An investigation of temporal regularization techniques for dynamic PET reconstructions using temporal splines.

Area of Science:

• Medical Imaging
• Nuclear Medicine
• Image Reconstruction

Background:

• Dynamic positron emission tomography (PET) requires accurate reconstruction of time-activity curves (TACs).
• Temporal basis functions are crucial for modeling dynamic PET data.
• Evaluating different reconstruction algorithms and basis function parameters is essential for optimizing image quality.

Purpose of the Study:

• To investigate the efficacy of temporal B-spline basis functions for dynamic PET data reconstruction.
• To compare Maximum Likelihood (ML) and Maximum A-Posteriori (MAP) reconstruction methods.
• To evaluate the impact of B-spline parameters and develop an adaptive knot placement strategy.

Main Methods:

• Simulated dynamic list-mode PET data were used for reconstruction tasks.
• Reconstructions were performed using ML and MAP frameworks with varying B-spline parameters (order, number, knot placement).
• MAP reconstructions incorporated a penalty on the integrated squared curvature of TACs.

Main Results:

• Higher order B-spline bases reduced both bias and variance in reconstructions.
• Increased basis functions improved modeling of fast TAC changes but increased noise.
• MAP and ML reconstructions outperformed Gaussian post-smoothed ML in bias-variance properties.
• Adaptive knot placement with limited temporal basis functions provided effective regularization, especially for fast-changing TACs.

Conclusions:

• Temporal B-spline basis functions are effective for dynamic PET reconstruction.
• Adaptive knot placement combined with a limited number of basis functions offers a robust regularization strategy.
• This approach enhances accuracy and reduces noise, particularly for complex TACs like blood input functions.