研究目的
To develop a hierarchical prior model based on Haar transformation and a Bayesian computational method for X-ray CT reconstruction, aiming to improve reconstruction performance with insufficient data (fewer projections or limited angles) in medical and industrial applications.
研究成果
The proposed HHBM method demonstrates superior reconstruction performance compared to QR and TV methods when dealing with insufficient projection data (fewer projections or limited angles). It is more robust to noise and hyperparameter initialization, making it suitable for practical applications in medical and industrial CT. Future work includes exploring other sparsity-enforcing priors and implementing posterior mean estimation via Variational Bayesian Approach.
研究不足
The method relies on Gaussian noise approximation, which may not hold for all X-ray CT scenarios (e.g., Poisson noise in low-count cases). Computational costs are high for large 3D data, and the JMAP estimator is used instead of more accurate but expensive methods like Variational Bayesian Approximation. Initialization of hyperparameters requires careful tuning, and the method's performance is sensitive to the choice of transformation level and prior distributions.
1：Experimental Design and Method Selection:
The study uses a Bayesian approach with a hierarchical structured prior model based on multilevel Haar transformation to enforce sparsity in the transform domain. The Joint Maximum A Posteriori (JMAP) estimation method is employed for optimization, with gradient descent algorithms for large 3D data sizes.
2：Sample Selection and Data Sources:
Simulations are conducted using a 3D simulated 'Shepp-Logan' phantom and a 3D real 'head' object, both of size 256^3, with projections generated from these objects.
3：List of Experimental Equipment and Materials:
The ASTRA toolbox is used for GPU-accelerated projection and back-projection operations. MATLAB is used for implementation, with codes available on GitHub.
4：Experimental Procedures and Operational Workflow:
Projections are acquired with varying numbers (e.g., 180, 90, 60, 45, 36, 18) and angles (e.g., 0-180 degrees, limited ranges). The HHBM method is compared with Quadratic Regularization (QR) and Total Variation (TV) methods. Metrics like RMSE, ISNR, PSNR, and SSIM are computed.
5：Data Analysis Methods:
Performance is evaluated using relative mean squared error (RMSE), improvement in signal-to-noise ratio (ISNR), peak signal-to-noise ratio (PSNR), and structural similarity index (SSIM).
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