Rapid 3D regularized EM reconstruction for Compton cameras using GPU

Abstract

This paper describes the development of rapid 3-D regularized EM (expectation maximization) reconstruction methods for Compton cameras using commodity graphics hardware. Since the size of the system matrix for a typical Compton camera is extremely large, it is impractical to use a caching scheme that reads pre-stored values of the elements of the system matrix instead of repeatedly calculating conical projection and backprojection which are the most time consuming operations. In this paper we propose GPU (graphics processing unit) accelerated methods that can rapidly perform conical projection and backprojection on the fly. Since the conventional ray-based backprojection method is inefficient for GPU, we develop fully voxel-based conical backprojection methods using two different approaches. In the first approach, we approximate the intersecting chord length of the ray passing through a voxel with the normal distance from the center of the voxel to the ray. In the second approach, each voxel is regarded as a dimensionless point, and the backprojection is performed without the need for calculating intersecting chord lengths. Our experimental studies with the M-BSREM (modified block sequential regularized EM) algorithm show that GPU-based methods significantly outperforms the conventional CPU-based method in computation time without a considerable loss of reconstruction accuracy.