PET images are reconstructed in a similar fashion to CT. The main difference is in how the signal
is detected, in CT we project an external beam through tissue and measure attenuation.
In PET we detect the signal from an injected radioactive isotope in the tissue. Here we
see a typical PET image that has been overlaid on a gray CT image. Note that the resolution
is substantially less than that of CT or MRI, this lower resolution is largely due to the
smaller amount of information and lower signal to noise that is available during acquisition.
In order to understand PET reconstruction we first need to review the process by which
the PET signal is acquired. In a PET system the subject is placed in the scanner. The
scanners detector is called a scintillator ring and can detect extremely low signals,
in PET's case this signal consists of a single positron. In order to detect this each detector
element is quite large. Recent advances in technology have enabled smaller and smaller
elements in this array which in turn leads to better resolution. The use of cascade photo
diodes to replace the scintillator ring also increases the speed of acquisition that in
turn will also increase resolution. In PET imaging a radio tracer is then injected and
once this binds with the target tissue a collision event occurs, represented here as a star.
This results in two positrons being emitted in exactly opposite directions to each other
at the speed of light. Given their velocity, irrespective of their location in the object
these two positrons will hit the detector ring at essentially the same time. When this
happens the scanner records what is called a co-incidence event. As more of the PET tracer
binds at a location more collision events are then recorded as time progresses. The
time scale over which this happens is dependant on the tracers binding potential and the abundance
of what is being bound but typically is between 6 and 12 nanoseconds. Note that not all collision
events will be recorded, only those that occur in the same plane as the scintillator ring.
This is another factor that reduces the amount of signal that is available in a PET scanner.
Note that some modern scanners can detect some of the out of plane coincidence events
but only a small percentage more. If we now look at the case of where multiple simultaneous
tracer bindings are occurring. We can see that there will be multiple over-lapping co-incidence
events. While the events themselves are occurring simultaneously, the detection of the co-incidence
events will still occur independently given the immense speed of the positrons. The raw
output data from the scanner is then a series of points that represent the co-incidence
events, each event is represented as two points through which a line can be drawn. This is
called a Line or Response or LOR. From the data we don't know where along the LOR the
event occurred. More modern detectors with a higher time resolution can give an approximation
of where the event occurred within an accuracy of about a hundred millimetres. These systems
are called Time of Flight or TOF detectors and operate on a time scale of approximately
three nanoseconds. We can now visualise the reconstruction process by placing a probabilistic
line between each of the two points from the co-incidence event raw data. As we add more
and more of these events. The result is a final probabilistic map of the source of the
events. We haven't displayed the exact technical details of how this occurs as there are many
differing techniques. The most typically used technique involves first sorting the LOR's
into similar directions, grouping them into what are called sinograms and then reconstructing
them as per CT backprojection. Other techniques used statistical techniques such as expectation
maximisation to generate an inverse solution. What is similar between all these techniques
is that the end result is a probabilistic map of the source of the co-incidence events.