TABLE I.

Summary of the Pixelation Density Functions Compared

PDF	Formulations	Note
D 1	$D_1{\mid }_j=\{\begin{array}{ccc}\hfill \mathrm{int}\left\{{\log }_s\frac{\max \left[Q_j,j=1,\dots ,N\right]}{Q_j}\right\},\hfill & \hfill \mathit{when}\hfill & \hfill j\notin \Re \hfill \\ \hfill 0,\hfill & \hfill \mathit{otherwise}\hfill & \hfill \hfill \end{array}\phantom{\}}$	PDF depends on the weighted correlation between the responses of the system to gamma ray emissions in the target-region and in other regions. Defined based on FIM.
D 2	$D_2{\mid }_j=\{\begin{array}{ccc}\hfill \mathrm{int}\left\{{\log }_s\frac{\max \left[Q_j\cdot \left(1∕r_j^t\right),j=1,\dots ,N\right]}{Q_{\mathit{ij}}\cdot \left(1∕r_j^t\right)}\right\},\hfill & \hfill \mathit{when}\hfill & \hfill j\notin \Re \hfill \\ \hfill 0,\hfill & \hfill \mathit{otherwise}\hfill & \hfill \hfill \end{array}\phantom{\}}$	PDF depends on both FIM and how far a pixel is from the center of a target-region. More aggressive in reducing the number of pixels in object space.
D 3	$D_3{\mid }_j=\{\begin{array}{ccc}\hfill \mathrm{int}\left\{{\log }_s\frac{\max \left[1∕r_j^t\right],j=1,\dots ,N}{1∕r_j^t}\right\},\hfill & \hfill \mathit{when}\hfill & \hfill j\notin \Re \hfill \\ \hfill 0,\hfill & \hfill \mathit{otherwise}\hfill & \hfill \hfill \end{array}\phantom{\}}$	PDF depends on the linear distance r only. Emphasize the importance of the target-region only, without considering the correlation with other regions in the object-space.