Fast Splitting-Based Ordered-Subsets X-Ray CT Image Reconstruction

Using non-smooth regularization in X-ray computed tomography (CT) image reconstruction has become more popular these days due to the recent resurgence of the classic augmented Lagrangian (AL) methods in fields such as totalvariation (TV) denoising and compressed sensing (CS). For example, undersampling projection views is one way to reduce radiation dose in CT scans; however, this causes strong streak artifacts in FBP images that degrade image quality. To overcome this problem, the split Bregman (SB) method, an alias of the AL method in the context of `1-regularized image reconstruction problems, has been investigated using strong non-smooth TV and sparsity regularizations. Unfortunately, existing SB-based methods are slow due to the iterative updates for the challenging inner least-squares problem. This paper proposes to solve Xray CT image reconstruction problems with TV or sparsity regularization using a splitting-based ordered-subsets (OS) algorithm, split OS-LALM, and evaluates the proposed algorithm using a few-view X-ray CT image reconstruction problem with TV regularization. Experimental results show that the proposed algorithm significantly accelerates the convergence of X-ray CT image reconstruction with non-smooth TV regularization over the standard (linearized) SB method and demonstrates the effectiveness of OS acceleration with splitting-based algorithms.