Generalized source-conditions and uncertainty bounds for deconvolution problems
Jake D. Rezac, Andrew M. Dienstfrey, Nicholas A. Vlajic, Akobuije D. Chijioke, Paul D. Hale
Many problems in time-dependent metrology can be phrased mathematically as deconvolution problems. In such cases, measured data is modeled as the convolution of a known system response function with an unknown input signal, and the goal is to estimate the later. As deconvolution is ill-posed, regularization is required to stabilize this inversion given uncertainties in the problem data. Tikhonov regularization is a well-studied method to achieve this task. In this paper we derive new uncertainty bounds on the input signal using the Tikhonov framework for its estimation. Assuming we have bounds on the Fourier coefficients of the true input, and a structural model for the uncertainties in the system response function, we derive pointwise-in- time confidence intervals on the true signal. Importantly, our analysis is practical as the uncertainty bounds are centered on the estimated waveform and are computed entirely from these general assumptions in combination with measured data. We demonstrate the new technique with simulations relevant to measurement contexts for high-speed communication systems.
Journal of Physics: Conference Series
September 3-6, 2018
XXII World Congress of the International Measurement Confederation