Euromedim 2006 :1st European Conference on Molecular Imaging Technology

3-D Reconstruction from Compton Scattered Data Using Two Different Approaches to Implementing Projector-Backprojector Pair

9 May 2006, 14:00

1h

Palais du Pharo, Marseille

poster • Image reconstruction and processing Poster Session :Simulation, Modeling, Reconstruction

Speaker

Ms Soo Mee Kim (Department of Nuclear Medicine, Seoul National University College of Medicine)

Description

Iterative image reconstruction for Compton camera is computationally challenging since the projection and backprojection are performed on conical surfaces rather than along straight lines and there is a number of possible combinations of position and energy measurements. Therefore, computationally efficient implementation of a projector-backprojector pair without loss of quantitative accuracy is required. Methods: Two different approaches to conical surface integral were investigated for rapid calculations of an approximately factorized system matrix used for 3-D EM (expectation maximization) reconstruction: the ellipse-stacking method (ESM) and the ray-tracing method (RTM). For every possible position in two detectors and scattering angles, the axis and half angle of the conic surface were determined. Elements for system matrix were then calculated by the product of differential cross-section of Compton scattering in scatterer and the probability with which the voxel belongs to a given conic surface. The belonging probability for ESM was determined by the distance from the voxel center to the ellipse on a plane parallel to the scatterer. For RTM, the belonging probability was determined by the intersection length of the voxel with a straight line through the apex of the cone. It was assumed that Compton camera consisted of a pair of parallel scatterer and absorber with 16x16 detector elements in 5x5 cm2 active areas spaced by 5 cm. The scattering angle of the incident photon at the scatterer was quantized into 30 discrete angles between 10 and 100 degrees. Projection data for point source and three-cylinder phantom were simulated using both ESM and RTM. The iterative EM reconstruction algorithms were also implemented using both ESM and RTM. Computation time (for projections) and percent error between the mathematical phantom and reconstructed image (64x64x64 matrix with pixel size of 1.56 mm) were compared. Results: Computation time for projection using ESM was approximately 3 times longer than RTM. Percent errors (normalized root-mean squared errors) measured at the 30th iteration for three-cylinder phantom were 44% for ESM and 39% for RTM. Point source images were well reconstructed by both methods: FWHMs measured by the profile across the point image reconstructed with 30 iterations were 1.0 pixels for both methods in the plane parallel to the scatterer, and were 1.3 and 1.8 pixels for ESM and RTM, respectively, in the plane perpendicular to the scatterer. Conclusions: Two different approaches to implementing projector-backprojector pairs for 3-D reconstruction from Compton scattered data were developed. While RTM was more efficient than ESM in computation time, accuracies of the reconstructions by both methods were equivalent. The use of geometrical symmetry along with an efficient caching scheme could greatly reduce the computation time for both methods.