Spline Driven: High Accuracy Projectors for Tomographic Reconstruction From Few Projections

Area of Science:

• Medical Imaging
• Computational Science
• Image Reconstruction

Background:

• Accurate data modeling is crucial for tomographic iterative reconstruction, particularly with limited projections.
• Current voxel and ray-driven projectors offer speed but sacrifice accuracy.
• Existing methods like distance-driven models and blobs have limitations in accuracy or computational cost.

Purpose of the Study:

• To develop and evaluate a novel projector using separable B-splines as object basis functions.
• To approximate the projection of B-splines using a computationally efficient 2D separable model.
• To assess the trade-off between approximation quality and computational complexity by adjusting B-spline degree and sampling.

Main Methods:

• Utilized separable B-splines as basis functions for object representation.
• Developed a 2D separable model to approximate the projection of these B-spline basis functions.
• Quantitatively compared the proposed projector's accuracy against distance-driven and Long et al.'s models through numerical experiments.

Main Results:

• The proposed B-spline projector demonstrates improved accuracy compared to existing methods.
• Reconstruction quality is better preserved with fewer projections using the new projector.
• Cubic B-spline projector requires approximately double the operations of voxel basis function models but offers higher accuracy.

Conclusions:

• Separable B-spline projectors offer a viable alternative for accurate tomographic reconstruction.
• This approach can enhance system resolution or reduce required projection counts, potentially lowering patient radiation dose.
• The B-spline projector provides a flexible trade-off between accuracy and computational demands.