Proposed Maximum Likelihood Method Research Articles

The properties of the positronium lifetime image reconstruction based on maximum likelihood estimation

The positronium lifetime imaging (PLI) reconstruction is a technique used in time-of-flight (TOF) positron emission tomography (PET) imaging that involves measuring the lifespan of positronium, which is a metastable electron-positron pair that arises when a PET molecule releases a positron, prior to its annihilation. We have previously developed a maximum likelihood (ML) algorithm for PLI reconstruction and demonstrated that it can generate quantitatively accurate lifetime images for a 570 ps (pico-seconds) TOF PET system. In this study, we conducted further investigations into the statistical properties of the algorithm, including the variability of the reconstruction results, the sensitivity of the algorithm to the number of acquired PLI events and its robustness to hyperparameter choices. Our findings indicate that the proposed ML method produces sufficiently stable lifetime images to enable reliable distinction of regions of interest. Moreover, the number of PLI events required to produce quantitatively accurate lifetime images is computationally plausible. These results demonstrate the potential of our ML algorithm for advancing the capabilities of TOF PET imaging.

Energy-Based Maximum Likelihood Spectrum Sensing Method for the Cognitive Radio

In the rapid development of current wireless communication systems, how to effectively utilize the limited system spectrum to provide the high-speed data rate service becomes a very critical issue for the system operators. To improve the utilization efficiency of the wireless spectrum, the cognitive radio (CR) had been proposed currently. The key issue of applying the CR technique successfully is how to sense exactly and quickly whether or not the primary user exists, and looking for the spectrum holes to provide the secondary user. In this paper, an energy-based maximum likelihood (ML) spectrum sensing method for the CR is proposed. The proposed method avoids the troublesome calculation of the required threshold and has almost the optimal performance for the conventional energy-based method. Besides, incorporated with the double threshold, an extension of the proposed ML method is also provided to speed up the sensing period without degrading the detection performance.

Maximum likelihood estimation of partially observed diffusion models

This paper develops a maximum likelihood (ML) method to estimate partially observed diffusion models based on data sampled at discrete times. The method combines two techniques recently proposed in the literature in two separate steps. In the first step, the closed form approach of Aït-Sahalia (2008) is used to obtain a highly accurate approximation to the joint transition probability density of the latent and the observed states. In the second step, the efficient importance sampling technique of Richard and Zhang (2007) is used to integrate out the latent states, thereby yielding the likelihood function. Using both simulated and real data, we show that the proposed ML method works better than alternative methods. The new method does not require the underlying diffusion to have an affine structure and does not involve infill simulations. Therefore, the method has a wide range of applicability and its computational cost is moderate.

A New Method for Maximum Likelihood Parameter Estimation of Gamma-Gamma Distribution

We propose a method to obtain the maximum likelihood (ML) parameter estimation of the Gamma-Gamma (Γ-Γ) distribution representing the free space optical (FSO) channel irradiance fluctuations. The proposed method is based on the expectation maximization (EM) algorithm and the generalized Newton method using a non-quadratic approximation. The numerical results show that, for all turbulence conditions, the proposed ML method is more accurate than the fractional moments (FMOM) method and the numerical ML method (two dimensional numerical maximization of log-likelihood function using the Nelder-Mead algorithm). Moreover, the proposed ML is a fast and stable iterative method, because the iterations always converge to the global optimum with high convergence rate.

Disbond Thickness Evaluation Employing Multiple-Frequency Near-Field Microwave Measurements

Near-field microwave nondestructive evaluation (NDE) techniques have shown great potential for disbond detection in multilayer dielectric composite structures. The high detection capability associated with these techniques stems from the fact that near-field microwave signals are sensitive to minute variations in the dielectric properties and geometry of the medium in which they propagate. In the past, the sensitivity of the near-field microwave NDE techniques to the presence and properties of disbonds in multilayer dielectric composites has been investigated extensively. However, a quantitative disbond thickness estimation method has yet to be introduced. In this paper, we propose a maximum-likelihood (ML) disbond thickness evaluation method utilizing multiple independent measurements obtained at different frequencies. We also introduce a statistical lower limit on the thickness resolution based on the mean-squared error in thickness estimation and a given confidence interval. The effectiveness of the proposed ML method is also verified by comparing simulation results with actual measurements.

Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks

A maximum likelihood (ML) acoustic source location estimation method is presented for the application in a wireless ad hoc sensor network. This method uses acoustic signal energy measurements taken at individual sensors of an ad hoc wireless sensor network to estimate the locations of multiple acoustic sources. Compared to the existing acoustic energy based source localization methods, this proposed ML method delivers more accurate results and offers the enhanced capability of multiple source localization. A multiresolution search algorithm and an expectation-maximization (EM) like iterative algorithm are proposed to expedite the computation of source locations. The Crame/spl acute/r-Rao Bound (CRB) of the ML source location estimate has been derived. The CRB is used to analyze the impacts of sensor placement to the accuracy of location estimates for single target scenario. Extensive simulations have been conducted. It is observed that the proposed ML method consistently outperforms existing acoustic energy based source localization methods. An example applying this method to track military vehicles using real world experiment data also demonstrates the performance advantage of this proposed method over a previously proposed acoustic energy source localization method.

Maximum likelihood method for integer frequency offset estimation of OFDM systems

A novel method for integer frequency offset estimation of OFDM systems is derived, which is based on the maximum likelihood (ML) technique and exploits the differential information between two consecutive blocks of OFDM data symbols in the frequency domain. The reason why the proposed ML method has better performance than the conventional method is analysed.

Maximum likelihood method for parameter estimation in non-linear models with below detection data

The maximum likelihood (ML) method for regression analyzes of censored data (below detection limit) for nonlinear models is presented. The proposed ML method has been translated into an equivalent least squares method (ML-LS). A two stage iterative algorithm is proposed to estimate statistical parameters from the derived least squares translation. The developed algorithm is applied to a nonlinear model for prediction of ambient air CO concentration in terms of concentrations of respirable particulate matter (RSPM) and NO2. It has been shown that if censored data are ignored or estimated through simplifications such as (i) censored data are equal to detection limit, (ii) censored data are half of the difference between detection limit and lower limit (e.g., zero or background level) or (iii) censored data are equal to lower limit, this can cause significant bias in estimated parameters. The developed ML-LS method provided better estimates of parameters than any of the simplifications in censored data.

A maximum likelihood method for estimating P S N curves

A maximum likelihood method for estimating P S N curves is proposed in order to minimize the time and the number of specimens required for laboratory testing. The S N curves are assumed in a three-parameter form. The proposed maximum likelihood method can conveniently be used to estimate the three parameters of the S N curves. The required number of test specimens for the maximum likelihood method is less than that for the conventional method. Based on the test results of notched steel specimens subject to axial loads, it is shown here that the P S N curves obtained by the maximum likelihood method agree well with those obtained by the conventional method.

Maximum Likelihood Method for Parameter Estimation in Linear Model with below-Detection Data

The maximum likelihood (ML) method for regression analyzes of censored data (below detection limit) for nonlinear models is presented. The proposed ML method has been translated into an equivalent least squares method (ML-LS). A two stage iterative algorithm is proposed to estimate statistical parameters from the derived least squares translation. The developed algorithm is applied to a nonlinear model for prediction of ambient air CO concentration in terms of concentrations of respirable particulate matter (RSPM) and NO2. It has been shown that if censored data are ignored or estimated through simplifications such as (i) censored data are equal to detection limit, (ii) censored data are half of the difference between detection limit and lower limit (e.g., zero or background level) or (iii) censored data are equal to lower limit, this can cause significant bias in estimated parameters. The developed ML-LS method provided better estimates of parameters than any of the simplifications in censored data.

Maximum likelihood parameter estimation of suddenly-commencing equatorial Pi2 pulsations

The data sequence is assumed to be an output from a finite impulse response (FIR) filter with a superposition of suddenly-commencing, exponentially damped sinusoids as an input. A maximum likelihood (ML) method is proposed to estimate the parameters of the damped sinusoids directly from the filtered data. Equatorial Pi2 pulsations are guessed to be such a superposition. In addition, since the signal-to-noise ratio is improved and the undesired components are rejected by filtering, the filtered data is usually analyzed. The proposed ML method is a new one for spectral estimation. The ML method was applied to an equatorial Pi2 event which was observed simultaneously at two stations, and evidence to strongly support the suggestion of the global cavity resonance mode of Pi2 waves was found in the event. That is, the Pi2 showed a very similar discrete spectral structure, despite a large longitudinal separation (∼ 150°) of the stations. By means of the proposed ML method, more detailed and precise discussions on Pi2 pulsations than expected from the customary data analysis methods, will become possible.