Purpose: The reconstruction of positron emission tomography images is a computationally intensive task which benefits from the use of increasingly complex physical models. Aiming to reduce the computational burden by means of a reduced system matrix, we present a list mode reconstruction approach based on maximum likelihood-expectation maximization and a sliced mesh support. Approach: The reconstruction strategy uses a fully 3D projection along series of 2D meshes arranged in the axial plane of the scanner. These series of meshes describe the continuous volumetric activity using a piece-wise linear function interpolated from the mesh elements. The mesh support is automatically adapted to the underlying structure of the activity by means of a remeshing process. This process finds a high-quality compact mesh representation constrained to a controlled interpolation error. Results: The method is tested using a Monte Carlo simulation of a Hoffman brain phantom and a National Electrical Manufacturers Association image quality phantom acquisition, using different sets of statistics. The reconstructions are compared against a voxelized reconstruction under different conditions, achieving similar or superior results. The number of parameters needed to reconstruct the image in voxel and mesh support is also compared, and the mesh reconstruction permits to reduce the number of nodes used to represent a complex image. Conclusions: The proposed reconstruction strategy reduces the number of parameters needed to describe the activity distribution by more than one order of magnitude for similar voxel size and with similar accuracy than state-of-the-art methods.
Keywords: compact representation; expectation maximization; iterative reconstruction; list mode; mesh modeling; positron emission tomography.
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