Biomedical Engineering Reference
In-Depth Information
2.11.4 Randoms Correction
As mentioned before, the basis of PET imaging is the coincidence detection
scheme, which registers a coincidence event (as well as LoR) if two photons
are detected within the coincidence timing window. This finite timing window
(typically 12 ns for BGO), however, cannot prevent the coincidence detectors
from registering random events that occur when two unrelated photons do not
originate from the same site of positron annihilation. The rate of registering ran-
dom coincidences by a detector pair relates to the rate of single events on each
detector and the width of the timing window. The random rate for a particular
LoR,
R
ij
, for a given pair of detectors
i
and
j
is
R
ij
=
2
τ
×
S
i
×
S
j
(2.14)
where
S
i
and
S
j
are the rate of single events of detector
i
and detector
j
, and 2
τ
is coincidence timing window. As the radioactivity increases, the event rate in
each detector also increases. The random event rate will increase as the square
of the activity and therefore correction for random coincidences is essential.
The most commonly used method for estimating the random coincidences
is the delayed coincidence detection method which employs two coincidence
detection circuits with an offset inserted within their coincidence timing win-
dows. The first coincidence detection circuit (called
prompt circuit
) is used to
measure the prompt coincidences, which equal the sum of the true coincidences
and the random coincidences. The second circuit is set up with an offset which
is much longer than the time width of the coincidence window. Because of the
offset in timing window, the second circuit records the so-called
delayed
coinci-
dences which are random events, whereas all true coincidences are effectively
discarded. To correct for random coincidences, the counts obtained from the
delayed circuit are subtracted from those obtained from the prompt circuit. The
resultant prompt events are then the “true” coincidences. However, because
the random events obtained from the first circuit are not exactly the same as
those obtained from the delayed circuit, subtraction of random events increases
the statistical noise.
2.11.5 Attenuation Correction
One of the most important data correction techniques for PET (and also SPECT)
studies is the correction for attenuation. Although the basic principles of image
