Non-Binary Discrete Tomography by Continuous Non-Convex Optimization

Matthias Zisler, Joerg Hendrik Kappes, Claudius Schnörr, Stefania Petra, Christoph Schnoerr

Abstract:

We study an energy formulation for non-binary discrete tomography and introduce a non-convex coupling term in order to combine discrete constraints with a continuous reconstruction method based on total variation regularization. The optimization is carried out by a generalized forward–backward splitting algorithm for non-convex functions, which exploits the problem structure and is guaranteed to globally converge to a local optimum. A detailed numerical evaluation on standard test-datasets demonstrates that the proposed algorithm returns more accurate
reconstructions from a few number of projection angles than competing methods.

Index Terms—Discrete tomography, limited-angle tomography, non-binary, non-convex optimization, reconstruction, relaxation, total variation regularization.