Noise Analysis and Optimization of Spatial Partition in Functional Imaging

Abstract

Sequential data obtained in the tracer kinetic study is usually expressed by a sum of decaying exponentials q (t) = pΣi=1 A_i exp (-α_it) . In this study propagation of the Poissonian fluctuation of radioactivity to the fluactuation of parameters a and A was discussed by using the Fisher's information matrix and the Cramér-Rao's inequality. Thus the effect of the variations of temporal sampling interval and of total observation time on the coefficient of variations for parameters a and A were investigated.
The increased coefficient of variations due to the super-shortlife of radionuclide was also discussed.
A fundamental theorem relevant to the functional imaging was observed, which states that the coefficient of variations of parameters are inversely proportional to square root of the administered tracer dose.
Hence, S/N ratio given by the inverse of the coefficient of variation for each pixel of N×N-partitioned image is one N-th of that of the total kinetic parameters provided that the kinetics is spatially uniform. Then the information capacity on each pixel was defined. Finally, an analytical expression of the optimal number of the partition maximizing the total information capacity given by N² times the information capacity of each pixel was derived.
These theories were successfully applied to the ¹³³Xe washout curves from lung.