scholarly journals Comparison of Phase Estimation Methods for Quantitative Susceptibility Mapping Using a Rotating-Tube Phantom

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Kathryn E. Keenan ◽  
Ben P. Berman ◽  
Slávka Rýger ◽  
Stephen E. Russek ◽  
Wen-Tung Wang ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Data Acquisition ◽  
Relative Error ◽  
Region Growing ◽  
Susceptibility Mapping ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Phase Estimation ◽  
Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) is an MRI tool with the potential to reveal pathological changes from magnetic susceptibility measurements. Before phase data can be used to recover susceptibility ( Δ χ ), the QSM process begins with two steps: data acquisition and phase estimation. We assess the performance of these steps, when applied without user intervention, on several variations of a phantom imaging task. We used a rotating-tube phantom with five tubes ranging from Δ χ = 0.05 ppm to Δ χ = 0.336  ppm. MRI data was acquired at nine angles of rotation for four different pulse sequences. The images were processed by 10 phase estimation algorithms including Laplacian, region-growing, branch-cut, temporal unwrapping, and maximum-likelihood methods, resulting in approximately 90 different combinations of data acquisition and phase estimation methods. We analyzed errors between measured and expected phases using the probability mass function and Cumulative Distribution Function. Repeatable acquisition and estimation methods were identified based on the probability of relative phase errors. For single-echo GRE and segmented EPI sequences, a region-growing method was most reliable with Pr (relative error <0.1) = 0.95 and 0.90, respectively. For multiecho sequences, a maximum-likelihood method was most reliable with Pr (relative error <0.1) = 0.97. The most repeatable multiecho methods outperformed the most repeatable single-echo methods. We found a wide range of repeatability and reproducibility for off-the-shelf MRI acquisition and phase estimation approaches, and this variability may prevent the techniques from being widely integrated in clinical workflows. The error was dominated in many cases by spatially discontinuous phase unwrapping errors. Any postprocessing applied on erroneous phase estimates, such as QSM’s background field removal and dipole inversion, would suffer from error propagation. Our paradigm identifies methods that yield consistent and accurate phase estimates that would ultimately yield consistent and accurate Δ χ estimates.

scholarly journals Validation of Data Acquisition and Phase Estimation for Quantitative Susceptibility Mapping with a Rotating-Tube Phantom

2021 ◽  
Author(s):  
Kathryn E Keenan ◽  
Benjamin Paul Berman ◽  
Slavka Carnicka ◽  
Stephen E Russek ◽  
Wen-Tung Wang ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Data Acquisition ◽  
Relative Error ◽  
Region Growing ◽  
Susceptibility Mapping ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Phase Estimation ◽  
Quantitative Susceptibility Mapping

Purpose: Quantitative Susceptibility Mapping (QSM) is an MRI tool with the potential to reveal pathological changes from magnetic susceptibility measurements. Before phase data can be used to recover susceptibility (Δχ), the QSM process begins with two steps: data acquisition and phase estimation. We assess the performance of these steps, when applied without user intervention, on several variations of a phantom imaging task. Approach: We used a rotating-tube phantom with five tubes ranging from Δχ=0.05 ppm to Δχ=0.336 ppm. MRI data was acquired at nine angles of rotation for four different pulse sequences. The images were processed by 10 phase estimation algorithms including Laplacian, region-growing, branch-cut, temporal unwrapping and maximum-likelihood methods. We analyzed errors between measured and expected phase using the probability mass function and Cumulative Distribution Function. Results: Repeatable acquisition and estimation methods were identified based on the probability of relative phase errors. For single-echo GRE and segmented EPI sequences, a region-growing method was most reliable with Pr(relative error<0.1)=0.95 and 0.90 respectively. For multi-echo sequences, a Maximum-Likelihood method was most reliable with Pr(relative error<0.1)=0.97. The most repeatable multi-echo methods outperformed the most repeatable single-echo methods. Conclusions: We found a wide range of repeatability and reproducibility for off-the-shelf MRI acquisition and phase estimation approaches. The error was dominated in many cases by spatially discontinuous phase unwrapping errors. Any post-processing applied on erroneous phase estimates, such as QSM's background field removal and dipole inversion, would suffer from error propagation. Our paradigm identifies methods that yield consistent and accurate phase estimates that would ultimately yield consistent and accurate Δ𝜒 estimates.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

scholarly journals Estimation of Critical Headway at Small Urban Roundabout

2020 ◽  
Vol 32 (1) ◽  
pp. 103-117
Author(s):  
Danijela Maslać ◽  
Dražen Cvitanić ◽  
Ivan Lovrić
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Project Design ◽  
Capacity Estimation ◽  
Local Conditions ◽  
Large Numbers ◽  
The World

