Non-uniform attenuation correction in SPET using a modified conjugate gradient reconstruction method.

We describe a non-uniform iterative attentuation correction method for single photon emission tomography (SPET) which uses transmission data. The method was derived using the general inverse problem theory. A cost functional which includes noise was derived and minimized using a weighted-least-square maximum a posteriori conjugate gradient (CG) method. The Hessian of the cost functional was modified by adding a noise term. The a priori value of the model data vector was neglected. The method was tested in a clinical cardiac SPET perfusion study. Prior to the emission scan, blank and transmission scans were acquired and used to obtain the non-uniform map of linear attenuation coefficients. The results of the study show that the new iterative method has a slightly better convergence rate than the standard CG method. Also, the corrected emission slices obtained by the new method were less noisy. Noise was measured as rms% and was reduced by a factor of 2.3 for the transmission scans and by a factor of 1.9 for the emission scans when reconstructed with the new method compared to the CG method. The new method provides a stable solution, whereas the standard CG method, for higher iterative steps, diverges. There is potential for improvement in the approach described here.