukumar, Yvonne W. Lui, Riccardo Lattanzi

TL;DR

This work tackles the absence of automatic diagnostic-quality assessment for undersampled MRI reconstructions by introducing a pixelwise uncertainty framework based on conformalized quantile regression (QR) integrated with a state-of-the-art reconstruction network (E2E VarNet). The two-U-Net uncertainty module estimates lower and upper quantiles, which are calibrated on held-out data with a conformal prediction factor $\lambda$ to ensure finite-sample coverage at a $0.9$ level, yielding spatially resolved uncertainty maps. Quantitative results show strong alignment between calibrated QR uncertainty and true reconstruction error across brain and knee datasets and multiple acceleration factors, outperforming magnitude-based residual uncertainty, with regional and lesion-focused uncertainty localization. The framework supports adaptive acquisition by providing reliable uncertainty estimates without ground-truth references, enabling faster anomaly detection and potential dynamic balancing of scan time and diagnostic reliability in clinical MRI. The approach demonstrates robust uncertainty quantification that scales with undersampling and highlights pathologies, marking a step toward practical, time-adaptive MRI protocols.

Abstract

Parallel imaging techniques reduce magnetic resonance imaging (MRI) scan time but image quality degrades as the acceleration factor increases. In clinical practice, conservative acceleration factors are chosen because no mechanism exists to automatically assess the diagnostic quality of undersampled reconstructions. This work introduces a general framework for pixel-wise uncertainty quantification in parallel MRI reconstructions, enabling automatic identification of unreliable regions without access to any ground-truth reference image. Our method integrates conformal quantile regression with image reconstruction methods to estimate statistically rigorous pixel-wise uncertainty intervals. We trained and evaluated our model on Cartesian undersampled brain and knee data obtained from the fastMRI dataset using acceleration factors ranging from 2 to 10. An end-to-end Variational Network was used for image reconstruction. Quantitative experiments demonstrate strong agreement between predicted uncertainty maps and true reconstruction error. Using our method, the corresponding Pearson correlation coefficient was higher than 90% at acceleration levels at and above four-fold; whereas it dropped to less than 70% when the uncertainty was computed using a simpler a heuristic notion (magnitude of the residual). Qualitative examples further show the uncertainty maps based on quantile regression capture the magnitude and spatial distribution of reconstruction errors across acceleration factors, with regions of elevated uncertainty aligning with pathologies and artifacts. The proposed framework enables evaluation of reconstruction quality without access to fully-sampled ground-truth reference images. It represents a step toward adaptive MRI acquisition protocols that may be able to dynamically balance scan time and diagnostic reliability.

Pixelwise Uncertainty Quantification of Accelerated MRI Reconstruction

TL;DR

This work tackles the absence of automatic diagnostic-quality assessment for undersampled MRI reconstructions by introducing a pixelwise uncertainty framework based on conformalized quantile regression (QR) integrated with a state-of-the-art reconstruction network (E2E VarNet). The two-U-Net uncertainty module estimates lower and upper quantiles, which are calibrated on held-out data with a conformal prediction factor to ensure finite-sample coverage at a level, yielding spatially resolved uncertainty maps. Quantitative results show strong alignment between calibrated QR uncertainty and true reconstruction error across brain and knee datasets and multiple acceleration factors, outperforming magnitude-based residual uncertainty, with regional and lesion-focused uncertainty localization. The framework supports adaptive acquisition by providing reliable uncertainty estimates without ground-truth references, enabling faster anomaly detection and potential dynamic balancing of scan time and diagnostic reliability in clinical MRI. The approach demonstrates robust uncertainty quantification that scales with undersampling and highlights pathologies, marking a step toward practical, time-adaptive MRI protocols.

