This paper introduces a parametric level-set method for tomographic reconstruction of partially discrete images. Such images consist of a continuously varying background and an anomaly with a constant (known) grey-value. We express the geometry of the anomaly using a level-set function, which we represent using radial basis functions. We pose the reconstruction problem as a bi-level optimization problem in terms of the background and coefficients for the level-set function. To constrain the background reconstruction, we impose smoothness through Tikhonov regularization. The bi-level optimization problem is solved in an alternating fashion; in each iteration we first reconstruct the background and consequently update the level-set function. We test our method on numerical phantoms and show that we can successfully reconstruct the geometry of the anomaly, even from limited data. On these phantoms, our method outperforms Total Variation reconstruction, DART and P-DART.

Discrete tomography, Geometric inversion, Level-set method, Model splitting
Discrete Geometry for Computer Imagery
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Kadu, A.A, van Leeuwen, T, & Batenburg, K.J. (2017). A parametric level-set method for partially discrete tomography. In Lecture Notes in Computer Science/Lecture Notes in Artificial Intelligence (pp. 122–134). doi:10.1007/978-3-319-66272-5_11