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A drift-rate estimator constructed from four values of the cumulative sum of clock residuals is shownn to have good error performance in the presence of the five standard power-law noises.
Purpose: Current clinical image quality assessment techniques mainly analyze image quality for the imaging system in terms of factors such as the capture system modulation transfer function, noise power spectrum, detective quantum efficiency, and the exposure technique. While these elements form the basic underlying components of image quality, when assessing a clinical image, radiologists seldom refer to these factors, but rather examine several specific regions of the displayed patient images, further impacted by a particular image processing method applied, to see whether the image is suitable for diagnosis. In this paper, the authors developed a novel strategy to simulate radiologists' perceptual evaluation process on actual clinical chest images. Methods: Ten regional based perceptual attributes of chest radiographs were determined through an observer study. Those included lung grey level, lung detail, lung noise, rib-lung contrast, rib sharpness, mediastinum detail, mediastinum noise, mediastinum alignment, subdiaphragm-lung contrast, and subdiaphragm area. Each attribute was characterized in terms of a physical quantity measured from the image algorithmically using an automated process. A pilot observer study was performed on 333 digital chest radiographs, which included 179 PA images with 10:1 ratio grids (set 1) and 154 AP images without grids (set 2), to ascertain the correlation between image perceptual attributes and physical quantitative measurements. To determine the acceptable range of each perceptual attribute, a preliminary quality consistency range was defined based on the preferred 80% of images in set 1. Mean value difference ({mu}{sub 1}-{mu}{sub 2}) and variance ratio ({sigma}{sub 1}{sup 2}/{sigma}{sub 2}{sup 2}) were investigated to further quantify the differences between the selected two image sets. Results: The pilot observer study demonstrated that our regional based physical quantity metrics of chest radiographs correlated very well with their corresponding perceptual attributes. The distribution comparisons, mean value difference estimations, and variance ratio estimations of each physical quantity between sets of images from two different techniques matched our expectation that the image quality of set 1 should be better than that of set 2. Conclusions: The measured physical quantities provide a robust reflection of perceptual image quality in clinical images. The methodology can be readily applied for automated evaluation of perceptual image quality in clinical chest radiographs.
Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. The use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio is investigated.
Maximum likelihood estimation of parameters in linear structural relationships under normality assumptions requires knowledge of one or more of the model parameters if no replication is available. The most common assumption added to the model definition is that the ratio of the error variances of the response and predictor variates is known. This paper investigates the use of asymptotic formulae for variances and mean squared errors as a function of sample size and the assumed value for the error variance ratio.
Concurrent engineering offers a great many benefits to engineers and mission designers throughout the world of aerospace. The only downside of concurrent engineering, and this is somewhat unavoidable, is that you don’t know the results of a design session until the end when it is completed. Usually, this is not a problem – you wouldn’t start building a spacecraft before the design is finished. However, within mass and cost constrained systems, you may end up with a final design that although technically sound – is not feasible due to mass or cost limits. Employing in-session mass and cost models with flexible inputs that refine their estimates and variance as more detailed information comes in throughout a design session allows major design changes to be made when the probability of breaching a mass or cost cap exceeds a threshold level. This enables mission designers to re-focus the study, and avoid spending 3-days with 15 engineers designing a non-feasible mission. By understanding key correlations and nested relationships within mass or cost, and specifically mass or cost allocations per mission element by mission type, it’s possible to get flexible-input, statistically based mass and cost estimates very early in the design process. Baseline models are seeded using mission characteristics and general parameters (outer planetary orbiter-probe mission, $500M cost cap for example) to provide a rough estimate of the expected mass or cost. As information gets solidified during the session, it gets added to the model and the estimates are updated. Continuing the orbiter-probe mission example, modeling probe heat shield cost as a percent of total probe cost, and probe cost as a percent of total flight system cost, and total flight system cost as a percent of total mission cost allows a design team to roll-up solidified information to estimate the probability of fitting within a mass or cost constraint early in a concurrent design session. When only the heat shield cost is known, the variance of the final estimate is higher, whereas when the full probe gets defined, naturally, the variance of the estimate decreases. A methodology, model, verification and demo implementation for cost limit breach are presented.
