A Comparative Study of Regression Methods for Solving the Timepix Calibration Task

In this article, we provide a study of the energy calibration model used for Timepix-type detectors. The Timepix detectors, operating in Time-over-Threshold mode, measure information that needs to be mapped into the corresponding energies using a non-linear function. We consider three iterative algorithms, Gradient-Descent, Gauss-Newton and Levenberg-Marquardt algorithm, which we modify according to the calibration model constraints to perform better in terms of the convergence properties. Moreover, based on the variable projection method, we suggest a partial linearization of the calibration problem and provide results for this novel method.