High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

Abstract

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.

Qualitative and Quantitative Evaluation of Blob-Based Time-of-Flight PET Image Reconstruction in Hybrid Brain PET/MR Imaging

“…This study showed that all reconstructions up to four iterations are executed within 30 min and almost all combinations could be executed within an hour. These results are consistent with previous studies [ 13 ]. Therefore, all proposed parameter combinations could be used in a clinical setting.…”

“…However, due to statistical noise, filtering is often required at the expense of reduced contrast and spatial resolution loss. The use of spherically symmetric basis functions (blobs) as opposed to voxels improves upon the former, with the blob-based reconstruction resulting in less image noise, without loss of resolution within a range of basis function parameters [ 10 – 13 ]. In addition, the smoother, overlaying spatial distribution of blobs will better represent the smoother biological transitions compared to the discontinuous sharp boundaries of voxels [ 14 ].…”

Medical image processing on the GPU – Past, present and future

“…Several papers have focused on new algorithms for image reconstruction, including a sparse matrix approach (Zhou and Qi, 2011), a particle filter approach (Yu et al, 2011a) and a spherical basis approach (Cabello et al, 2012). Image quality can be further improved by including scatter correction in the reconstruction algorithm (Wirth et al, 2009;Barker et al, 2009;Kim and Ye, 2011;Magdics et al, 2011), which adds an additional computational load.…”

Massively parallelizable list‐mode reconstruction using a Monte Carlo‐based elliptical Gaussian model

“…The method was validated using simulated and real NEMA 2008 image quality phantoms, Derenzo phantoms and a real Na 22 point source. The results were compared with a specifi commercial histogram-mode OSEM algorithm based on a precalculated system matrix.…”

“…19 When the SM is calculated using MC methods, real measurements, or complex numerical approximations, it must be precomputed and stored off line to keep the reconstruction time low, thus requiring enormous storage space for 3D PET imaging. Size reduction is provided by histogram compression, axial and rotational symmetries, 20,21 polarvoxel symmetries, 22,23 quasi-symmetries, 8 axial mashing, 24 and factorization as a product of sparse matrices. 25 It has been shown that MC calculated SM can be stored in programmable graphic processing units (GPUs), which have typically very limited memory resources.…”