Generalized Fourier slice theorem for cone-beam image reconstruction

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• Cone-beam reconstruction theory has evolved since the 1960s.
• The Fourier slice theorem, initially for parallel beams, was extended to fan beams.
• A unified Fourier slice theorem for cone-beam geometry was proposed in 1995.

Purpose of the Study:

• To provide a detailed derivation and implementation of the Fourier slice theorem for cone-beam geometry.
• To address and resolve the 0/0 limit problem at the origin of Fourier space.
• To demonstrate the practical application and efficiency of the proposed method.

Main Methods:

• Derivation of the Fourier slice theorem for cone-beam geometry.
• Handling of the 0/0 type limit at the Fourier space origin.
• Implementation and testing with single circle and perpendicular circle source orbits.

Main Results:

• Successful derivation and implementation of the cone-beam Fourier slice theorem.
• Resolution of the 0/0 singularity, enabling accurate reconstruction.
• Demonstrated feasibility with example source orbits.

Conclusions:

• The developed Fourier slice theorem provides a robust method for cone-beam image reconstruction.
• Computational complexity can be managed, with potential for avoidance of interpolation.
• This work advances the field of cone-beam computed tomography reconstruction algorithms.