A preliminary investigation of 3D preconditioned conjugate gradient reconstruction for cone-beam CT

Model-based iterative reconstruction (MBIR) methods based on maximum a posteriori (MAP) estimation have been recently introduced to multi-slice CT scanners. The model-based approach has shown promising image quality improvement with reduced radiation dose compared to conventional FBP methods, but the associated high computation cost limits its widespread use in clinical environments. Among the various choices of numerical algorithms to optimize the MAP cost function, simultaneous update methods such as the conjugate gradient (CG) method have a relatively high level of parallelism to take full advantage of a new generation of many-core computing hardware. With proper preconditioning techniques, fast convergence speeds of CG algorithms have been demonstrated in 3D emission and 2D transmission reconstruction. However, 3D transmission reconstruction using preconditioned conjugate gradient (PCG) has not been reported. Additional challenges in applying PCG in 3D CT reconstruction include the large size of clinical CT data, shift-variant and incomplete sampling, and complex regularization schemes to meet the diagnostic standard of image quality. In this paper, we present a ramp-filter based PCG algorithm for 3D CT MBIR. Convergence speeds of algorithms with and without using the preconditioner are compared.