Implementation of uniform and simultaneous ART for 3-D reconstruction in an X-ray imaging system

The authors propose a 3-D volume reconstruction method using X-ray images with a calibration method to implement it in an X-ray imaging system. Previously the authors have proposed an advanced 3-D reconstruction algorithm based on an algebraic reconstruction technique (ART), called a uniform and simultaneous ART (USART). In practice, however, there are two main issues in implementing it in a realised X-ray imaging system. The first one is the huge computation time and memory required in achieving 3-D volume, which is a common limitation in most ART methods. The second issue is the system calibration for determining the geometry of the X-ray imaging conditions needed for the ART method. These two critical problems are addressed. A fast computing model of USART is proposed, where spherical voxel elements are employed in computation to reduce the computation time and memory. Then, a calibration method is proposed to identify the X-ray imaging geometry based on a cone beam projection model. For this purpose, a set of X-ray images of a reference grid pattern is used and the X-ray source positions are determined from the analysis of the image features, the centres of the grid points in the X-ray images. The validity of the proposed 3-D reconstruction method is investigated using a series of experiments.