Asymmetric Gaussian Distribution Research Articles

Overlapping microbubble localization based on multiscale statistical features for ultrasound super-resolution imaging

Ultrasound localization microscopy enables visualization of the microvasculature through the localization and tracking of isolated microbubbles (MBs). Currently, improving the precision for localizing overlapping MBs at high concentration to decrease the acquisition time remains a challenge. This study introduces multiscale statistical feature localization (MSFL) to address this challenge. First, the overlapping MBs are separated by local energy and blobness filters constructed from the Hessian matrix of texture features and its eigenvalues. Then, multiscale and orientation kernels are modeled to adapt to the appearance of various MBs; their amplitude and gradient convolution response results jointly determine the credibility of the MBs. Finally, precise MB localization is obtained by the weighted average of the local maxima of the response maps at each scale to achieve super-resolution (SR) imaging. The proposed method is evaluated using simulation and in-vivo datasets. Simulation results demonstrate that MSFL can adapt to asymmetric Gaussian distributions and improve overlapping MB localization, with a 9.28 % improvement in localization precision and a 5 % greater Jaccard index compared to the Gaussian fitting method. Additionally, the strong robustness of MSFL under noise interference maintains its ability to locate more MBs, and reconstruct the same saturation vessels with 36 % acquisition time reduction compared to Radial symmetry method. For SR images, MSFL can draw smoother interlaced vessels when more overlapping MBs are present, and quickly reconstructs more saturated in vivo microvasculature with a resolution is 10.5 μm(λ/10). These results validate the advantages of MSFL in achieving precise SR imaging with a short acquisition time.

Tight Lower Bound on Differential Entropy for Mixed Gaussian Distributions

In this paper, a tight lower bound for the differential entropy of the Gaussian mixture model is presented. First, the probability model of mixed Gaussian distribution that is created by mixing both discrete and continuous random variables is investigated in order to represent symmetric bimodal Gaussian distribution using the hyperbolic cosine function, on which a tighter upper bound is set. Then, this tight upper bound is used to derive a tight lower bound for the differential entropy of the Gaussian mixture model introduced. The proposed lower bound allows to maintain its tightness over the entire range of the model's parameters and shows more tightness when compared with other bounds that lose their tightness over certain parameter ranges. The presented results are then extended to introduce a more general tight lower bound for asymmetric bimodal Gaussian distribution, in which the two modes have a symmetric mean but differ in terms of their weights.

An Interpretable Channelwise Attention Mechanism based on Asymmetric and Skewed Gaussian Distribution

Channelwise attention mechanisms have recently been demonstrated to boost the performance of deep convolutional neural networks (CNNs). The hypothesis on the negative correlation between channelwise responses and their importance levels has been verified. Therefore, according to the shifted means and unbalanced responses that are observed in attention distribution, two empirical hypotheses are proposed in this paper. Then, as an interpretable attention module, bilateral asymmetric skewed Gaussian attention (bi-SGA) is utilized to combine skewed and asymmetric properties into the Gaussian context transformer (GCT), which is the state-of-the-art. Finally, extensive experiments on the different benchmarks validate the rationality of the hypotheses. The proposed bi-SGA improves the overall performance of GCT attention mechanisms with only two extra parameters to be learned. Moreover, our attention mechanism also provides a perspective on analyzing the channelwise importance levels in deep neural networks in an interpretable and logical manner.

Neutron spectrum unfolding of the magnetic proton recoil spectrometer using the GRAVEL and MLEM algorithms

The magnetic proton recoil (MPR) spectrometer is a high-resolution neutron spectrometer, which provides critical information about the deuterium–tritium (DT) fusion yield, collective fuel velocity, and ion temperature. For precise measurements, the MPR spectrometer operates in a high-resolution mode; however, its detection efficiency is low. The trade-off between energy resolution and detection efficiency limits its widespread applications. Herein, we apply the spectrum unfolding technique to obtain a precise energy spectrum using the MPR spectrometer in a low-resolution mode and to achieve high detection efficiency. Numerical experiments and Geant4 simulations are conducted to compare the GRAVEL and the maximum likelihood expectation maximization (MLEM) algorithms in different cases. A new stopping criterion for iterations is adopted and works well. The source focuses on the primary DT neutrons with single Gaussian, asymmetric, and dual Gaussian distributions. All the cases demonstrate an accurate and stable unfolded energy spectrum, revealing the potential of the MPR spectrometer in a wide range of applications.

Natural surfactant system: precursor flow in one-shot two-dimensional foam drainage.

