Alpha-stable Model Research Articles

Image Quality Score Distribution Prediction via Alpha Stable Model

Based on potentially subjective and diverse image quality scores given by a group of subjects, we propose to predict the distribution of image quality scores rather than the mean opinion score (MOS) of image quality. Therefore, in this paper, we use an alpha stable model to parameterize the image quality score distribution (IQSD), and propose an objective method to predict the alpha-stable-model-based IQSD. First, the LIVE database is re-recorded. Specifically, we invite a large group of subjects (187 valid subjects) to evaluate the quality of all 808 images in the LIVE database, with their scores forming reliable IQSDs. All images in the LIVE database and their collected subjective quality scores form a new image quality assessment database, named the SJTU IQSD database. We then propose a framework and algorithm to predict the alpha-stable-model-based IQSD, in which quality features are extracted from the structural and natural statistical information of each image, and support vector regressors are trained to predict the alpha stable model parameters. Experiments carried out on the SJTU IQSD database verify the feasibility of using the alpha stable model to describe the IQSD, and the experimental results show that the alpha-stable-model-based IQSD can reflect a large amount of subjective information on image quality. We also prove that the objective alpha-stable-model-based IQSD prediction method is effective. The code and the SJTU IQSD database can be downloaded at ‘https://github.com/YixuanGao98/Image-Quality-Score-Distribution-Prediction-via-Alpha-Stable-Model.git’.

Information theoretic evaluation of Lorentzian, Gaussian, Voigt, and symmetric alpha-stable models of reversible transverse relaxation in cervical cancer in vivo at 3T.

To better characterize cervical cancer at 3T. MRI transverse relaxation patterns hold valuable biophysical information about cellular scale microstructure. Lorentzian modeling is typically used to represent intravoxel frequency distributions, resulting in mono-exponential decay of reversible transverse relaxation. However, deviations from mono-exponential decay are expected theoretically and observed experimentally. We compared the information content of four models of signal attenuation with reversible transverse relaxation. Biological phantoms and six women with cervical squamous cell carcinoma were imaged using a gradient-echo sampling of the spin-echo (GESSE) sequence. Lorentzian, Gaussian, Voigt, and Symmetric α-Stable (SAS) models were ranked using Akaike's Information Criterion (AIC), and the model retaining the highest information content was identified at each voxel as the best model. The Lorentzian model resulted in information loss in large fractions of the phantoms and cervix. Gaussian and SAS models frequently had higher information content than the Lorentzian in much of the areas of interest. The Voigt model rarely surpassed the three other models in terms of information content. Gaussian and SAS models provide better fitting of data in much of the human cervix at 3T. Minimizing information loss through improved tissue modeling may have important implications for identifying reliable biomarkers of tumor hypoxia and iron deposition.

Enhanced Temporal Feature Integration in Audio Semantics via Alpha-Stable Modeling

Enhanced Temporal Feature Integration in Audio Semantics via Alpha-Stable Modeling

A Wavelet-Predominant Algorithm Can Evaluate Quality of THz Security Image and Identify Its Usability

This paper presents an aggregate wavelet-predominant algorithm to measure the distortions in THz security images. The algorithm integrates a spectral-based sharpness estimator, a noise estimator derived alpha-stable model and an overall viewing experience estimator based on free-energy principle. Among them, the greater weight is assigned to the spectral-based sharpness estimator considering that the main quality factor in THz security image is sharpness. To verify the feasibility of the proposed metric, we construct the THz security image dataset including a total of 181 THz security images, and each image has the mean opinion score (MOS) collected via subjective quality evaluation experiment. Quantitative experimental results on the constructed THz security image dataset show that the aggregate wavelet-predominant estimator produces the promising overall performance for the estimation of MOS values, with PLCC, SROCC, and RMSE of 0.900, 0.873, and 0.386, respectively. This performance is superior to other opinion-unaware approaches, viz. , FISBLIM, SISBLIM, NIQE, CPBD, SINE, S3, FISH, and noise estimator. The determination coefficient ( ${R} ^{{2}}$ ) of linear regression between reference and predicted MOSs is 0.81. The result of Bland–Altman analysis further validates that the aggregate wavelet-predominant estimator can substitute for the subjective IQA of THz security image, with approximately 94.5% of data points locating within the limits of agreement. For usability identification, the wavelet-predominant estimator gives the satisfactory results, with accuracy, precision, recall rate, and false positive rate of 84.0%, 79.8%, 95.0%, and 29.6%, respectively. Furthermore, the potential application perspectives of the proposed metric can refer to commercial applications (guarantee THz security images of good quality) and scientific researches (assist in software development for THz security image analysis). The dataset is available at https://doi.org/10.6084/m9.figshare.7700123.v3 . Possible researches on this dataset may include the development of THz quality standards, the selection of the best display mode, the enhancement of images, the modeling of image noise, and the detection of prohibited goods.

