ℓ1/2 Norm Based Directional Total Variation Algorithm for Limited-Angle CT Reconstruction

Limited-angle computed tomography (CT) remains a topic of active research due to its potential to address practical challenges such as scanning constraints and low dose demands. This reconstruction problem is very challenging because it is highly ill-conditioned. The directional total variation (DTV) algorithm, based on the ℓ1 norm, has demonstrated high accuracy in limited-angle CT. Studies have demonstrated the superiority of ℓ1/2 norm over ℓ1 norm and may be solved by the (closed form) half thresholding algorithm. Based on this observation, in this work, we develop a novel ℓ1/2 norm based DTV algorithm, referred to simply as half DTV (HDTV) algorithm. The HDTV model is a constrained non-convex optimization model. The objective function is the anisotropic DTV regularization term, whereas the constraint term is the data fidelity term. We use the fully linearized alternating direction method of multipliers (FL-ADMM) algorithm to solve this model to avoid step-size line-search and inner-iteration, thereby improving computational efficiency. Specifically, the key point is the use of the half thresholding algorithm for solving the corresponding ℓ1/2 norm related sub-problems. Additionally, we conducted comprehensive comparisons among the HDTV, TV, and DTV algorithms. Experiments demonstrate that the HDTV algorithm accurately recovers the images from data collected over a significantly reduced limited angular range and considerably diminishes artifacts observed otherwise in reconstructions of some existing algorithms.