3D anisotropic total variation method for limitedangle CT reconstruction

Nowadays, limited-angle problems are common in many Computed Tomography (CT) applications. In order to achieve a more satisfactory reconstruction in these problems, a compressed sensing (CS) based method Total Variation (TV) is developed. Usually, iterative methods are proposed to get a better stability as the projection views are less than theoretical requirements. Thus, these problems are achieved by a minimizing process on the total variation of CT images under data consistency constraint. However, in limited-angle problems, due to the missing views the strength of data consistency constraint becomes direction relevant while the TV minimization constraint is isotropy. In this paper, a new anisotropic total variation (ATV) method is proposed. The new method is a combination of 1D TV in multiple directions with different weights determined by the actual scanned angular range. The ATV minimization method improves the insufficient of TV and achieves a better balance between restriction strength and noise level, reconstruction with ATV constraint is more suitable than that with TV constraint in limited-angle problems. Numerical simulation was done and the results confirmed the validity of our work, these basic researches are meaningful and useful for tomosynthesis reconstruction.