Table 1.
Definitions of the variables used in this work, listed in the sequence of appearance.
| Variables | Definitions |
|---|---|
| x, y, z | Coordinates of the PET image space reference frame XYZ. |
| r, u | The in-plane variables of the LOR-PDF function. The r and u axes are parallel to x and z axes, respectively. |
| d | The depth variable along LOR, starts from one predetermined (e.g., higher detector block index) end of LOR. |
| j, J | Image voxel index, and the number of image voxels, respectively. |
| i, I | LOR index, and the number of LORs, respectively. |
| Vi | The rectangular tube volume of LORi. |
| p() | Probability density function. |
| cij | Probability of emission from voxel j contributing to LOR i. |
| φ, θ | In-plane and out-of-plane orientation angle of LOR at the starting-side of LOR. |
| b | The separation between a LOR’s ending and starting side detector block indices. |
| N | The number of detector blocks in a detector ring. |
| L | Length of LOR |
| D | Diameter of detector ring |