Exploring Out-of-distribution Detection for Sparse-view Computed Tomography with Diffusion Models

TL;DR

This work tackles detecting out-of-distribution (OOD) inputs in sparse-view CT reconstruction by repurposing diffusion models as learned priors for image reconstruction. It redefines input and reconstruction-error notions for sparse measurements, employing multi-scale reconstructions started from partially diffused inputs and evaluating OOD-ness via reconstruction errors in both sinogram and image domains. A weighting scheme balances conditional (data-fidelity–driven) and unconditional (prior-driven) reconstructions to improve robustness against highly informative measurements, though at the cost of potential false positives. The approach is demonstrated using a one-class MNIST-based setup to simulate CT-like reconstruction scenarios, revealing that sinogram-domain comparisons with conditional sampling are often most effective, while conditioning can sometimes mask OOD signals; the study outlines practical directions for improving reliability, such as adaptive weighting and multi-scale reconstruction strategies, toward real-world CT applications.

Abstract

Recent works demonstrate the effectiveness of diffusion models as unsupervised solvers for inverse imaging problems. Sparse-view computed tomography (CT) has greatly benefited from these advancements, achieving improved generalization without reliance on measurement parameters. However, this comes at the cost of potential hallucinations, especially when handling out-of-distribution (OOD) data. To ensure reliability, it is essential to study OOD detection for CT reconstruction across both clinical and industrial applications. This need further extends to enabling the OOD detector to function effectively as an anomaly inspection tool. In this paper, we explore the use of a diffusion model, trained to capture the target distribution for CT reconstruction, as an in-distribution prior. Building on recent research, we employ the model to reconstruct partially diffused input images and assess OOD-ness through multiple reconstruction errors. Adapting this approach for sparse-view CT requires redefining the notions of ``input'' and ``reconstruction error''. Here, we use filtered backprojection (FBP) reconstructions as input and investigate various definitions of reconstruction error. Our proof-of-concept experiments on the MNIST dataset highlight both successes and failures, demonstrating the potential and limitations of integrating such an OOD detector into a CT reconstruction system. Our findings suggest that effective OOD detection can be achieved by comparing measurements with forward-projected reconstructions, provided that reconstructions from noisy FBP inputs are conditioned on the measurements. However, conditioning can sometimes lead the OOD detector to inadvertently reconstruct OOD images well. To counter this, we introduce a weighting approach that improves robustness against highly informative OOD measurements, albeit with a trade-off in performance in certain cases.

Figures (9)

• Figure 1: Schematic of sparse-view imaging setup and reconstruction framework augmented with out-of-distribution detector.
• Figure 2: Diffusion-based OOD detection illustrations from a data manifold perspective. In each figure, input images undergo partial diffusion (green arrows) followed by denoising (orange arrows). Ideally, the reconstruction error is represented by the distance between the input and output, shown as matching-colored stars and circles in (a), and matching-colored circles and rhombuses in (b) and (c). In (a), the reconstruction is directed toward the learned ID data manifold, pulling $\hat{\textbf{x}}_{\text{out}}$ away from $\textbf{x}_{\text{out}}$, resulting in a larger reconstruction error. In (b) and (c), the inputs are FBP mappings of measurements (sinograms), which may lie on their own manifolds. The reconstruction errors between the ground-truth images and the reconstructions are not available due to the absence of ground-truths (stars). The subfigures (b) and (c) compare unconditional and conditional sampling for OOD detection, respectively. In (c), three different measurement subspaces are displayed. Regardless of the solver used, the measurement subspace always acts as an attractor and may confuse the OOD detector by diminishing the influence of the ID data manifold, as $\left\{ \textbf{x} \mid \textbf{A}\textbf{x} = \textbf{y}^1_{\text{out}}\right\}$ could potentially does.
• Figure 3: Example thumbnails from a scenario in which the diffusion model is trained on handwritten "4"s from the MNIST dataset lecun1998mnistdeng2012mnist to serve as a prior for the sparse-view CT reconstruction task. Performing OOD detection under these conditions requires distinguishing the FBP reconstructions of partially measured "4"s from those of other digits. Similar to semantic anomaly detection, the detector should treat covariate-shifted images as ID while identifying semantic shifts as OOD.
• Figure 4: Block diagrams illustrating alternative components across various spaces for reconstruction error. The black-bordered box encapsulates the diffusion model, which, given $t_0$ and the input $\mathbf{x}_0$ (the filtered-backprojected $y$), performs reconstruction starting from corrupted $\mathbf{x}_0$. Curved double arrows indicate potential comparisons used to measure the reconstruction error. The red dashed arrow indicates the classical comparison between the input and the output of the diffusion model, which does not seem valid in our case. The blue arrow extends the comparison to the projection domain by forward projecting the reconstruction. In the case of the purple arrow, the output is subjected to both forward projection and FBP, to further map the sparse-view reconstruction back into the image domain. In (b), the same comparisons are shown but this time by considering the conditional sample obtained through the CT reconstruction from partially diffused FBP images, represented by the red-bordered box surrounding the black-bordered one.
• Figure 5: Example unconditional and conditional reconstructions for nine different $t_0$'s, from the model trained on MNIST4. Rows 1-3 present reconstructions from full-view input images from MNIST4, MNIST6, and MNIST7, respectively, whereas rows 4-6 display reconstructions from FBP mappings of sparse measurements with 5 projection angles for the same images. The images in the final column of the conditional reconstruction section correspond to the estimated CT reconstructions, which can be compared to the ground-truths (GT) shown in the last column of the plot.