Limited-angle CT reconstruction via the L1/L2 minimization

In this paper, we consider minimizing the L1/L2 term on the gradient for a limit-angle scanning problem in computed tomography (CT) reconstruction. We design a splitting framework for both constrained and unconstrained optimization models. In addition, we can incorporate a box constraint that is reasonable for imaging applications. Numerical schemes are based on the alternating direction method of multipliers (ADMM), and we provide the convergence analysis of all the proposed algorithms (constrained/unconstrained and with/without the box constraint). Experimental results demonstrate the efficiency of our proposed approaches, showing significant improvements over the state-of-the-art methods in the limit-angle CT reconstruction. Specifically worth noticing is an exact recovery of the Shepp-Logan phantom from noiseless projection data with 30 scanning angle.