Simon Bellens | Searcharxiv

arXiv2024

FISTA-Condat-Vu: Automatic Differentiation for Hyperparameter Learning in Variational Models

Motivated by industrial computed tomography, we propose a memory efficient strategy to estimate the regularization hyperparameter of a non-smooth variational model. The approach is based on a combination of FISTA and Condat-Vu algorithms exploiting the convergence rate of the former and the low per-iteration complexity of the latter. The estimation is cast as a bilevel learning problem where a first-order method is obtained via reduced-memory automatic differentiation to compute the derivatives. The method is validated with experimental industrial tomographic data with the numerical implementation available.

math.NA↗

arXiv2023

Automatic and Computationally Efficient Alignment in Fan- and Cone-beam Tomography

This work is concerned with fan- and cone-beam computed tomography with circular source trajectory, where the reconstruction inverse problem requires an accurate knowledge of source, detector and rotational axis relative positions and orientations. We address this additional inverse problem as a preceding step of the reconstruction process directly from the acquired projections. In the cone-beam case, we present a method that estimates both the detector shift (orthogonal to both focal and rotational axes) and the in-plane detector rotation (over the focal axis) based on the variable projection optimization approach. In addition and for the fan-beam case, two new strategies with low computational cost are presented to estimate the detector shift based on a fan-beam symmetry condition. The methods are validated with simulated and experimental industrial tomographic data with code examples available for both fan- and cone-beam geometries.

math.NA↗