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

## TL;DR

This paper compares different regression methods for calibrating Timepix detectors, aiming to improve energy measurement accuracy.

## Contribution

The paper introduces a novel partial linearization method based on variable projection for Timepix calibration.

## Key findings

- Gradient-Descent, Gauss–Newton, and Levenberg–Marquardt algorithms were adapted for better convergence.
- A novel partial linearization method was proposed and tested for the calibration problem.
- The modified algorithms showed improved performance in energy calibration tasks.

## Abstract

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.