Before choosing an intersection project design, an important step is to examine the justification of the construction on the basis of defined criteria. One of the key criteria is the analysis of capacity. Large numbers of roundabout capacity models are present in the world, most of them adapted to the conditions of the country they originate from and they need to be calibrated for local conditions. Key parameters for calibration are critical headway and follow-up headway. Follow-up headway can be measured directly in the field, while critical headway cannot be measured, but is estimated. Many critical headway estimation methods exist (over 30) and each of them provides different values. Different values of critical headway result in different capacity estimation values. This raises the question which method provides more realistic estimations under certain conditions. In this paper, four most frequently used critical headway estimation methods (Raff, Maximum likelihood method, Wu, Logit) were selected to be tested by comparison of theoretical capacity models and actual measured capacity at a small urban roundabout.

scholarly journals Truncated Akash distribution: properties and applications

2020 ◽  
Vol 9 (5) ◽  
pp. 179-184
Author(s):  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Coefficient Of Variation ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
Proposed Model ◽  
Rate Functions ◽  
Mean And Variance

In this paper, Truncated Akash distribution has been proposed. Its mean and variance have been derived. Nature of cumulative distribution and hazard rate functions have been derived and presented graphically. Its moments including Coefficient of Variation, Skenwness, Kurtosis and Index of dispersion have been derived. Maximum likelihood method of estimation has been used to estimate the parameter of proposed model. It has been applied on three data sets and compares its superiority over one parameter exponential, Lindley, Akash, Ishita and truncated Lindley distribution.

scholarly journals A New Approach to Assess Wind Potential

2021 ◽  
Keyword(s):  
Distribution Function ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Wind Power ◽  
Cumulative Distribution Function ◽  
Maximum Likelihood Method ◽  
New Method ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Wind Distribution

<p>Weibull Cumulative Distribution Function (C.D.F.) has been employed to assess and compare wind potentials of two wind stations Europlatform and Stavenisse of The Netherland. Weibull distribution has been used for accurate estimation of wind energy potential for a long time. The Weibull distribution with two parameters is suitable for modeling wind data if wind distribution is unimodal. Whereas wind distribution is generally unimodal, random weather changes can make the distribution bimodal. It is always desirable to find a method that accurately represents actual statistical data. Some well-known statistical methods are Method of Moment (MoM), Linear Least Square Method (LLSM), Maximum Likelihood Method (M.L.M.), Modified Maximum Likelihood Method (MMLM), Energy Pattern Factor Method (EPFM), and Empirical Method (E.M.), etc. All these methods employ Probability Density Function (PDF) of Weibull distribution, except LLSM, which uses Cumulative Distribution Function (C.D.F.). In this communication, we are presenting a newly proposed method of evaluating Weibull parameters. Unlike most methods, this new method employs a cumulative distribution function. A MATLAB® GUI-based simulation is developed to estimate Weibull parameters using the C.D.F. approach. It is found that the Mean Square Error (M.S.E.) is the lowest when using the new method. The new method, therefore, estimates wind power density with reasonable accuracy. Wind Power (W.P.) is estimated by considering four different Wind Turbine (W.T.) models for two sites, and maximum W.P. is found using Evance R9000.</p>

Different inference approaches for the estimators of the sushila distribution

2021 ◽  
Vol 16 (4) ◽  
pp. 251-260
Author(s):  
Marcos Vinicius de Oliveira Peres ◽  
Ricardo Puziol de Oliveira ◽  
Edson Zangiacomi Martinez ◽  
Jorge Alberto Achcar
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Bayesian Method ◽  
Weighted Least Squares ◽  
Computational Cost ◽  
Estimation Method ◽  
Computation Time ◽  
Ordinary Least Squares ◽  
Likelihood Method ◽  
Estimation Methods

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost.

Water-Fat Decomposition by IDEAL-MRI With Phase Estimation: A Method to Determine Chemical Contents In Vivo

2010 ◽  
Author(s):  
Jing Xu ◽  
Xiaofei Hu ◽  
Haiying Tang ◽  
Richard Kennan ◽  
Karim Azer
Keyword(s):  
Least Squares ◽  
Small Animal ◽  
Region Growing ◽  
Least Squares Estimation ◽  
Estimation Methods ◽  
Chemical Components ◽  
Proton Density ◽  
Phase Estimation ◽  
Field Inhomogeneity