Foam drainage, the downward flow of the intervening liquid due to gravity, surface tension and viscosity, is an important factor for foam stability. Forced drainage (adding liquid to a foam column from the top) is used to study liquid flow characteristics in foam. The different competing phenomena involved in the vertical and horizontal movement is studied by visually monitoring the draining liquid using a dye. Hence, this study is called two-dimensional (2D) drainage, horizontal movement being considered as just one dimension. We report, for the first time, 2D forced drainage in a natural surfactant extracted from Sapindus mukorossi. Draining wave front flows vertically and spreads horizontally. Vertical front position proceeds with time in a power law whose exponent indicates a Poiseuille flow, like synthetic surfactants. The wave front begins as a conic form downstream producing an expanding ellipsoid with time. The liquid fraction, taken as light intensity at any point, follows a Gaussian distribution along the horizontal. There is an asymmetric Gaussian distribution along the vertical which distorts after 10 s, indicating two types of flow occurring simultaneously. Two such liquid movements through foam have not been reported in the literature. The reason behind these two types of flow needs further investigations.

Bayesian inference for infinite asymmetric Gaussian mixture with feature selection

Data clustering is a fundamental unsupervised learning approach that impacts several domains such as data mining, computer vision, information retrieval, and pattern recognition. In this work, we develop a statistical framework for data clustering which uses Dirichlet processes and asymmetric Gaussian distributions. The parameters of this framework are learned using Markov Chain Monte Carlo inference approaches. We also integrate a feature selection technique to choose the features that are most informative in order to construct an appropriate model in terms of clustering accuracy. This paper reports results based on experiments that concern dynamic textures clustering as well as scene categorization.

Resonant plasmon enhancement of light emission from CdSe/CdS nanoplatelets on Au nanodisk arrays.

Semiconducting nanoplatelets (NPLs) have attracted great attention due to the superior photophysical properties compared to their quantum dot analogs. Understanding and tuning the optical and electronic properties of NPLs in a plasmonic environment is a new paradigm in the field of optoelectronics. Here, we report on the resonant plasmon enhancement of light emission including Raman scattering and photoluminescence from colloidal CdSe/CdS nanoplatelets deposited on arrays of Au nanodisks fabricated by electron beam lithography. The localized surface plasmon resonance (LSPR) of the Au nanodisk arrays can be tuned by varying the diameter of the disks. In the case of surface-enhanced Raman scattering (SERS), the Raman intensity profile follows a symmetric Gaussian shape matching the LSPR of the Au nanodisk arrays. The surface-enhanced photoluminescence (SEPL) profile of NPLs, however, follows an asymmetric Gaussian distribution highlighting a compromise between the excitation and emission enhancement mechanisms originating from energy transfer and Purcell effects. The SERS and SEPL enhancement factors depend on the nanodisk size and reach maximal values at 75 and 7, respectively, for the sizes, for which the LSPR energy of Au nanodisks coincides with interband transition energies in the semiconductor platelets. Finally, to explain the origin of the resonant enhancement behavior of SERS and SEPL, we apply a numerical simulation to calculate plasmon energies in Au nanodisk arrays and emission spectra from NPLs in such a plasmonic environment.

Nonparametric hierarchical mixture models based on asymmetric Gaussian distribution

Mixture models are broadly applied in image processing domains with hierarchical Bayesian approaches popularly considered for grouped data. The related inference process takes into consideration both the approximation of exact data shapes and estimation of adequate component numbers. In our work, we develop nonparametric hierarchical Bayesian models using the Dirichlet and Pitman-Yor processes with asymmetric Gaussian distribution. The parameters of these models are learned using variational inference methods. The effectiveness and merits of the proposed approaches are validated using the challenging real-life application of dynamic texture clustering.

A novel centerline extraction algorithm for a laser stripe applied for turbine blade inspection

Line-laser 3D scanning is a novel and promising automation technique for turbine blade inspection. One key task encountered in line-laser 3D scanning is centerline extraction of the laser stripes. In some regions, there is asymmetry of the line profiles caused by high curvature, such as the leading and trailing edges of a blade. According to the asymmetric Gaussian distribution line profile, this paper presents a new algorithm to extract the centerline of a laser stripe based on sub-pixel boundary extraction and medial axis transformation. The candidate boundary points of the laser stripe are extracted by zero crossing. Based on Taylor expansion and interpolation, the gray gradient distribution of the boundary can be estimated accurately. Following this, the accurate boundary points are extracted by extreme values of the gray gradient, and the centerline is calculated by medial axis transformation of the accurate boundary points. The proposed method can effectively reduce errors caused by the asymmetry of line profiles in areas of high curvature. The effectiveness of this method is verified using simulation and measuring experiments. The experiment results show that the extraction error of the asymmetric Gaussian line profile is within ± 0.15 pixels, and the root mean square error in measurement accuracy experiments does not exceed 0.015 mm.

