Box-Constrained $L_1/L_2$ Minimization in Single-View Tomographic Reconstruction

Abstract

We present a note on the implementation and efficacy of a box-constrained $L_1/L_2$ regularization in numerical optimization approaches to performing tomographic reconstruction from a single projection view. The constrained $L_1/L_2$ minimization problem is constructed and solved using the Alternating Direction Method of Multipliers (ADMM). We include brief discussions on parameter selection and numerical convergence, as well as detailed numerical demonstrations against relevant alternative methods. In particular, we benchmark against a box-constrained TVmin and an unconstrained Filtered Backprojection in both cone and parallel beam (Abel) forward models. We consider both a fully synthetic benchmark, and reconstructions from X-ray radiographic image data.