Signal inference with unknown response: Calibration-uncertainty renormalized estimator

TL;DR

CURE is a novel method based on information field theory that jointly infers signals and unknown calibration parameters from data, using a renormalization approach to incorporate calibration uncertainty.

Contribution

The paper introduces CURE, a non-iterative, renormalization-based estimator for simultaneous signal reconstruction and calibration uncertainty handling.

Findings

CURE matches the accuracy of existing self-calibration methods.

It operates as a non-iterative alternative to traditional calibration schemes.

Validated on a toy example, demonstrating effective calibration and signal inference.

Abstract

The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of CURE, developed in the framework of information field theory, is starting with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify CURE by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov Chain Monte Carlo sampling. We conclude that the method is able to keep up in accuracy with the best self-calibration methods and serves as a non-iterative alternative to it.