Iterative image reconstruction using inverse fourier rebinning for fully 3-D PET

Area of Science:

• Medical Imaging
• Physics
• Computer Science

Background:

• Iterative image reconstruction is crucial for 3D positron emission tomography (PET).
• Accurate system modeling is essential for high-quality PET images.
• Computational efficiency remains a challenge in 3D PET reconstruction.

Purpose of the Study:

• To introduce a fast forward and back projector pair for 3D PET iterative image reconstruction.
• To integrate Fourier rebinning with accurate system models for improved computational performance.
• To address inaccuracies in inverse Fourier rebinning for cylindrical PET scanners.

Main Methods:

• Developed a projector pair based on inverse Fourier rebinning.
• Incorporated shift-variant sinogram blur kernels for detector-pair response.
• Implemented a 2D projector followed by exact inverse rebinning for the forward projector.
• Utilized the transpose of the forward projector for the back projector.
• Compensated for nonuniform radial sampling and nonconstant oblique angles.

Main Results:

• The new projector pair achieves an order of magnitude less computation than fully 3D geometric projectors.
• A small loss in resolution at the edge of the field-of-view was observed.
• Corrections for sampling and oblique angle inaccuracies improved sinogram accuracy and image quality.
• Evaluated performance using maximum a posteriori (MAP) reconstruction on simulated and in vivo data.

Conclusions:

• The developed projector pair offers a computationally efficient alternative for 3D PET iterative reconstruction.
• The method successfully combines the speed of Fourier rebinning with the accuracy of detailed system models.
• The corrections implemented enhance the reliability of inverse Fourier rebinning in practical PET scanners.