  Positron emission tomographs (PET) do not measure an image directly. Instead,
they measure at the boundary of the field-of-view (FOV) of PET tomograph a
sinogram that consists of measurements of the sums of all the counts along the
lines connecting two detectors. As there is a multitude of detectors build-in
typical PET tomograph structure, there are many possible detector pairs that
pertain to the measurement. The problem is how to turn this measurement into an
image (this is called imaging). Decisive improvement in PET image quality was
reached with the introduction of iterative reconstruction techniques. This
stage was reached already twenty years ago (with the advent of new powerful
computing processors). However, three dimensional (3D) imaging remains still a
challenge. The purpose of the image reconstruction algorithm is to process this
imperfect count data for a large number (many millions) of lines-of-responce
(LOR) and millions of detected photons to produce an image showing the
distribution of the labeled molecules in space.
