2 research outputs found
Improving self-calibration
Response calibration is the process of inferring how much the measured data
depend on the signal one is interested in. It is essential for any quantitative
signal estimation on the basis of the data. Here, we investigate
self-calibration methods for linear signal measurements and linear dependence
of the response on the calibration parameters. The common practice is to
augment an external calibration solution using a known reference signal with an
internal calibration on the unknown measurement signal itself. Contemporary
self-calibration schemes try to find a self-consistent solution for signal and
calibration by exploiting redundancies in the measurements. This can be
understood in terms of maximizing the joint probability of signal and
calibration. However, the full uncertainty structure of this joint probability
around its maximum is thereby not taken into account by these schemes.
Therefore better schemes -- in sense of minimal square error -- can be designed
by accounting for asymmetries in the uncertainty of signal and calibration. We
argue that at least a systematic correction of the common self-calibration
scheme should be applied in many measurement situations in order to properly
treat uncertainties of the signal on which one calibrates. Otherwise the
calibration solutions suffer from a systematic bias, which consequently
distorts the signal reconstruction. Furthermore, we argue that non-parametric,
signal-to-noise filtered calibration should provide more accurate
reconstructions than the common bin averages and provide a new, improved
self-calibration scheme. We illustrate our findings with a simplistic numerical
example.Comment: 17 pages, 3 figures, revised version, title change