How Do Detected Objects Affect the Noise Distribution of Terahertz Security Images?

The purpose of this paper is to analyze how detected objects affect the noise distribution of terahertz (THz) security images. Noise in THz image caused by hardware deteriorates the image quality seriously, limiting the application. In addition, there are a few papers on the noise analysis of THz screenings. Due to the special attributes of the THz image compared with the natural image, an alpha-stable distribution is used to fit the noise of THz image instead of the commonly-used Gaussian distribution. The database used in this paper is composed of 181 THz image cubes with a test object as well as two empty image cubes. After analyzing the four parameters of alpha-stable distribution, we can observe that the noise patterns of THz images are indeed different from those of natural image obtained by RGB camera. The possible reasons are given based on the principles of the THz imaging device. The analysis of the distribution of four parameters of alpha-stable model demonstrates that there exists a nonlinear effect due to the change of reflected wave’s pattern caused by the body structure. This paper provides an efficient and flexible model for THz images and a useful guidance for the design of THz image denoising algorithms and the development of imaging hardware.

Bayesian Cointegrated Vector Autoregression Models Incorporating -Stable Noise for Inter-Day Price Movements Via Approximate Bayesian Computation

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.

Case Studies for Bearing Fault Diagnosis based on Adaptive Myriad Filter and Alpha Stable Model

Case Studies for Bearing Fault Diagnosis based on Adaptive Myriad Filter and Alpha Stable Model

Reliability and Performance Improvement of MIMO-PLC System Under Alpha-Stable Noise

Recently Power Line Communications (PLC) have acquired a growing interest and expansion. Furthermore by harnessing MIMO (Multiple Input Multiple Output) technique, the PLC system reached more improvements in term of capacity and robustness. Unfortunately PLC channel is a very hostile environment, this is due to the fact that severe impairments adhering this medium. In this paper an alternative and an accurate noise model based symmetric alpha-stable distribution is considered in the evaluation of coded OSTBC-OFDM through MIMO PLC channel. Results show the improvement of MIMO-PLC using coded system and the effectiveness of considering a more realistic noise model compared with the models close to the Gaussian case in symmetric alpha-stable model, which leads to an overestimation of the overall performance studies of coded MIMO-PLC system.

Recurrence quantification analysis of denoised index returns via alpha-stable modeling of wavelet coefficients: detecting switching volatility regimes

AbstractIn this paper we propose an enhancement of recurrence quantification analysis (RQA) performance in extracting the underlying non-linear dynamics of market index returns, under the assumption of data corrupted by additive white Gaussian noise. More specifically, first we show that the statistical distribution of wavelet decompositions of distinct index returns is best fitted using members of the alpha-stable distributions family. Then, an efficient maximum a posteriori (MAP) estimator is applied on pairs of wavelet coefficients at adjacent levels to suppress the noise effect, prior to performing RQA. Quantitative and qualitative results on 22 future indices indicate an improved interpretation capability of RQA when applied on denoised data using our proposed approach, as opposed to previous methods based solely on a Gaussian assumption for the underlying statistics, in terms of extracting the underlying dynamical structure of index returns generating processes. Furthermore, our results reveal an increased accuracy of the proposed method in detecting switching volatility regimes, which is important for estimating the risk associated with a financial instrument.

A new statistical modeling and detection method for rolling element bearing faults based on alpha–stable distribution

Due to limited information given by traditional local statistics, a new statistical modeling method for rolling element bearing fault signals is proposed based on alpha–stable distribution. In order to fully take advantages of complete information provided by alpha–stable distribution, this paper focuses on testing the validity of the proposed statistical model. A number of hypothetical test methods were applied to practical bearing fault vibration signals with different fault types and degrees. Through testing on the consistency of three alpha–stable parameter estimation methods, and the probability density function fitting level between fault signals and their corresponding hypothetical alpha–stable distributions, it can be concluded that such a non-Gaussian model is sufficient to thoroughly describe the statistical characteristics of bearing fault signals with impulsive behaviors, and consequently the alpha–stable hypothesis is verified. In the meantime, a new bearing fault detection method based on kurtogram and α parameter of the alpha–stable model is proposed, experimental results have shown that the proposed method has better performance on detecting incipient bearing faults than that based on the traditional kurtogram.

