A Forward Regridding Method With Minimal Oversampling for Accurate and Efficient Iterative Tomographic Algorithms.

Area of Science:

• Medical Imaging
• Computational Science

Background:

• Reconstructing underconstrained tomographic data is challenging.
• Standard methods yield unsatisfactory results due to limited information.
• Iterative algorithms offer solutions by integrating prior knowledge.

Purpose of the Study:

• To present a novel, efficient Fourier-based forward projector for tomographic reconstruction.
• To address the computational bottleneck in iterative algorithms.
• To improve the speed of reconstructing underconstrained tomographic data sets.

Main Methods:

• Developed a Fourier-based forward projector using the regridding method with minimal oversampling.
• Implemented the Radon transform and its adjoint (backprojector) for iterative algorithms.
• Analyzed the computational complexity and accuracy compared to existing methods.

Main Results:

• The Fourier-based projector achieves O(N^2 log^2 N) complexity, outperforming current state-of-the-art operators.
• Demonstrated comparable accuracy to more sophisticated projectors.
• Significantly reduced computational cost for tomographic data reconstruction.

Conclusions:

• The proposed regridding method offers a substantial decrease in reconstruction time for iterative algorithms.
• This approach maintains high-quality results in tomographic data reconstruction.
• The Fourier-based projector is a valuable tool for accelerating iterative tomographic reconstruction processes.