Segmentation-guided MRI reconstruction for meaningfully diverse reconstructions

TL;DR

This work tackles the inherent uncertainty in accelerated MRI reconstruction, where ill-posed inverse problems yield numerous plausible images and segmentation outcomes. It introduces Segmentation Guided Reconstruction (SGR), a diffusion-model–based approach that guides sampling with segmentation-loss gradients to produce two reconstructions per class, yielding an upper-bound segmentation $S^{\uparrow}$ and a lower-bound segmentation $S^{\downarrow}$ with volumes $V_{seg}^{\uparrow}$ and $V_{seg}^{\downarrow}$ and an uncertainty boundary $S_{unc}$ between them. Compared to Repeated Reconstruction (RR), SGR delivers more reliable and meaningful segmentation diversity across acceleration factors, with higher precision in the lower-bound segmentation and higher recall in the upper-bound segmentation, while maintaining high image quality ($SSIM$, $PSNR$) and an expanding uncertainty boundary $V_{unc}$ at higher accelerations. The method enforces data-consistency during diffusion refinement and leverages a U-Net segmentation model trained on fully-sampled data, evaluated on the SKM-TEA dataset; code is available at the authors’ repository. Overall, SGR provides a practical, uncertainty-aware framework for MRI reconstruction that can support safer clinical decision-making by explicitly quantifying segmentation uncertainty through an upper/lower bound paradigm.

Abstract

Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as semantic segmentation. This uncertainty, however, is mostly not analyzed in the literature, even though probabilistic reconstruction models are commonly used. These models can be prone to ignore plausible but unlikely solutions like rare pathologies. Building on MRI reconstruction approaches based on diffusion models, we add guidance to the diffusion process during inference, generating two meaningfully diverse reconstructions corresponding to an upper and lower bound segmentation. The reconstruction uncertainty can then be quantified by the difference between these bounds, which we coin the 'uncertainty boundary'. We analyzed the behavior of the upper and lower bound segmentations for a wide range of acceleration factors and found the uncertainty boundary to be both more reliable and more accurate compared to repeated sampling. Code is available at https://github.com/NikolasMorshuis/SGR

Figures (6)

• Figure 1: Motivation. Repeated reconstruction tends to create MRI reconstructions that are conceptually similar and not meaningfully diverse. Similar results are also observed in downstream tasks like segmentation in our experiments. Our method in contrast only reconstructs two images, an upper bound ($x_0^{\uparrow}$) and a lower bound ($x_0^{\downarrow}$) reconstruction, corresponding to an upper ($V_{seg}^{\uparrow}$) and lower bound ($V_{seg}^{\downarrow}$) on the segmentation volume, giving an intuitive understanding of the segmentation uncertainty.
• Figure 2: Method explanation. For each inverse diffusion step $t$, we calculate $\nabla_{x_t} \mathcal{L}^{\uparrow /\downarrow}$ and include the gradient in the calculation of $x_{t-1}$, in order to increase (decrease) the segmentation volume and to get an upper- and lower-bound segmentation ($S^{\uparrow}$ and $S^{\downarrow}$).
• Figure 3: Sampling vs. adversarial guidance. Examples of lower- ($x_0^{\downarrow}$) and upper-bound ($x_0^{\uparrow}$) reconstructions (16x acc.) and segmentations ($S^{\downarrow}$, $S^{\uparrow}$) using our SGR method and the standard RR method. ($S^{f}$ is the segmentation of the fully-sampled image. Green: $S^{f} \& S^{\uparrow}$ or $S^{f} \& S^{\downarrow}$, Blue: $S^{f} > S^{\downarrow}$ or $S^{f} < S^{\uparrow}$, Red: $S^{f} < S^{\downarrow}$ or $S^{f} > S^{\uparrow}$)
• Figure 4: Analysis of different acceleration factors. For RR, we see that the uncertainty does not increase, even though very high accelerations are tested. Our method, in contrast, generates more reliable uncertainty boundaries.
• Figure 5: Results. Median score and percentile boundaries (25%, 75%) for different acceleration factors. Note that the upper and lower bound segmentation of our method are mostly correctly capturing the inherent uncertainty even for high acceleration factors: we have high precision (small amount of false-positives in $S^{\downarrow}$) and recall (small amount of false-negatives in $S^{\uparrow}$). The ratio of uncertain volume $V_{unc}=V_{seg}^{\uparrow}-V_{seg}^{\downarrow}$ over $V_{seg}^{\uparrow}$ also increases, better reflecting the true underlying uncertainty.