![]() Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Practical implementation of tetrahedral mesh reconstruction in emission tomography The results show that, with an appropriately generated set of mesh points, the irregular grid reconstruction methods can out-perform reconstructions on a regular grid for mathematical phantoms, in terms of the performance measures evaluated. The unconstrained nature of point placement in some of the irregular mesh-based reconstruction strategies has superior activity recovery for small, low-contrast image regions. The exact parallel projection data of this object are obtained analytically using a parallel projector, and multiple Poisson noise realizations of these exact data are generated and reconstructed using the different point generation strategies. For evaluation purposes, an object consisting of overlapping spheres with varying activity is simulated. For the tetrahedral reconstructions, of the five point generation methods that are evaluated, three use image priors. The maximum likelihood expectation maximization reconstruction algorithm is used. A similar analysis is performed for regular grid reconstructions that use voxel basis functions. The evaluation is performed using the recovery coefficient, as well as voxel- and template-based estimates of bias and variance measures, computed over specific regions in the reconstructed image. A linear image model is employed to obtain the reconstruction system matrix and five point generation strategies are studied. In this work, a 3D point cloud tetrahedral mesh reconstruction method is evaluated for quantitative tasks. Accordingly, a number of reconstruction-related parameters must be optimized for best performance. This is achieved through an appropriate choice of the image space model, the selection of an optimal set of points and the use of any available prior information during the reconstruction process. Tomographic reconstruction on an irregular grid may be superior to reconstruction on a regular grid. ![]() ![]() Evaluation of a 3D point cloud tetrahedral tomographic reconstruction method
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