System matrix computation for iterative reconstruction algorithms in SPECT based on direct measurements

Abstract

A method for system matrix calculation in the case of iterative reconstruction algorithms in SPECT was implemented and tested. Due to a complex mathematical description of the geometry of the detector set-up, we developed a method for system matrix computation that is based on direct measurements of the detector response. In this approach, the influence of the acquisition equipment on the image formation is measured directly. The objective was to obtain the best quality of reconstructed images with respect to specified measures. This is indispensable in order to be able to perform reliable quantitative analysis of SPECT images. It is also especially important in non-hybrid gamma cameras, where not all physical processes that disturb image acquisition can be easily corrected. Two experiments with an 131 I point source placed at different distances from the detector plane were performed allowing the detector response to be acquired as a function of the point source distance. An analytical Gaussian function was fitted to the acquired data in both the one-and the two-dimensional case. A cylindrical phantom filled with a water solution of 131 I containing a region of "cold" spheres as well as a uniform solution (without any spheres) was used to perform algorithm evaluation. The reconstructed images obtained by using four different of methods system matrix computation were compared with those achieved using reconstruction software implemented in the gamma camera. The contrast of the spheres and uniformity were compared for each reconstruction result and also with the ranges of those values formulated by the AAPM (American Association of Physicists in Medicine). The results show that the implementation of the OSEM (Ordered Subsets Expectation Maximization) algorithm with a one-dimensional fit to the Gaussian CDR (Collimator-Detector Response) function provides the best results in terms of adopted measures. However, the fit of the two-dimensional function also gives satisfactory results. Furthermore, the CDR function has the potential to be applied to a fully 3D OSEM implementation. The lack of the CDR in system matrix calculation results in a very noisy image that cannot be used for diagnostic purposes.

Detection models for freehand SPECT reconstruction

“…To solve this inverse problem the system matrix A = (a ij ) has to be computed. Typical methods to obtain the system matrix are analytical models of the detector response of the system (Frey et al 1994, King et al 1996, or measurements of a point source at the positions of all voxels of the volume of interest (Tohme et al 2009, Borys et al 2011 and Monte Carlo simulations of the whole system (Bitar et al 2005). In Freehand SPECT, however, there is no fixed acquisition geometry, as the nuclear probe is moved by hand around the volume of interest.…”

Estimation of optimized timely system matrix with improved image quality in iterative reconstruction algorithm: A simulation study

“…The system matrix (SM) indicating relationship between the object and projection space is a main part of statistical image reconstruction algorithms. It is calculated by three methods as; (i) analytical method in which the common regions (CR) considering as interacting probability of emitted gamma photons with detector elements are calculated by geometrical relations [17,18,19,20,21]; (ii) Monte Carlo (MC) simulations by modeling a digital phantom and estimating projections, which the ratio of counts in i-th element of detector for the originated photons from j-th pixel of object matrix is considered as a i,j element of the SM [22,23,24]; and (iii) experimental method where the SM is obtained by measuring projections around the phantoms [25,26].…”