Relaxed Linearized Algorithms for Faster X-Ray CT Image Reconstruction

Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate statistical methods, many optimization techniques have been investigated. Over-relaxation is a common technique to speed up convergence of iterative algorithms. For instance, using a relaxation parameter that is close to two in alternating direction method of multipliers (ADMM) has been shown to speed up convergence significantly. This paper proposes a relaxed linearized augmented Lagrangian (AL) method that shows theoretical faster convergence rate with over-relaxation and applies the proposed relaxed linearized AL method to X-ray CT image reconstruction problems. Experimental results with both simulated and real CT scan data show that the proposed relaxed algorithm (with ordered-subsets [OS] acceleration) is about twice as fast as the existing unrelaxed fast algorithms, with negligible computation and memory overhead.