Research on Software Reliability Growth Model Based on Gaussian New Distribution

Abstract The Gaussian new distribution is extended from the normal distribution. Its main function is to fully fit the objectively existing asymmetric Gaussian distribution, and accurately express the frequency distribution of the random variable with the expected value in the single peak. Error and probability distribution under conditions. The proposed software reliability growth model based on Gaussian new distribution helps people to analyze the error errors generated in the software process, and reduces the uncertainty caused by human subjective factors in the software process.

Wind Power Curve Modeling With Asymmetric Error Distribution

Wind power curves play important roles in developing and utilizing wind energy, including wind power forecasting, wind turbine condition monitoring, wind energy potential estimation, and wind turbine selection. In this paper, we show that the error distribution in wind power curve modeling is asymmetric and complex, rather than a Gaussian distribution. Considering this error characteristic, we develop two novel asymmetric spline regression models, MoAG-ASR and MoAEP-ASR, in which the error terms are assumed to obey mixture of asymmetric Gaussian distributions (MoAG) and mixture of asymmetric exponential power distribution (MoAEP), respectively. We compare the proposed models with 16 popular wind power curve fitting models, and find that the proposed models rank higher than the others. Moreover, besides the asymmetry, two statistics (skewness and kurtosis) also show that the error distribution in wind power curve modeling is thick-tailed and leptokurtic. However, MoAG and MoAEP can precisely fit such complex error distribution. Thus, MoAG-ASR and MoAEP-ASR are effective tools for wind power curve modeling.

A level set method for brain MR image segmentation under asymmetric distributions

Magnetic resonance (MR) image segmentation plays an essential role for brain disease diagnosis; however, suffered from low contrast, intensity inhomogeneity, noise and asymmetry of the intensity distribution, segmentation methods are always difficult to achieve satisfactory results. In this paper, we propose a novel level set method for brain MR image segmentation with consideration of these problems. We firstly generate a new region descriptor based on asymmetric Gaussian distributions in order to fit different shapes of observed nonsymmetric data. Secondly, we utilize the spatial distance and intensity similarity information of neighborhood pixels to extract local anisotropic spatial information to balance the noise reduction and detail preservation. After that, the extracted information and bias field information are combined to improve the asymmetric region descriptor utilized in the level set framework. Finally, we define a maximum likelihood energy functional on the whole image, integrating the local anisotropic spatial information, the bias field information and the asymmetric distributions. The experimental results on synthetic and clinical images demonstrated that our method can achieve desirable performance in spite of the severe noise and intensity inhomogeneity.

Improved image quality in pinhole SPECT by accurate modeling of the point spread function in low magnification systems

Single photon emission computed tomography (SPECT) has become an important noninvasive imaging technique in small-animal research. Due to the high resolution required in small-animal SPECT systems, the spatially variant system response needs to be included in the reconstruction algorithm. Accurate modeling of the system response should result in a major improvement in the quality of reconstructed images. The aim of this study was to quantitatively assess the impact that an accurate modeling of spatially variant collimator/detector response has on image-quality parameters, using a low magnification SPECT system equipped with a pinhole collimator and a small gamma camera. Three methods were used to model the point spread function (PSF). For the first, only the geometrical pinhole aperture was included in the PSF. For the second, the septal penetration through the pinhole collimator was added. In the third method, the measured intrinsic detector response was incorporated. Tomographic spatial resolution was evaluated and contrast, recovery coefficients, contrast-to-noise ratio, and noise were quantified using a custom-built NEMA NU 4-2008 image-quality phantom. A high correlation was found between the experimental data corresponding to intrinsic detector response and the fitted values obtained by means of an asymmetric Gaussian distribution. For all PSF models, resolution improved as the distance from the point source to the center of the field of view increased and when the acquisition radius diminished. An improvement of resolution was observed after a minimum of five iterations when the PSF modeling included more corrections. Contrast, recovery coefficients, and contrast-to-noise ratio were better for the same level of noise in the image when more accurate models were included. Ring-type artifacts were observed when the number of iterations exceeded 12. Accurate modeling of the PSF improves resolution, contrast, and recovery coefficients in the reconstructed images. To avoid the appearance of ring-type artifacts, the number of iterations should be limited. In low magnification systems, the intrinsic detector PSF plays a major role in improvement of the image-quality parameters.

