An accelerated threshold-based back-projection algorithm for Compton camera image reconstruction

Abstract

Purpose: Compton camera imaging (CCI) systems are currently under investigation for radiotherapy dose reconstruction and verification. The ability of such a system to provide real-time images during dose delivery will be limited by the computational speed of the image reconstruction algorithm. In this work, the authors present a fast and simple method by which to generate an initial back-projected image from acquired CCI data, suitable for use in a filtered back-projection algorithm or as a starting point for iterative reconstruction algorithms, and compare its performance to the current state of the art. Methods: Each detector event in a CCI system describes a conical surface that includes the true point of origin of the detected photon. Numerical image reconstruction algorithms require, as a first step, the back-projection of each of these conical surfaces into an image space. The algorithm presented here first generates a solution matrix for each slice of the image space by solving the intersection of the conical surface with the image plane. Each element of the solution matrix is proportional to the distance of the corresponding voxel from the true intersection curve. A threshold function was developed to extract those pixels sufficiently close to the true intersection to generate a binary intersection curve. This process is repeated for each image plane for each CCI detector event, resulting in a three-dimensional back-projection image. The performance of this algorithm was tested against a marching algorithm known for speed and accuracy. Results: The threshold-based algorithm was found to be approximately four times faster than the current state of the art with minimal deficit to image quality, arising from the fact that a generically applicable threshold function cannot provide perfect results in all situations. The algorithm fails to extract a complete intersection curve in image slices near the detector surface for detector event cones having axes nearly parallel to the image plane. This effect decreases the sum of the image, thereby also affecting the mean, standard deviation, and SNR of the image. All back-projected events associated with a simulated point source intersected the voxel containing the source and the FWHM of the back-projected image was similar to that obtained from the marching method. Conclusions: The slight deficit to image quality observed with the threshold-based back-projection algorithm described here is outweighed by the 75% reduction in computation time. The implementation of this method requires the development of an optimum threshold function, which determines the overall accuracy of the method. This makes the algorithm well-suited to applications involving the reconstruction of many large images, where the time invested in threshold development is offset by the decreased image reconstruction time. Implemented in a parallel-computing environment, the threshold-based algorithm has the potential to provide real-time dose verification for radiation therapy.