Generalized source-conditions and uncertainty bounds for deconvolution problems

J. D. Rezac, A. Dienstfrey, N. Vlajic, A. Chijioke, P. D. Hale

Research output: Contribution to journalConference articlepeer-review

Abstract

Many problems in time-dependent metrology can be phrased mathematically as a deconvolution problem. In such a problem, measured data is modeled as the convolution of a known system response function with an unknown source signal. The goal of deconvolution is to estimate the unknown source signal given knowledge about the system response function. A well-studied method for calculating this estimate is Tikhonov regularized deconvolution which attempts to balance the average difference between the estimated solution and true source signal with the variance in the estimated solution. In this article we study this so-called bias-variance tradeoff in the context of estimating a source measured by a high speed oscilloscope. By assuming we have bounds on the true source's Fourier coefficients and a structural model for the uncertainties in the system response function, we derive pointwise-in-time confidence intervals on the true signal based on the estimated signal. We demonstrate the new technique with simulations relevant to the high speed measurement context.

Original languageEnglish (US)
Article number212025
JournalJournal of Physics: Conference Series
Volume1065
Issue number21
DOIs
StatePublished - Nov 13 2018
Event22nd World Congress of the International Measurement Confederation, IMEKO 2018 - Belfast, United Kingdom
Duration: Sep 3 2018Sep 6 2018

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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