This documents reports on the initial Assessment Specification and Validation (ASV) of Maxar satellite imagery as a geolocation system. Validation is a prerequisite for using geolocation for applications that require quantified uncertainty. A Variance Component Estimation (VCE) calibration of the provider’s co- variance matrices concluded that they were exaggerated. However, we currently lack enough independent validation data to quantify the improvement from the VCE. The current ASV process is slow and expensive. It will not be able to keep up with growing numbers of satellite systems. We proposed a method to automate ASV using controlled imagery. The proposed method will allow us to keep up with new sensors and generate unbounded amounts of calibration data, leading to unprecedented accuracy.
Abstract missing.
The author has identified the following signficant results. Examination of both machine estimates and stratified areal estimates produced by clustering and classification reveal no significant differences between the proportion estimates and ground truth estimates. When testing the variances of the machine estimates, a significant reduction in the variances was found when the number of starting dots was increased from 30 to 45. The variances were again reduced, although not significantly, when the number of starting dots was increased from 45 to 60. From these results, 60 starting dots are recommended for a three-category classifier. When examining the variances of the estimates for the four estimation procedures (using 60 dots), no significant differences were found between procedures. Thus, only the machine clustering may be used to produce an estimate, and the stratified areal estimate computations and maximum likelihood classification can be deleted.
We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.
We present a new global time-variable gravity mascon solution derived from Gravity Recovery and Climate Experiment (GRACE) Level 1B data. The new product from the NASA Goddard Space Flight Center (GSFC) results from a novel approach that combines an iterative solution strategy with geographical binning of inter-satellite range-acceleration residuals in the construction of time-dependent regularization matrices applied in the inversion of mascon parameters. This estimation strategy is intentionally conservative as it seeks to maximize the role of the GRACE measurements on the final solution while minimizing the influence of the regularization design process. We fully reprocess the Level 1B data in the presence of the final mascon solution to generate true post-fit inter-satellite residuals, which are utilized to confirm solution convergence and to validate the mascon noise uncertainties. We also present the mathematical case that regularized mascon solutions are biased, and that this bias, or leakage, must be combined with the estimated noise variance to accurately assess total mascon uncertainties. The estimated leakage errors are determined from the monthly resolution operators. We present a simple approach to compute the total uncertainty for both individual mascon and regional analysis of the GSFC mascon product, and validate the results in comparison with independent mascon solutions and calibrated Stokes uncertainties. Lastly, we present the new solution and uncertainties with global analyses of the mass trends and annual amplitudes, and compute updated trends for the global ocean, and the respective contributions of the Greenland Ice Sheet, Antarctic Ice Sheet, Gulf of Alaska, and terrestrial water storage. This analysis highlights the successful closure of the global mean sea level budget, that is, the sum of global ocean mass from the GSFC mascons and the steric component from Argo floats agrees well with the total determined from sea surface altimetry.
The problem of determining the stratum variances required for an optimum sample allocation for remotely sensed crop surveys is investigated with emphasis on an approach based on the concept of stratum variance as a function of the sampling unit size. A methodology using the existing and easily available information of historical statistics is developed for obtaining initial estimates of stratum variances. The procedure is applied to variance for wheat in the U.S. Great Plains and is evaluated based on the numerical results obtained. It is shown that the proposed technique is viable and performs satisfactorily with the use of a conservative value (smaller than the expected value) for the field size and with the use of crop statistics from the small political division level.