Two Efficient Twin ELM Methods With Prediction Interval.

In the operational optimization and scheduling problems of actual industrial processes, such as iron and steel, and microelectronics, the operational indices and process parameters usually need to be predicted. However, for some input and output variables of these prediction models, there may exist a lot of uncertainties coming from themselves, the measurement error, the rough representation, and so on. In such cases, constructing a prediction interval (PI) for the output of the corresponding prediction model is very necessary. In this paper, two twin extreme learning machine (TELM) models for constructing PIs are proposed. First, we propose a regularized asymmetric least squares extreme learning machine (RALS-ELM) method, in which different weights of its squared error loss function are set according to whether the error of the model output is positive or negative in order that the above error can be differentiated in the parameter learning process, and Tikhonov regularization is introduced to reduce overfitting. Then, we propose an asymmetric Bayesian extreme learning machine (AB-ELM) method based on the Bayesian framework with the asymmetric Gaussian distribution (AB-ELM), in which the weights of its likelihood function are determined as the same method in RALS-ELM, and the type II maximum likelihood algorithm is derived to learn the parameters of AB-ELM. Based on RALS-ELM and AB-ELM, we use a pair of weights following the reciprocal relationship to obtain two nonparallel regressors, including a lower-bound regressor and an upper-bound regressor, respectively, which can be used for calculating the PIs. Finally, some discussions are given, about how to adjust the weights adaptively to meet the desired PI, how to use the proposed TELMs for nonlinear quantile regression, and so on. Results of numerical comparison on data from one synthetic regression problem, three University of California Irvine benchmark regression problems, and two actual industrial regression problems show the effectiveness of the proposed models.

Characterizing the effects of multidirectional motion adaptation.

Recent sensory experience can alter our perception and change the response characteristics of sensory neurons. These effects of sensory adaptation are a ubiquitous property of perceptual systems and are believed to be of fundamental importance to sensory coding. Yet we know little about how adaptation to stimulus ensembles affects our perception of the environment as most psychophysical experiments employ adaptation protocols that focus on prolonged exposure to a single visual attribute. Here, we investigate how concurrent adaptation to multiple directions of motion affects perception of subsequently presented motion using the direction aftereffect. In different conditions, observers adapted to a stimulus ensemble comprised of dot directions sampled from different distributions or to bidirectional motion. Increasing the variance of normally distributed directions reduced the magnitude of the peak direction aftereffect and broadened its tuning profile. Sampling of asymmetric Gaussian and uniform distributions resulted in shifts of direction aftereffect tuning profiles consistent with changes in the perceived global direction of the adapting stimulus. Adding dots in a direction opposite or orthogonal to a unidirectional adapting stimulus led to a pronounced reduction in the direction aftereffect. A simple population-coding model, in which adaptation selectively alters the responsivity of direction-selective neurons, can accommodate the effects of multidirectional adaptation on the perceived direction of motion.

Reconstruction of semiautomated cardiac regions of interest using iodine-123 metaiodobenzylguanidine myocardial scintigraphy.

Analysis using cardiac iodine-123 metaiodobenzylguanidine (MIBG) scintigraphy with regions of interest (ROIs) is useful for assessing myocardial sympathetic activity. However, manual placement of the cardiac ROI is sometimes difficult because myocardial MIBG uptake is reduced in patients with heart failure. A new method was developed to reconstruct the semiautomated cardiac ROI in a sympathetic denervated heart. Using dynamic planar data, a summed image was generated and the matrix size was changed. Then, the radial count profiles originating from the center of the left ventricle were generated to extract the myocardial count profiles. An asymmetric Gaussian distribution was fitted to each profile and the epicardial border was defined by the threshold method. This program was tested in 50 patients, and its reproducibility was validated when compared with the manual tracing method. The semiautomated method yielded a better quality image compared with the standard image with higher counts. Cardiac ROIs were generated successfully in each patient within normal limits. The intraobserver and interobserver agreements were excellent (P<0.0001 each). This approach showed a significantly higher consistency in measuring the heart-to-mediastinum ratio as compared with the manual tracing method (P<0.05). The semiautomated method is useful in generating cardiac ROIs with high reproducibility in myocardial MIBG imaging.