Image fusion method based on bivariate alpha-stable model in multiwavelet domain

Considering statistical characteristics of multiwavelet coefficient vectors, an image fusion method with a window-based salience measure for vector fusion is proposed in the multiwavelet domain. After analyzing joint probability distribution of multiwavelet coefficient vectors, we respect the joint probability distribution as a peaky and heavy tailed two-dimensional non-Gaussian distribution, and hence model it by using a bivariate symmetric alpha-stable ( BiSαS ) distribution. Model parameters of the BiS α S distribution can be estimated from samples of multiwavelet coefficient vectors. In a sliding window, the estimated parameters can reveal the impulsive shape of the histogram of the multiwavelet coefficient vectors within the window. So we employ these model parameters to form the new salience measure indicating the degree of prominent information. In our method, vector fusion rule is introduced to avoid inconsistency of decision maps between the component sub-bands and, consequently, to lessen ringing artifacts in final fusion results. Experimental results support the effectiveness of our proposed method in the area of visual quality and objective evaluations.

PLC Impulsive Noise in Industrial Zone: Measurement and Characterization

 Abstract—Noise in PLC is of relatively complex structure of which the most important component is the asynchronous impulsive noise. Based on measurements realized in an industrial zone, this paper shows the heavy tail phenomenon observed in experimental measures. Consequently, the alpha stable model is the most natural to be used in describing the statistics of PLC impulsive noise in industrial zones. Furthermore, the inter-arrival time is of Pareto distribution while the duration of impulses follows a mixed exponential distribution. All parameters of the alpha stable model as well as the Pareto parameters and the mixed exponents are statistically estimated. The variation of these parameters with time is also discussed.

A Comparison of Some Univariate Models for Value-at-Risk and Expected Shortfall

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum - stability assumption or the max - stability assumption, that respectively imply alpha-stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that alpha-stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Anomaly Detection in Network Traffic Based on Statistical Inference and \alpha-Stable Modeling

This paper proposes a novel method to detect anomalies in network traffic, based on a nonrestricted α-stable first-order model and statistical hypothesis testing. To this end, we give statistical evidence that the marginal distribution of real traffic is adequately modeled with α-stable functions and classify traffic patterns by means of a Generalized Likelihood Ratio Test (GLRT). The method automatically chooses traffic windows used as a reference, which the traffic window under test is compared with, with no expert intervention needed to that end. We focus on detecting two anomaly types, namely floods and flash-crowds, which have been frequently studied in the literature. Performance of our detection method has been measured through Receiver Operating Characteristic (ROC) curves and results indicate that our method outperforms the closely-related state-of-the-art contribution described in. All experiments use traffic data collected from two routers at our university-a 25,000 students institution-which provide two different levels of traffic aggregation for our tests (traffic at a particular school and the whole university). In addition, the traffic model is tested with publicly available traffic traces. Due to the complexity of α-stable distributions, care has been taken in designing appropriate numerical algorithms to deal with the model.

Segmentation-Driven Image Fusion Based on Alpha-Stable Modeling of Wavelet Coefficients

A novel region-based image fusion framework based on multiscale image segmentation and statistical feature extraction is proposed. A dual-tree complex wavelet transform (DT-CWT) and a statistical region merging algorithm are used to produce a region map of the source images. The input images are partitioned into meaningful regions containing salient information via symmetric alpha-stable (S alphaS) distributions. The region features are then modeled using bivariate alpha-stable (B alphaS) distributions, and the statistical measure of similarity between corresponding regions of the source images is calculated as the Kullback-Leibler distance (KLD) between the estimated B alphaS models. Finally, a segmentation-driven approach is used to fuse the images, region by region, in the complex wavelet domain. A novel decision method is introduced by considering the local statistical properties within the regions, which significantly improves the reliability of the feature selection and fusion processes. Simulation results demonstrate that the bivariate alpha-stable model outperforms the univariate alpha-stable and generalized Gaussian densities by not only capturing the heavy-tailed behavior of the subband marginal distribution, but also the strong statistical dependencies between wavelet coefficients at different scales. The experiments show that our algorithm achieves better performance in comparison with previously proposed pixel and region-level fusion approaches in both subjective and objective evaluation tests.

A low complexity robust detector in impulsive noise

This paper demonstrates the effectiveness of a nonlinear extension to the matched filter for signal detection in certain kinds of non-Gaussian noise. The decision statistic is based on a new measure of similarity that can be considered as an extension of the correlation statistic used in the matched filter. The optimality of the matched filter is predicated on second order statistics and hence leaves room for improvement, especially when the assumption of Gaussianity is not applicable. The proposed method incorporates higher order moments in the decision statistic and shows an improvement in the receiver operating characteristics (ROC) for non-Gaussian noise, in particular, those that are impulsive distributed. The performance of the proposed method is demonstrated for detection in two types of widely used impulsive noise models, the alpha-stable model and the two-term Gaussian mixture model. Moreover, unlike other kernel based approaches, and those using the characteristic functions directly, this method is still computationally tractable and can easily be implemented in real-time.

