Gradient-based geometry learning for fan-beam CT reconstruction

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• Differentiable computed tomography (CT) reconstruction operators enhance image analysis.
• Current methods often fix acquisition geometry, neglecting its impact on reconstruction quality.
• Precise acquisition geometry is crucial for high-quality CT reconstruction.

Purpose of the Study:

• To extend differentiable fan-beam CT reconstruction to optimize acquisition geometry.
• To enable gradient propagation from image space to geometry parameters.
• To apply this method for motion compensation and other calibration tasks.

Main Methods:

• Analytically derived fan-beam CT reconstruction with respect to acquisition geometry.
• Propagated gradient information from image loss functions to geometry parameters.
• Applied to rigid motion compensation using a neural network-parameterized cost function.

Main Results:

• Improved Structural Similarity Index Measure (SSIM) from 0.848 to 0.946 for motion-affected reconstructions.
• Generalization to real fan-beam sinograms (helical trajectory) with SSIM increase from 0.639 to 0.742.
• First autofocus-inspired algorithm optimized using analytical gradients.

Conclusions:

• The proposed method enables optimization of CT acquisition geometry for improved image reconstruction.
• Demonstrated effectiveness in motion compensation and potential for scanner calibration.
• Paves the way for hybrid deep learning and analytical gradient techniques in CT.