LED-based spectrally tunable light source with optimized f itting

According to the LED spectra measured in the rated current, Gauss distribution function and asymmetric Gaussian distribution function methods are used to simulate the individual LED spectrum. Based on this mathematical model, 32 LEDs are used to synthesize arbitrary spectral distribution of the light source. Processing the spectral data with multiple linear regressions, CIE illuminant A and CIE illuminant D65 are simulated. The results show that for each LED, different Gauss models should be used. The simulation results are quite satisfying. However, there is a difference between the simulation results and the experimental results. The spectral evaluation indices of fitted both CIE illuminant A and CIE illuminant D65 do not exceed 2.5%. But in experiment, because of the changes of the peak wavelength and the FWHM caused by the current, the spectral evaluation indices of fitted CIE illuminant A and CIE illuminant D65 are around 5%.

Development of Target Person Detecting and Tracking Method for Mobile Robots Based on Gradual Updating Multi Color HS-histogram

This paper presents that the novel target person detecting and tracking method for mobile robots based on updating multi color HS-histogram. To detect and track a specific person, the image processing with color camera is common method for vision based navigation system of mobile robot. The image processing for the target person detecting and tracking by robot vision has many problems such as the image from the vision device located on robot is often influenced by the change of target size, target moving direction and lighting condition. Moreover, it is difficult to detect a target person in the crowd. To solve these problems, we propose “GRUMIC-HS-hist method (Gradual Updating Multi Color HS-histogram method)”. In the proposed method, the colors of the tracking object are extracted by HSV color space. To decrease the influence of the illumination changes, a HS-histogram is proposed. The extracting colors on HS-histogram are clustered by Nearest Neighbor Method. The colors on HS-histogram are weighted by the anisotropic asymmetric Gaussian distribution to update the HS-histogram without spreading. This proposed “GRUMIC-HS-hist method” achieves the robust target person detecting and tracking by a mobile robot. In addition, the quantitative evaluation method is also proposed to evaluate the proposed target person detecting and tracking method. The quantitative evaluation method is composed with “Extraction Rate”, “Object Detecting Rate” and “Tracking Error”. The quantitatively experimental results show that the proposed “GRUMIC-HS-hist method ” is the robust method for many problems.

Bayesian analysis of quantitative traits using skewed distributions

Statistical models for genetic evaluation often make use of Gaussian distributions. However, some new statistical developments allow the use of an asymmetric distribution for the residuals. Within this context, we analysed three different patterns for the residual term on a data set consisting of 63 208 litter-size records, belonging to 19 255 sows, with a pedigree including 27 911 individuals. The three different residual distributions were: (1) Gaussian distribution, (2) asymmetric Gaussian distribution and (3) asymmetric Gaussian distribution with a hierarchical scheme for the asymmetry parameter. The operational model always included order of parity and herd-year-season as systematic effects, and the permanent environmental and infinitesimal genetic effect of each sow as random effects. The most suitable model using the deviance information criterion (DIC) and posterior predictive checking was model 3. This implies systematic, additive genetic and permanent environmental control of both litter size and the asymmetry parameter of the residual distribution. The asymmetry parameter can be understood as a measure of sensitivity to negative (or positive) environmental influences on phenotypes. The posterior mean (standard deviation) of the additive genetic variance was 0.28 (0.06) for litter size and 0.07 (0.01) for the asymmetry parameter. The posterior mean (standard deviation) of the additive genetic correlation between litter size and the asymmetry parameter was 0.21 (0.07).

A study on antibacterial properties of Ag +-implanted pyrolytic carbon

The bactericidal properties of Ag +-implanted pyrolitic carbon were investigated using Gram positive S. aureus and negative E. coli. The pyrolitic carbon samples were implanted by silver ions with the dose ranging from 5 × 10 14 to 5 × 10 18 ions/cm 2 at an energy of 70 keV. The samples were characterized by Rutherford Backscatter Spectrometry (RBS), Auger analysis (AES), and Scanning Electron Microscopy (SEM) respectively. The results show that the bactericidal ratios for both S. aureus and E. coli increase with the ion dose when the silver ion dose is under the saturated dose of 5 × 10 17 ions/cm 2. The bactericidal ratio is over 97% when the ion dose exceeds that dose. RBS analysis shows that the silver atoms penetrate into the sample surface and forms an asymmetric Gaussian distribution so as to form a silver rich surface region which plays an important role in killing bacteria. AES analysis also confirms this distribution. SEM characterization shows that the surface morphology is another factor for killing bacteria.