Accelerating ordered-subsets X-ray CT image reconstruction using the linearized augmented Lagrangian framework

The augmented Lagrangian (AL) optimization method has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical fast convergence rate under weak conditions. However, for problems, e.g., X-ray computed tomography (CT) image reconstruction, where the inner least-squares problem is challenging, the AL method can be slow due to its iterative inner updates. In this paper, using a linearized AL framework, we propose an ordered-subsets (OS) accelerable linearized AL method, OS-LALM, for solving penalized weighted least-squares (PWLS) X-ray CT image reconstruction problems. To further accelerate the proposed algorithm, we also propose a deterministic downward continuation approach for fast convergence without additional parameter tuning. Experimental results show that the proposed algorithm significantly accelerates the "convergence" of X-ray CT image reconstruction with negligible overhead and exhibits excellent gradient error tolerance when using many subsets for OS acceleration.