High-resolution Magnetic Resonance Imaging (MRI) of humans and animals in vivo is routine and non-invasive. Identifying and quantifying chemical composition of tissue from acquired images is a challenge. MR spectroscopy (MRS) may be used to identify chemical components accurately over a finite volume in the tissue. However, the temporal and spatial resolutions are limited. Multi-spectral MRI exploits the multiple modes of MR such as T1, T2 and proton density maps and classifies voxels into different tissue types, but the chemical identity of the tissue remains unknown. Many fat suppression methods were developed because the unwanted fat signal often compromises image interpretability in clinical MRI, but these techniques are sensitive to MR field inhomogeneity. Multi-point Dixon methods separate MR images into water and fat images and are less sensitive to field inhomogeneity [1] and IDEAL-MRI (iterative decomposition of water and fat with echo asymmetry and least-squares estimation) improved upon the Dixon methods by avoiding the problem of phase unwrapping [2]. However, special care has to be taken when estimating the field map to avoid erroneous solutions to the least-squares estimation problem which lead to artifacts such as swapping of water and fat. The use of region growing schemes (with a reliable seed) mitigates this problem as demonstrated in previous studies [3][4]. However, the seed is not always reliable and growing schemes can be sensitive to phase discontinuities. Moreover, although the technology was successfully demonstrated on many clinical scanners, only limited applications were found in preclinical scanners with high MR field where the field inhomogeneity can be far worse [5]. We developed a robust and accurate algorithm to compute water and fat content on an 11.7T small animal scanner by improving upon existing phase estimation methods through multiple starting pixels and consensus-based region growing. The method, after further validation, has the potential of providing a translatable assay to study disease progression and regression related to fat and water contents in various animal models, such as studying atherosclerotic plaque composition.

scholarly journals Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 100
Author(s):  
Hisham M. Almongy ◽  
Fatma Y. Alshenawy ◽  
Ehab M. Almetwally ◽  
Doaa A. Abdo
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Type Ii ◽  
Type Ii Censoring ◽  
Progressive Type ◽  
Transformer Insulation ◽  
Censoring Scheme ◽  
Progressive Type Ii Censoring

In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton–Raphson algorithm. The Bayesian estimation is done using the Metropolis–Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.

scholarly journals Comparing estimation methods of non-stationary errors-in-variables models

2019 ◽  
Vol 3 (1) ◽  
pp. 73-101 ◽  
Author(s):  
Naoto Kunitomo ◽  
Naoki Awaya ◽  
Daisuke Kurisu
Keyword(s):  
Maximum Likelihood ◽  
Measurement Errors ◽  
Likelihood Function ◽  
Asymptotic Properties ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Errors In Variables ◽  
Economic Time Series ◽  
Finite Sample ◽  
Ml Estimation

AbstractWe investigate the estimation methods of the multivariate non-stationary errors-in-variables models when there are non-stationary trend components and the measurement errors or noise components. We compare the maximum likelihood (ML) estimation and the separating information maximum likelihood (SIML) estimation. The latter was proposed by Kunitomo and Sato (Trend, seasonality and economic time series: the nonstationary errors-in-variables models. MIMS-RBP-SDS-3, MIMS, Meiji University. http://www.mims.meiji.ac.jp/, 2017) and Kunitomo et al. (Separating information maximum likelihood method for high-frequency financial data. Springer, Berlin, 2018). We have found that the Gaussian likelihood function can have non-concave shape in some cases and the ML method does work only when the Gaussianity of non-stationary and stationary components holds with some restrictions such as the signal–noise variance ratio in the parameter space. The SIML estimation has the asymptotic robust properties in more general situations. We explore the finite sample and asymptotic properties of the ML and SIML methods for the non-stationary errors-in variables models.

Estimation of aerodynamic parameters near stall using maximum likelihood and extreme learning machine-based methods

2020 ◽  
pp. 1-21
Author(s):  
H.O. Verma ◽  
N.K. Peyada
Keyword(s):  
Maximum Likelihood ◽  
Extreme Learning Machine ◽  
Unsteady Aerodynamics ◽  
Estimation Algorithm ◽  
Neural Model ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Aerodynamic Parameters ◽  
Learning Machine ◽  
And Control

ABSTRACT The stability and control derivatives are essential parameters in the flight operation of aircraft, and their determination is a routine task using classical parameter estimation methods based on maximum likelihood and least-squares principles. At high angle-of-attack, the unsteady aerodynamics may pose difficulty in aerodynamic structure determination, hence data-driven methods based on artificial neural networks could be an alternative choice for building models to characterise the behaviour of the system based on the measured motion and control variables. This research paper investigates the feasibility of using a recurrent neural model based on an extreme learning machine network in the modelling of the aircraft dynamics in a restricted sense for identification of the aerodynamic parameters. The recurrent extreme learning machine network is combined with the Gauss–Newton method to optimise the unknowns of the postulated aerodynamic model. The efficacy of the proposed estimation algorithm is studied using real flight data from a quasi-steady stall manoeuvre. Furthermore, the estimates are validated against the parameters estimated using the maximum likelihood method. The standard deviations of the estimates demonstrate the effectiveness of the proposed algorithm. Finally, the quantities regenerated using the estimates present good agreement with their corresponding measured values, confirming that a qualitative estimation can be obtained using the proposed estimation algorithm.

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