# A parametric level-set method for partially discrete tomography

## TL;DR

This paper presents a parametric level-set approach for partially discrete tomography, effectively reconstructing anomalies with known grey-value within a smooth background, even from limited data, outperforming existing methods.

## Contribution

The paper introduces a novel parametric level-set method using radial basis functions for anomaly geometry representation in tomography, with a bi-level optimization framework.

## Key findings

- Successfully reconstructs anomaly geometry from limited data
- Outperforms Total Variation, DART, and P-DART methods
- Effective in numerical phantom tests

## Abstract

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 represent 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.