Initial value selection of the model parameters in the curve fitting phase of the dynamic SPECT imaging

摘要

The dynamic SPECT (Single Photon Emission Computed Tomography) reconstruction algorithm developed in our prior work reconstructs the parameters of the time activity curve for each image voxel directly from the projection images. In each iterations of the SPECT reconstruction beyond the static 3D MLEM (Maximum Likelihood Expectation Maximization) step, the algorithm performs a fitting process for each voxel in order to estimate the parameters describing the function of the examined organ considering that the time frames are not independent from each other. In real cases the fitted curve is nonlinear function of these parameters, it is usually described as the sum of exponential functions. In order to estimate the parameters properly, an iterative root-finding method is applied. In the current study the Newton-Raphson method is used. The selection of a proper initial value for the root-finding method is critical in order to achieve convergence of the fitting process. If the initial guess is not appropriate, the root-finding algorithm can diverge or converge to an inappropriate parameter set that can result in unacceptable reconstructed parameters. This affects then the subsequent MLEM iterations, also neighboring voxels and breaks the reconstruction.In this work we investigated different methods to calculate the initial values of the fitting process and evaluated the reconstructed parameter set of the dynamic SPECT reconstruction algorithm. Three different methods are investigated, one that uses the fitted parameters of the previous MLEM iteration, one that is based on the sum of the geometrical series of the exponentials and one that calculates the best guess using both methods. The three methods were compared by benchmark reconstruction cases using a mathematical phantom. In each reconstruction different initial value selection method was applied then the time activity curves of the voxels belonging to the same tissue were statistically evaluated using the reconstructed parameters. In the study no significant differences were found in the mean value of the reconstructed parameters. The standard deviation of the parameters was similar between the two simple approaches, however, the combination of the methods resulted in better statistical performance.