Abstract
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Objectives We evaluate the noise propagation characteristics of a tomographic reconstruction method based on an adaptive tetrahedral mesh image representation.
Methods Analysis of the reconstruction matrix was done using the singular value decomposition (SVD), followed by the Truncated-SVD (TSVD) reconstruction. Simulated SPECT projections were used. A mean projection dataset with approximately 4 million count was created by summing 100 noisy projection datasets, each generated using SIMSET. Using the mean dataset, the tetrahedral reconstruction mesh and system matrix were generated. TSVD reconstructions of the mean and noisy projection data was performed for varying truncation points and corresponding to each point, a mean signal-to-noise-ratio (SNR) was computed using the entire reconstructed dataset. The mean of the reconstructed mean dataset was taken as the signal value. Noise in the reconstruction was approximated from the variance of the reconstructed noisy datasets. A similar analysis was performed for a regular voxel based reconstruction system matrix and for a region of interest (ROI) based reconstruction using the tetrahedral mesh.
Results The SNR of the adaptive mesh based system matrix depends on the number of nodes in the reconstructed image. The average SNR for the tetrahedral case is higher by at least 15 dB compared to the voxel based case. The computed condition numbers show that the tetrahedral mesh system matrix is better conditioned than the regular-grid system matrix.
Conclusions Within the framework of the TSVD reconstruction method, the adaptive mesh-grid based system matrix has superior noise propagation characteristics compared to the regular voxel based system matrix.
Research Support This work was supported in part by the National Cancer Institute, National Institutes of Health under Grant R21 CA123057 and American Heart Association, Scientist Development Grant, Grant 0735328N.
- © 2009 by Society of Nuclear Medicine