Fan beam image reconstruction with generalized Fourier slice theorem

Area of Science:

• Medical Imaging
• Image Reconstruction
• Computational Imaging

Background:

• The Fourier slice theorem is fundamental for parallel beam image reconstruction.
• Extending Fourier slice theorem to fan-beam geometry presents unique challenges for image reconstruction.

Purpose of the Study:

• To detail the generalized Fourier slice theorem (GFST) method for fan-beam image reconstruction.
• To compare the GFST method with the filtered backprojection (FBP) method for fan-beam geometry.

Main Methods:

• The GFST method directly populates the Fourier plane using fan-beam projection data in Cartesian coordinates, avoiding polar-to-Cartesian interpolation.
• An inverse fast Fourier transform is applied to the populated Fourier plane to obtain the reconstructed image.
• Comparison with the filtered backprojection (FBP) method involves analyzing interpolation strategies, filtering domains, and performance in short scan scenarios.

Main Results:

• GFST interpolates projection data, while FBP interpolates filtered projection data.
• GFST applies filtering in the Fourier domain, yielding location-invariant resolution, whereas FBP uses a ramp filter in the projection domain with location-variable resolution.
• GFST achieves an exact solution in short scan situations, a capability lacking in FBP.

Conclusions:

• The GFST method provides a robust alternative for fan-beam image reconstruction, particularly advantageous in short scan configurations.
• GFST offers advantages in interpolation and filtering strategies compared to FBP, leading to consistent resolution.
• Both GFST and FBP exhibit a computational complexity of O(N^3).