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Differentiable Score-Based Likelihoods: Learning CT Motion Compensation From Clean Images

Mareike Thies, Noah Maul, Siyuan Mei, Laura Pfaff, Nastassia Vysotskaya, Mingxuan Gu, Jonas Utz, Dennis Possart, Lukas Folle, Fabian Wagner, Andreas Maier

TL;DR

This work trains a score-based model to act as a probability density estimator for clean head CT images, and demonstrates that the likelihood can be utilized as a surrogate metric for motion artifact severity in the CT image facilitating the application of an iterative, gradient-based motion compensation algorithm.

Abstract

Motion artifacts can compromise the diagnostic value of computed tomography (CT) images. Motion correction approaches require a per-scan estimation of patient-specific motion patterns. In this work, we train a score-based model to act as a probability density estimator for clean head CT images. Given the trained model, we quantify the deviation of a given motion-affected CT image from the ideal distribution through likelihood computation. We demonstrate that the likelihood can be utilized as a surrogate metric for motion artifact severity in the CT image facilitating the application of an iterative, gradient-based motion compensation algorithm. By optimizing the underlying motion parameters to maximize likelihood, our method effectively reduces motion artifacts, bringing the image closer to the distribution of motion-free scans. Our approach achieves comparable performance to state-of-the-art methods while eliminating the need for a representative data set of motion-affected samples. This is particularly advantageous in real-world applications, where patient motion patterns may exhibit unforeseen variability, ensuring robustness without implicit assumptions about recoverable motion types.

Differentiable Score-Based Likelihoods: Learning CT Motion Compensation From Clean Images

TL;DR

This work trains a score-based model to act as a probability density estimator for clean head CT images, and demonstrates that the likelihood can be utilized as a surrogate metric for motion artifact severity in the CT image facilitating the application of an iterative, gradient-based motion compensation algorithm.

Abstract

Motion artifacts can compromise the diagnostic value of computed tomography (CT) images. Motion correction approaches require a per-scan estimation of patient-specific motion patterns. In this work, we train a score-based model to act as a probability density estimator for clean head CT images. Given the trained model, we quantify the deviation of a given motion-affected CT image from the ideal distribution through likelihood computation. We demonstrate that the likelihood can be utilized as a surrogate metric for motion artifact severity in the CT image facilitating the application of an iterative, gradient-based motion compensation algorithm. By optimizing the underlying motion parameters to maximize likelihood, our method effectively reduces motion artifacts, bringing the image closer to the distribution of motion-free scans. Our approach achieves comparable performance to state-of-the-art methods while eliminating the need for a representative data set of motion-affected samples. This is particularly advantageous in real-world applications, where patient motion patterns may exhibit unforeseen variability, ensuring robustness without implicit assumptions about recoverable motion types.
Paper Structure (11 sections, 6 equations, 3 figures, 1 table)

This paper contains 11 sections, 6 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Score-Based Diffusion Models
  4. Likelihood Computation
  5. Neural ODEs and Likelihood Target Function
  6. Motion Compensation
  7. Experiments and Results
  8. Discussion
  9. Conclusion
  10. Acknowledgments.
  11. Disclosure of Interests.

Figures (3)

  • Figure 1: Overview of the proposed pipeline. After training on motion-free images, the score model $\mathbf{s}_{\mathbf{\theta}}(\mathbf{x}, t)$ is used inside the likelihood target function. For each step of the gradient descent optimizer, we perform an intermediate reconstruction and evaluate the gradient of the likelihood function to pull the image closer to the distribution of clean images seen during training.
  • Figure 2: Comparison of target functions using root mean squared error (RMSE) ($\downarrow$) and SSIM ($\uparrow$) of the motion-compensated images as well as reprojection error (RPE) ($\downarrow$). The proposed method achieves similar results as the autofocus method despite never having seen any motion-affected images during training. The MSE target function can be considered an upper performance bound since it requires knowledge of the motion-free image at optimization time which is unrealistic in a clinical workflow.
  • Figure 3: Two example slices before and after motion compensation with autofocus and likelihood objective. A $\times3$ zoom of a region of interest is shown in the orange frame.