An $\alpha$-Stable Model-Based Linear-Parameter-Varying Control for Managing Server Performance Under Self-Similar Workloads

Applying control-theoretic approaches to capacity provisioning and performance management of Web servers is gaining increasing popularity in the past several years. This paper presents a novel control-theoretic approach that is a combination of linear-parameter-varying (LPV) techniques and workload characterization using alpha-stable-model based stochastic envelopes. In particular, we parameterize a control-oriented Web-server model and resulting controller using scheduling variables that are workload-distribution parameters. By further applying an alpha-stable modeling technique to identify the load parameters and using them to online schedule the LPV model and controller, the presented solutions not only allow the system to adapt to load variations, but also show great promise in handling self-similar workloads. The proposed framework is applied to a Web-server CPU management problem, where the server CPU frequencies are dynamically tuned and implemented via the dynamic voltage scaling mechanism to achieve the target response time. Simulations using real Web-server traces are conducted to show the strength of the proposed approach.

Alpha stable modeling of human visual systems for digital halftoning in rectangular and hexagonal grids

Human visual system (HVS) modeling has become a critical component in the design of digital halftoning algorithms. Methods that exploit the characteristics of the HVS include the direct binary search (DBS) and optimized tone-dependent halftoning approaches. The spatial sensitivity of the HVS is low-pass in nature, reflecting the physiological characteristics of the eye. Several HVS models have been proposed in the literature, among them, the broadly used Näsänen’s exponential model, which was later shown to be constrained in shape. Richer models are needed to attain better halftone attributes and to control the appearance of undesired patterns. As an alternative, models based on the mixture of bivariate Gaussian density functions have been proposed. The mathematical characteristics of the HVS model thus play a key role in the synthesis of model-based halftoning. In this work, alpha stable functions, an elegant class of functions richer than mixed Gaussians, are exploited to design HVS models to be used in two different contexts: monochrome halftoning over rectangular and hexagonal sampling grids. In the two scenarios, alpha stable models prove to be more efficient than Gaussian mixtures, as they use less parameters to characterize the tails and bandwidth of the model. It is shown that a decrease in the model’s bandwidth leads to homogeneous halftone patterns, and conversely, models with heavier tails yield smoother textures. These characteristics, added to their simplicity, make alpha stable models a powerful tool for HVS characterization.

Classification of shallow-water acoustic signals via alpha-Stable modeling of the one-dimensional wavelet coefficients

A novel statistical scheme is presented for the classification of shallow water acoustic signals according to the environmental parameters of the medium through which they have propagated. An efficient way to classify these signals is important for inverse procedures in underwater acoustics aiming at the recovery of the geoacoustic parameters of an oceanic environment, using measurements of the acoustic field due to an acoustic source. An important issue in this procedure is the determination of an efficient “observable” of the acoustic signal (feature extraction), which characterizes the signal in connection with the recoverable parameters. The proposed method is based on a transformation of the acoustic signals via a one-dimensional (1D) wavelet decomposition and then by fitting the distribution of the subband coefficients using an appropriate function. We observe that statistical distributions with heavy algebraic tails, such as the alpha-Stable family, are often very accurate in capturing the non-Gaussian behavior of the subband coefficients. As a result, the feature extraction step consists of estimating the parameters of the alpha-Stable model, while the similarity between two distinct signals is measured by employing the Kullback–Leibler Divergence between their corresponding alpha-Stable distributions. The performance of the proposed classification method is studied using simulated acoustic signals generated in a shallow water environment.

A new algorithm for shot noise removal in medical ultrasound images based on alpha-stable model

Ultrasonic images are generally affected by multiplicative shot noise. Shot noise filtering is thus a critical pre-processing step in medical ultrasound imagery. This paper analyses and models the coefficients of 2-D multi-resolution wavelet decomposition of logarithmically transformed images using alpha-stable distribution model. Consequently, we propose a new function that performs a non-linear operation on the data of classifying the coefficients, thus achieving a novel form of noise removal based on multi-resolution wavelet decomposition and the alpha-stable model. We compare our new technique with current shot noise reduction methods applied on actual ultrasound medical images and simulations results show that the proposed new method is more robust than the methods based on Gaussian assumption. Copyright © 2006 John Wiley & Sons, Ltd.