Variable step size methods for solving simultaneous algebraic reconstruction technique (SART)-type CBCT reconstructions

Compared to analytical reconstruction by Feldkamp-Davis-Kress (FDK), simultaneous algebraic reconstruction technique (SART) offers a higher degree of flexibility in input measurements and often produces superior quality images. Due to the iterative nature of the algorithm, however, SART requires intense computations which have prevented its use in clinical practice. In this paper, we developed a fast-converging SART-type algorithm and showed its clinical feasibility in CBCT reconstructions. Inspired by the quasi-orthogonal nature of the x-ray projections in CBCT, we implement a simple yet much faster algorithm by computing Barzilai and Borwein step size at each iteration. We applied this variable step-size (VS)-SART algorithm to numerical and physical phantoms as well as cancer patients for reconstruction. By connecting the SART algebraic problem to the statistical weighted least squares problem, we enhanced the reconstruction speed significantly (i.e., less number of iterations). We further accelerated the reconstruction speed of algorithms by using the parallel computing power of GPU.