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We estimate the root-mean-square (RMS) value of timing jitter noise in simulated signals similar to measured highspeed sampled signals. The simulated signals are contaminated by additive noise, timing jitter noise, and time shift errors. Before estimating the RMS value of the jitter noise, we align the signals (unless there are no time shift errors) based on estimates of the relative shifts from cross-correlation analysis. We compute the mean and sample variance of the aligned signal based on repeated measurements at each time sample. We estimate the derivative of the noise-free signal based, in part, on a regression spline fit to the average of the aligned signals. Our initial estimate of the RMS value of the jitter noise depends on estimated derivatives and sample variances at time samples where the magnitude of the estimated derivative exceeds a selected threshold. This initial estimate is generally biased. Using a parametric bootstrap approach, we adaptively adjust this initial estimate of the RMS value of the jitter noise based on an estimate of this bias. We apply our method to real data collected at NIST. We study how results depend on the derivative threshold. [ABSTRACT FROM AUTHOR]

Reconstructions of positron emission tomography images are obtained with the iterative expectation maximization (EM) algorithm. The EM algorithm is halted according to a cross-validation procedure. For the cases studied, this method yields a reconstruction with high variability about its expected value. The variability of the reconstruction about its expected value is reduced by computing its bootstrap expectation. Based on the reconstruction computed from the observed projection data, synthetic projection data sets are simulated. Reconstructions of the synthetic projection data sets are averaged to yield the bootstrap expectation. This bootstrap procedure is a nonlinear filtering method. The procedure is automatic; no smoothing kernel or bandwidth parameter need be specified. For simulated data, the bootstrap method yielded somewhat sharper reconstructions than did an optimized linear approach. The method is applied to real data from a fluorodeoxiglucose study of the human brain. Near the boundaries, the resampling procedure yielded a sharper reconstruction. [ABSTRACT FROM AUTHOR]