Next: Triple-Weighted Integration Method
Up: Mathematical Analysis
Previous: Introduction
Since the time required to perform a least squares curve fitting would
be prohibitive, a simpler approach to solving the problem is required.
One technique is to use a weighted integration method. We initially
approached the problem by assuming that 
was negligibly small,
in which case the 
term is eliminated from equation
(4). Taking equation (4) with 
eliminated, and integrating both sides from time 0 to the end of the
last frame, we get:
We can then take this equation, and divide it by a weighted version
of itself:
cancels out of this equation, leaving us with an equation
that only involves 
. The left side of equation
(6) is easily evaluated by integrating the PET data.
The right side of equation (6) is not easily solved for
, so a different approach was taken. A look-up table was
generated relating values of 
to resulting values of the
right hand side of equation (6). A linear
interpolation was then performed to choose values of 
from
this look-up table for each point in the left hand side of equation
(6).