|
|
|
|
|
The GTM method according to Rousset [2] restricts the partial volume correction to the signal of the true objects which are constituted by VOIs. The relation of measured PET values (affected by the partial-volume effect) to the true PET values is given by the matrix equation below
with the following notations:
Ctrue |
Vector of the true average activity concentration in the different VOIs of interest. The vector length n equals the number of object VOIs. |
Cmeasured |
Actually measured average activity concentration in the different VOIs. |
GTM |
Geometric Transfer Matrix which describes the spill-over among all the VOIs. The matrix is square with nxn weighting elements wi,j which express the fraction of true activity spilled over from VOIi into VOIj. In practice, wi,j is calculated as follows: A binary map is created with 1 in all pixels of VOIi and 0 elsewhere. The map is convolved with the imaging Point-Spread Function (PSF), and in the resulting spillover map the average of all VOIj pixels calculated. |
The GTM equation above represents a system of linear equations. Once the weights have been calculated, the system can be solved for the true values Ctrue by matrix inversion. Rousset [2] has shown that this algorithm is robust to noise propagation during the correction process.