Generalizable preconditioning strategies for MAP PET reconstruction using Poisson likelihood.

Area of Science:

• Medical Imaging
• Computational Science
• Image Reconstruction

Background:

• Positron emission tomography (PET) reconstruction is computationally intensive due to ill-conditioned problems.
• Existing methods struggle with slow optimization, necessitating research into acceleration techniques.

Purpose of the Study:

• To introduce a novel preconditioner for maximum a posteriori (MAP) PET reconstruction.
• To achieve approximately uniform spatial resolution and improve convergence speed.

Main Methods:

• Decomposition of the Hessian matrix into diagonal and circulant components.
• Utilizing Hessian expectation for the diagonal term and an apodized 2D ramp filter for the circulant term.
• Implementation within a conjugate gradient descent algorithm.

Main Results:

• The proposed preconditioner consistently achieves convergence in fewer than 10 iterations.
• The circulant component significantly accelerates convergence compared to diagonal-only methods.
• Demonstrated effectiveness on the PET Rapid Image reconstruction Challenge dataset.

Conclusions:

• Decomposing the Hessian is an effective strategy for accelerating MAP PET reconstruction.
• The novel preconditioner substantially enhances convergence speed for ill-conditioned Poisson PET problems.
• The method shows promise for improving the efficiency of PET image reconstruction.