Abstract

Parallel imaging techniques reduce magnetic resonance imaging (MRI) scan time but image quality degrades as the acceleration factor increases. In clinical practice, conservative acceleration factors are chosen because no mechanism exists to automatically assess the diagnostic quality of undersampled reconstructions. This work introduces a general framework for pixel-wise uncertainty quantification in parallel MRI reconstructions, enabling automatic identification of unreliable regions without access to any ground-truth reference image. Our method integrates conformal quantile regression with image reconstruction methods to estimate statistically rigorous pixel-wise uncertainty intervals. We trained and evaluated our model on Cartesian undersampled brain and knee data obtained from the fastMRI dataset using acceleration factors ranging from 2 to 10. An end-to-end Variational Network was used for image reconstruction. Quantitative experiments demonstrate strong agreement between predicted uncertainty maps and true reconstruction error. Using our method, the corresponding Pearson correlation coefficient was higher than 90% at acceleration levels at and above four-fold; whereas it dropped to less than 70% when the uncertainty was computed using a simpler a heuristic notion (magnitude of the residual). Qualitative examples further show the uncertainty maps based on quantile regression capture the magnitude and spatial distribution of reconstruction errors across acceleration factors, with regions of elevated uncertainty aligning with pathologies and artifacts. The proposed framework enables evaluation of reconstruction quality without access to fully-sampled ground-truth reference images. It represents a step toward adaptive MRI acquisition protocols that may be able to dynamically balance scan time and diagnostic reliability.
Paper Structure (18 sections, 8 equations, 8 figures, 2 tables)

This paper contains 18 sections, 8 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Dataset
  4. Undersampling Strategy
  5. Baseline Reconstruction Network
  6. Uncertainty Estimation Framework
  7. Uncertainty Module Architecture
  8. Pixelwise Quantile Regression Training
  9. Magnitude of the Residual Training
  10. Conformal Prediction Calibration
  11. Evaluation of Uncertainty Reliability
  12. Correlation Metrics
  13. Results
  14. Quantitative assessment of uncertainty
  15. Qualitative assessment of uncertainty
  16. ...and 3 more sections

Figures (8)

  • Figure 1: E2E VarNet architecture. The input is the undersampled multi- coil k- space and the output is the reconstructed image. In each cascade, the inverse fast Fourier transform (iFFT) is applied to each undersampled k- space, and the resulting images are weighted with the corresponding coil sensitivities and are combined into a single image using the reduce operatorsriram2020end. The combined image is processed by a U- Net, whose output is then expanded sriram2020end back into individual coil images. These coil images are transformed to k- space using the FFT, after which data consistency is enforced. The final image is obtained using the root sum of squares (RSS) on the individual coil images obtained from the 12$^{\rm th}$ cascade.
  • Figure 2: (Left) Architecture of our proposed uncertainty estimation module. The output (reconstructed MR image) of the E2E VarNet is the input of two U- Nets, which learn pixelwise offsets that parameterize the lower and upper quantile bounds of the reconstruction uncertainty. Each U- Net output passes through a sigmoid activation, is multiplied by the E2E VarNet reconstruction, and is either added to or subtracted from the E2E VarNet's reconstruction to compute the upper and lower bound, respectively. The output that is added is treated as the upper quantile interval and the one that is subtracted is the lower quantile interval. (Right) In Calibration, the predicted offsets are scaled by the calibration factor $\lambda$ which is computed using conformal prediction in the calibration set. The uncertainty map is computed by subtracting the calibrated lower from the calibrated upper bound.
  • Figure 3: Distribution of Pearson correlations for the $4\times$ accelerated brain (top) and knee (bottom) reconstructions. The histograms compare QR- based (blue) and ResM- based (red) uncertainty estimates with the true reconstruction error for each case in the test datasets. QR- based correlations are systematically higher for both anatomies, indicating improved alignment with the true reconstruction error.
  • Figure 4: Comparison between the windowed absolute error (magnified 50 times), the QR- based, and the ResM- based uncertainty for one healthy and three abnormal brain cases. All reconstructions were performed with four- fold acceleration. Blurred versions of the error and the uncertainties, generated by Gaussian smoothing, are also shown. The QR- based uncertainty closely matches the absolute error distribution and in the abnormal cases it delineates the lesions, demonstrating superior localization of uncertainty compared to ResM.
  • Figure 5: Comparison between the windowed absolute error (magnified 50 times), the QR- based, and the ResM- based uncertainty for three knees. All reconstructions were performed with four- fold acceleration. Blurred versions of the error and the uncertainties, generated by Gaussian smoothing, are also shown. The QR- based uncertainty qualitatively matches the absolute error distribution unlike the ResM- based approach.
  • ...and 3 more figures