Multi-Material Decomposition Research Based on Spectral Diffusion Posterior Sampling

Background Introduction

In the field of medical imaging, CT (Computed Tomography) technology is widely used in disease diagnosis and treatment planning. In recent years, spectral CT has become a research hotspot due to its ability to provide energy-dependent attenuation information. By using projection data from multiple energy channels, spectral CT can reconstruct density distributions of different materials—a process known as material decomposition. However, material decomposition is a highly nonlinear inverse problem. Traditional decomposition methods such as analytical decomposition and iterative/model-based decomposition have many limitations, including low computational efficiency, high noise levels, and strong model dependency. Additionally, although deep learning-based decomposition methods show significant improvements in accuracy and speed, they often lack explicit use of physical models, resulting in insufficient robustness.

To address these issues, a research team from Johns Hopkins University and the University of Pennsylvania proposed a new framework—spectral diffusion posterior sampling (spectral DPS). This method combines learned prior information with physical models, aiming to achieve fast, accurate, and stable multi-material decomposition. The study was published in IEEE Transactions on Biomedical Engineering in 2023.

Research Team and Publication Information

The research was jointly completed by Xiao Jiang, Grace J. Gang, and J. Webster Stayman. Xiao Jiang and J. Webster Stayman are from the Department of Biomedical Engineering at Johns Hopkins University, while Grace J. Gang is from the Department of Radiology at the University of Pennsylvania. The research received partial funding from the U.S. National Institutes of Health (NIH), and the paper was officially published in 2023.

Research Process and Details

1. Research Objectives and Methods

The main objective of the study was to develop a material decomposition framework that integrates physical models with deep learning priors to improve the accuracy and robustness of material decomposition in spectral CT. To this end, the research team proposed the spectral diffusion posterior sampling (spectral DPS) method, which is based on the diffusion posterior sampling (DPS) framework and combines unconditional network training with a physical system model.

2. Construction of the Spectral DPS Framework

The core idea of spectral DPS is to capture the target domain distribution by unconditionally training a score-based generative model (SGM). Then, image parameters are estimated through a reverse process, alternating between SGM reverse sampling and model-based updates to ensure that the generated images conform both to the target distribution and measurement data consistency.

Specifically, the spectral DPS framework includes the following key steps:

1. Unconditional Training: First, a two-material (water and calcium) dataset was generated using public CT datasets. Then, an unconditional residual UNet network was trained to learn the material prior distribution.
2. Reverse Sampling: During the reverse process, researchers reduced computational costs and variability through strategies such as jumpstart sampling, simplified Jacobian computation, and multi-step optimization.
3. Physical Model Integration: Spectral DPS combines the physical model of spectral CT with diffusion posterior sampling to achieve material decomposition by maximizing posterior probability.

3. Experimental Design and Evaluation

The research team evaluated spectral DPS on simulated dual-layer CT systems and kV-switching CT systems and conducted experiments on a physical cone-beam CT (CBCT) test bench. Specific experimental steps were as follows:

1. Simulation Experiments: By simulating the generation of 720 projection data points, the research team compared the performance of spectral DPS with several other material decomposition algorithms, including image-domain decomposition (IDD), model-based material decomposition (MBMD), InceptNet, and conditional denoising diffusion probabilistic model (conditional DDPM).
2. Physical Experiments: A biomimetic chest phantom was scanned on the physical CBCT system for material decomposition. Performance of spectral DPS on real data was assessed by comparison with single-energy FB reconstruction images.
3. Parameter Optimization: The research team determined the optimal hyperparameter combination for spectral DPS, including jumpstart time steps, number of subsets, and step size, via parameter sweeping to minimize sampling variability.

4. Main Results

1. Simulation Experiment Results: Spectral DPS performed excellently on both dual-layer CT and kV-switching CT systems, significantly reducing sampling variability and computational costs. Compared with baseline DPS, spectral DPS showed significant improvements in imaging accuracy and robustness, especially in handling low-contrast structures.
2. Physical Experiment Results: In the physical CBCT experiment, spectral DPS successfully preserved details of bronchi and bones in the lungs and achieved an error of less than 1% in density estimation in homogeneous regions. Moreover, spectral DPS excelled in avoiding artifacts, reducing sampling variability by 65.34% compared to baseline DPS.
3. Parameter Optimization Results: Through parameter optimization, spectral DPS not only minimized sampling variability but also significantly improved image PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index), indicating that parameter optimization reduced variability and enhanced image quality.

Conclusion and Significance

The spectral diffusion posterior sampling (spectral DPS) framework proposed in this study successfully combined physical models with deep learning prior information, achieving fast, accurate, and stable multi-material decomposition in spectral CT. Compared with traditional decomposition methods, spectral DPS shows significant improvements in imaging accuracy, robustness, and computational efficiency. Furthermore, the unconditional training feature of spectral DPS allows it to adapt to different spectral CT systems and imaging protocols, offering broad application prospects.

Research Highlights

1. Innovative Framework: Spectral DPS is the first to apply diffusion posterior sampling to spectral CT material decomposition, combining physical models with deep learning prior information, solving the limitations of traditional methods.
2. Efficiency and Robustness: Through strategies like jumpstart sampling, simplified Jacobian computation, and multi-step optimization, spectral DPS significantly reduces sampling variability and improves computational efficiency.
3. Wide Applicability: The unconditional training feature of spectral DPS enables it to adapt to different spectral CT systems without retraining for specific systems, offering broad application potential.

Other Valuable Information

The research team also explored the application potential of spectral DPS in multi-material decomposition and low-dose CT imaging and plans to further optimize network architecture and parameter settings in future research to enhance its performance. Additionally, the successful application of spectral DPS provides new insights into solving inverse problems in other medical imaging fields.