Purpose: Dual-energy computed tomography (DECT) makes it possible to get two fractions of basis materials without segmentation. One is the soft-tissue equivalent water fraction and the other is the hard-matter equivalent bone fraction. Practical DECT measurements are usually obtained with polychromatic x-ray beams. Existing reconstruction approaches based on linear forward models without counting the beam polychromaticity fail to estimate the correct decomposition fractions and result in beam-hardening artifacts (BHA). The existing BHA correction approaches either need to refer to calibration measurements or suffer from the noise amplification caused by the negative-log preprocessing and the ill-conditioned water and bone separation problem. To overcome these problems, statistical DECT reconstruction approaches based on nonlinear forward models counting the beam polychromaticity show great potential for giving accurate fraction images.Methods: This work proposes a full-spectral Bayesian reconstruction approach which allows the reconstruction of high quality fraction images from ordinary polychromatic measurements. This approach is based on a Gaussian noise model with unknown variance assigned directly to the projections without taking negative-log. Referring to Bayesian inferences, the decomposition fractions and observation variance are estimated by using the joint maximum a posteriori (MAP) estimation method. Subject to an adaptive prior model assigned to the variance, the joint estimation problem is then simplified into a single estimation problem. It transforms the joint MAP estimation problem into a minimization problem with a nonquadratic cost function. To solve it, the use of a monotone conjugate gradient algorithm with suboptimal descent steps is proposed.Results: The performance of the proposed approach is analyzed with both simulated and experimental data. The results show that the proposed Bayesian approach is robust to noise and materials. It is also necessary to have the accurate spectrum information about the source-detector system. When dealing with experimental data, the spectrum can be predicted by a Monte Carlo simulator. For the materials between water and bone, less than 5% separation errors are observed on the estimated decomposition fractions.Conclusions: The proposed approach is a statistical reconstruction approach based on a nonlinear forward model counting the full beam polychromaticity and applied directly to the projections without taking negative-log. Compared to the approaches based on linear forward models and the BHA correction approaches, it has advantages in noise robustness and reconstruction accuracy.
Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system.
Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included.
This paper presents a sequential filtering strategy using observations corrupted with uniform measurement noise. While the Kalman filter remains the best linear estimator of the state, other filtering techniques provide minimum variance optimal estimates, a trait only enjoyed by the Kalman filter when the underlying noises are, in fact, Gaussian. This work develops a new approximate optimal estimator for uniform measurement noises. The resulting recursion requires just slightly more computational time to complete a measurement update than the Kalman filter, which generally cannot be claimed by other optimal strategies such as the particle or Gaussian mixture filters.
This paper presents a sequential filtering strategy using observations corrupted with uniform measurement noise. While the Kalman filter remains the best linear estimator of the state, other filtering techniques provide minimum variance optimal estimates, a trait only enjoyed by the Kalman filter when the underlying noises are, in fact, Gaussian. This work develops a new approximate optimal estimator for uniform measurement noises. The resulting recursion requires just slightly more computational time to complete a measurement update than the Kalman filter, which generally cannot be claimed by other optimal strategies such as the particle or Gaussian mixture filters.
The popular 3-cornered hat method used for evaluating the noise contributions of individual frequency standards is revisited. This method is used in several cases, but sometimes the results are not consistent because one or more estimated clock variances turn out to be negative. Different causes of this unacceptable result have been conjectured: among them one regards the hypothesis of uncorrelated clocks, essential in this method. Since recently realistic cases of correlation between clocks, mainly due to the environmental conditions, have been observed, this paper proposes an entirely revisited version of the 3-cornered hat method which permits to evaluate the individual variances and also the possible covariances between clocks, by relaxing the hypothesis of uncorrelation. The uncertainty and the lack of contemporaneity of the measurement series are assumed to be negligible. The lack of the uncorrelation hypothesis calls for a more general mathematical model leading to an underdetermined linear system. The estimates of the (co)variances of the measurement series us well us those of the individual clocks are introduced by means of the scalar product of the related time series and arranged in the respective covariance matrices S and R. Since covariance matrix is positive definite by definition, the problem consists in estimating the unknown R, subject to the constraint of positive definiteness, from the known S. Unfortunately, this constraint is not sufficient to estimate R. Therefore a suitable optimization criterion is proposed, which assures the positive definiteness of R and, at the same time, minimizes the global correlation among clocks. Examples of frequency instability measurements processed by the "classical" 3-cornered hat method and the here-revisited method are presented showing that the solutions are identical only when the uncorrelation hypothesis doesn't violate the positive definiteness of R.
Here, we present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity 1 < |η| < 3 in Au + Au collisions at √ s NN = 200 GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients v 2 {2}, v 2 {4}, v 2 {6}, and v 2 {8}, and triangular flow coefficients v3{2} and v3{4}. Using the small-variance limit, we estimate the mean and variance of the event-by-event v 2 distribution from v 2 {2} and v 2 {4}. In a complementary analysis, we also use a folding procedure to study the distributions of v 2 and v 3 directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final-state momentum distributions are discussed.