
C
Multinomial distribution of
single-voxel imaging
In this appendix we derive the distribution p(y
1
|d
1
) from the basic principles
where y
1
is the vector of the number of detected events originated in a voxel 1
and d
1
is the number of decays in voxel 1. Therefore it is a model of a simple
imaging system with many detector elements and a single voxel. A figure
showing a schematic of such a s ystem is shown in Chapter 3 in Fig ure 3.5.
The der ivation may seem at first quite complex and convoluted, and the
result quite obvious. We strongly encourage, however, careful study of the
appendix, as it provides insights into a general approach o n handling the
statistics ...