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CT Material Decomposition using Spectral Diffusion Posterior Sampling

Xiao Jiang, Grace J. Gang, J. Webster Stayman

TL;DR

This work tackles spectral CT material decomposition, an ill-posed inverse problem, by marrying a learned priors via score-based diffusion with a physics-informed data-fidelity term through diffusion posterior sampling (DPS). It introduces Jumpstarted Spectral DPS (JSDPS), incorporating a fast initialization and gradient-approximation to stabilize the reverse process and cut computation time substantially. Across dual-layer and dual-kVp CT systems, JSDPS delivers the highest accuracy, lowest uncertainty, and lowest computational cost compared with SDPS and traditional MBMD, while maintaining robustness to system variations. The approach holds promise for faster, more reliable material decomposition in spectral CT and demonstrates strong transferability of a learned prior across different spectral detectors.

Abstract

In this work, we introduce a new deep learning approach based on diffusion posterior sampling (DPS) to perform material decomposition from spectral CT measurements. This approach combines sophisticated prior knowledge from unsupervised training with a rigorous physical model of the measurements. A faster and more stable variant is proposed that uses a jumpstarted process to reduce the number of time steps required in the reverse process and a gradient approximation to reduce the computational cost. Performance is investigated for two spectral CT systems: dual-kVp and dual-layer detector CT. On both systems, DPS achieves high Structure Similarity Index Metric Measure(SSIM) with only 10% of iterations as used in the model-based material decomposition(MBMD). Jumpstarted DPS (JSDPS) further reduces computational time by over 85% and achieves the highest accuracy, the lowest uncertainty, and the lowest computational costs compared to classic DPS and MBMD. The results demonstrate the potential of JSDPS for providing relatively fast and accurate material decomposition based on spectral CT data.

CT Material Decomposition using Spectral Diffusion Posterior Sampling

TL;DR

This work tackles spectral CT material decomposition, an ill-posed inverse problem, by marrying a learned priors via score-based diffusion with a physics-informed data-fidelity term through diffusion posterior sampling (DPS). It introduces Jumpstarted Spectral DPS (JSDPS), incorporating a fast initialization and gradient-approximation to stabilize the reverse process and cut computation time substantially. Across dual-layer and dual-kVp CT systems, JSDPS delivers the highest accuracy, lowest uncertainty, and lowest computational cost compared with SDPS and traditional MBMD, while maintaining robustness to system variations. The approach holds promise for faster, more reliable material decomposition in spectral CT and demonstrates strong transferability of a learned prior across different spectral detectors.

Abstract

In this work, we introduce a new deep learning approach based on diffusion posterior sampling (DPS) to perform material decomposition from spectral CT measurements. This approach combines sophisticated prior knowledge from unsupervised training with a rigorous physical model of the measurements. A faster and more stable variant is proposed that uses a jumpstarted process to reduce the number of time steps required in the reverse process and a gradient approximation to reduce the computational cost. Performance is investigated for two spectral CT systems: dual-kVp and dual-layer detector CT. On both systems, DPS achieves high Structure Similarity Index Metric Measure(SSIM) with only 10% of iterations as used in the model-based material decomposition(MBMD). Jumpstarted DPS (JSDPS) further reduces computational time by over 85% and achieves the highest accuracy, the lowest uncertainty, and the lowest computational costs compared to classic DPS and MBMD. The results demonstrate the potential of JSDPS for providing relatively fast and accurate material decomposition based on spectral CT data.
Paper Structure (20 sections, 16 equations, 4 figures, 1 table, 2 algorithms)

This paper contains 20 sections, 16 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Spectral Deep Posterior Sampling
  4. Score-based Generative Model (SGM) for Inverse Problems
  5. Diffusion Posterior Sampling for Material Decomposition
  6. Strategies for Fast and Stable SPDS
  7. Instability of SDPS
  8. Jumpstarted Sampling
  9. Gradient Approximation
  10. Unconditional Multi-Material Generation
  11. Dataset Generation
  12. Network Training
  13. Conditional Posterior Sampling for Different Spectral Systems
  14. Evaluation
  15. Results
  16. ...and 5 more sections

Figures (4)

  • Figure 1: SDPS Workflow: Basis material images are concatenated to form $\textbf{x}_0$. The forward process progressively perturbs images with noise, and a noise prediction network is trained. The reverse process uses DDPM sampling to progressively denoise the image and uses a likelihood-based update to enforce data consistency.
  • Figure 2: Decomposed water (top, W/L: $1.2/0.6~g/ml$) and Calcium (bottom, W/L: $0.05/0.1~g/ml$) images. Left to right: Image-domain decomposition, JSDPS without gradient approximation, JSDPS with gradient approximation, ground truth. Computational time for eight outputs is provided in the bottom left corner.
  • Figure 3: Decomposed water (top, W/L: $1.2/0.6~g/ml$) and Calcium (bottom, W/L: $0.05/0.1~g/ml$) for (left to right): MBMD, SDPS, JSDPS, ground truth.
  • Figure 4: Bias and standard deviation map for SDPS and JSDPS. Here we only show the results of dual-kVp system, which is similar to that of the dual-layer system.