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

Area of Science:

• Medical Imaging
• Nuclear Medicine
• Image Reconstruction

Background:

• Iterative image reconstruction in 3D PET requires accurate system models.
• Computational demands of 3D projectors limit reconstruction speed.
• Fourier rebinning offers computational advantages but often lacks accuracy for complex systems.

Purpose of the Study:

• To develop a fast forward and back projector pair for 3D PET iterative image reconstruction.
• To integrate accurate system modeling with computationally efficient Fourier rebinning techniques.
• To improve the speed and accuracy of 3D PET image reconstruction.

Main Methods:

• A novel projector pair based on inverse Fourier rebinning was developed.
• A factored system matrix incorporating shift-variant sinogram blur kernels was used.
• Corrections for nonuniform radial sampling and nonconstant oblique angles were implemented.
• Maximum a posteriori (MAP) reconstruction was performed on simulated and in vivo data.

Main Results:

• The new projector pair significantly reduces computation time (by an order of magnitude) compared to traditional 3D projectors.
• It achieves accurate system modeling by accounting for detector-pair response.
• A small loss in resolution at the field-of-view edge was observed.
• Corrections improved sinogram accuracy and reconstructed image quality.

Conclusions:

• The developed projector pair offers a computationally efficient solution for 3D PET iterative image reconstruction.
• It successfully combines the speed of Fourier rebinning with the accuracy of detailed system models.
• This approach is suitable for both simulated and in vivo PET data, enhancing clinical applicability.