Fourier-based approach to interpolation in single-slice helical computed tomography

Area of Science:

• Medical Imaging
• Computed Tomography (CT)
• Image Reconstruction

Background:

• Longitudinal aliasing is a detrimental artifact in helical CT reconstructions.
• Undersampling in the longitudinal direction and incomplete exploitation of fanbeam data contribute to aliasing.
• Existing methods like linear interpolation do not fully eliminate aliasing.

Purpose of the Study:

• To demonstrate that redundant fanbeam data can eliminate longitudinal aliasing in helical CT.
• To develop and evaluate a Fourier-based algorithm (180FT) for aliasing suppression.
• To compare the performance of Fourier-based methods with linear interpolation approaches.

Main Methods:

• Development and evaluation of a Fourier-based algorithm (180FT) utilizing redundant fanbeam data.
• Implementation of a background Fourier-based approach (360FT) using only directly measured data.
• Comparison of 180FT and 360FT with linear interpolation counterparts (180LI and 360LI).
• Exploitation of fast Fourier transform and Fourier shift theorem for generating equispaced transverse slices.

Main Results:

• The 180FT algorithm effectively suppresses longitudinal aliasing when fanbeam data is properly utilized, especially for pitches near 1 or lower.
• Fourier-based approaches generate fanbeam sinograms for slice-by-slice reconstruction.
• 180FT demonstrates a clear advantage in aliasing suppression compared to linear interpolation methods.

Conclusions:

• Redundant fanbeam data, when used properly with algorithms like 180FT, can satisfy a generalized sampling theorem to eliminate longitudinal aliasing.
• The 180FT approach represents a significant advancement towards achieving uniform longitudinal resolution in helical CT.
• Fourier-based reconstruction offers superior aliasing suppression compared to linear interpolation techniques in helical CT.