Comparison of basis functions for 3D PET reconstruction using a Monte Carlo system matrix

Area of Science:

• Medical Imaging
• Computational Physics
• Nuclear Engineering

Background:

• Iterative statistical methods in emission tomography yield the best image quality.
• Scanner characterization using the system response matrix (SRM) is crucial for reconstruction accuracy.
• High-resolution small animal scanners present computational challenges for SRM calculation due to numerous crystal pairs and voxels.

Purpose of the Study:

• To optimize the calculation of the system response matrix (SRM) for emission tomography scanners.
• To evaluate the impact of different basis functions (polar, cubic, spherically symmetric) on image quality and computational efficiency.
• To compare the trade-offs between noise properties, spatial resolution, and computational cost using various reconstruction approaches.

Main Methods:

• Monte Carlo (MC) methods were employed to calculate the SRM, exploiting cylindrical symmetries to reduce simulation time and storage.
• The study utilized polar voxels, spherically symmetric basis functions on a polar grid, and cubic voxels.
• Reconstructed image quality was assessed based on noise and spatial resolution, comparing different basis functions and post-reconstruction filtering.

Main Results:

• Exploiting cylindrical symmetries in MC-based SRM calculation significantly reduces simulation time and storage requirements compared to standard methods.
• Polar voxels demonstrated comparable performance to cubic voxels in terms of image quality while offering computational advantages.
• Spherically symmetric basis functions (blobs) exhibited superior noise properties but slightly degraded spatial resolution compared to polar and cubic voxels.
• Post-reconstruction smoothing led to a ~50% degradation in spatial resolution, whereas spherically symmetric functions caused only ~6% degradation at similar noise levels.

Conclusions:

• Calculating the SRM using MC methods with cylindrical symmetries is an efficient approach for high-resolution emission tomography.
• Polar voxels provide a practical alternative to cubic voxels, balancing computational efficiency and image quality.
• Spherically symmetric basis functions offer significant noise reduction benefits, with minimal spatial resolution loss when compared to post-reconstruction filtering, making them advantageous for image quality trade-offs.