Second-order Statistical Methods Research Articles

Study of Interference Detection of Rail Transit Wireless Communication System Based on Fourth-Order Cyclic Cumulant.

The wireless communication system is used to provide dispatching, control, communication and other services for rail transit operations. In practice, interference from other wireless communication systems will affect the normal operation of trains, so it is an urgent problem to study the interference detection algorithms for rail transit applications. In this paper, the fourth-order cyclic cumulant (FOCC) of signals with different modulation modes is analyzed for the narrow-band wireless communications system of rail transit. Based on the analysis results, an adjacent-frequency interference detection algorithm is proposed according to the FOCC of the received signal within the predetermined cyclic frequency range. To detect interference with the same carrier frequency, a same-frequency interference detection algorithm using the relationship between the FOCC and the received power is proposed. The performance of the proposed detection algorithms in terms of correct rate and computational complexity is analyzed and compared with the traditional second-order statistical methods. Simulation results show that when an interference signal coexists with the expected signal, the correct rates of the adjacent-frequency and the same-frequency interference detection algorithms are greater than 90% when the signal-to-noise ratio (SNR) is higher than 2 dB and -4 dB, respectively. Under the practical rail transit wireless channel with multipath propagation and the Doppler effect, the correct rates of the adjacent-frequency and the same-frequency interference detection algorithms are greater than 90% when the SNR is higher than 3 dB and 7 dB, respectively. Compared with the existing second-order statistical methods, the proposed method can detect both the adjacent-frequency and the same-frequency interference when the interference signals coexist with the expected signal. Although the computational complexity of the proposed method is increased, it is acceptable in the application of rail transit wireless communication interference detection.

Повышение эффективности текстурной сегментации лесного полога по изображениям сверхвысокого пространственного разрешения

The issue of increasing the accuracy of tree canopy segmentation structures in the processing of very high spatial resolution satellite images by joint use of textural features extracted by different methods is considered. The TTSPCA method (Total Texture Statistics Principal Component Analysis) is proposed and its effectiveness is shown for a number of test cases. Estimates of TTSPCA effectiveness are obtained for the forest stands segmentation and growth types. The panchromatic Worldview-2 image of the test area (Bronnitskoye forestry, Moscow region) obtained in summer was used as remote data. To perform texture segmentation, in addition to TTSPCA, several standard second-order statistical methods and a spectral (energy) method based on the wavelet transform were also used. It is shown that almost all considered statistical and spectral methods provide forest stand segmentation with errors not exceeding 3–4 %. It has been established that the TTSPCA method makes it possible to reduce the probability of errors in the forest inventory zone, as well as to identify sections with a predominance of natural and artificial plantations with an accuracy of over 85 %. The results obtained can be further recommended for use in order to improve the system we are developing for joint spectral-textural processing of satellite images with different spatial resolutions.

A Parallel Solution of Timing Synchronization in High-Speed Remote Sensing Data Transmission

Considering the problem that the timing synchronization calculation in high-speed remote sensing signal reception is complex and it is difficult for it to be parallel, this paper deduces and designs a parallel timing error estimation and correction scheme. This paper presents the design of polyphase DFT filter banks with non-maximum decimation. The feedforward timing error estimation and correction method is then improved to enhance synchronization performance. Finally, an implementation scheme for parallel timing error estimation and correction is proposed using the polyphase filter bank time domain decomposition method and the filter polyphase model. In the estimation module, the parallel implementation structure of the joint second-order and fourth-order cyclic statistics methods is designed, which improves the estimation accuracy. In the correction module, a fractional delay filtering method with higher accuracy is adopted in order to improve the calibration accuracy and reduce the computational complexity. The timing synchronization of a high-speed remote sensing signal with timing error is simulated and verified. The experimental results show that the parallel method proposed in this paper greatly reduces the processing speed of subband data, and has a good synchronization performance, which is close to the theoretical limit in the demodulation error rate. This paper utilizes a multi-phase DFT filter bank architecture to achieve parallel timing synchronization, which presents a novel approach for the future parallel reception of high-speed remote sensing signals.

A novel Bayesian blind source separation approach for extracting non-stationary and discontinuous components from structural health monitoring data

We propose a new method to explore the blind source separation (BSS) of heterogeneous structural health monitoring (SHM) data containing non-stationary and temporally discontinuous components in the framework of Bayesian inference. Specifically, Gaussian process (GP) with a specially defined time-varying kernel function is introduced to encode the prior information about the unknown sources. The time-varying kernel function encompasses a state indicator hyperparameter which enables the expressivity of intermittently active and inactive source signals and incorporates smooth switch and composite kernels catering for the interpretation of complex sources. With the likelihood function elicited from monitoring data alongside with the priors for sources, mixing matrix and noise, the unknown sources are extracted from the posterior distributions formalized by Bayes’ theorem, where a sequential Metropolis − Hasting sampling algorithm is adopted to numerically compute the source statistics in a high-dimensional realm. Numerical simulations demonstrate that the proposed method performs satisfactorily in (i) extracting intermittently active and inactive (abruptly appearing and disappearing) non-stationary source signals, (ii) estimating inconsistent levels of noise contaminated in different sensors, and (iii) handling unknown number of sources. In the verification using real-world strain monitoring data collected from the Tsing Ma Bridge carrying both highway and railway traffic, it is shown that the proposed method well extracts the railway-induced non-stationary strain component with intermittence, and the structural condition index formulated by the Bayesian dynamic linear model (BDLM) is more robust when adopting the separated highway-induced strain data than using the combined railway- and highway-induced strain data. The results obtained by the proposed method are also compared with those by the two most common BSS techniques — the independent component analysis (ICA) and second-order statistics (SOS) methods.

Classification of PPMI MRI scans with voxel-based morphometry and machine learning to assist in the diagnosis of Parkinson’s disease

Background and objectives: Qualitative and quantitative analyses of Magnetic Resonance Imaging (MRI) scans are carried out to study and understand Parkinson’s Disease, the second most common neurodegenerative disorder in people at their 60’s. Some quantitative analyses are based on the application of voxel-based morphometry (VBM) on magnetic resonance images to determine the regions of interest, within gray matter, where there is a loss of the nerve cells that generate dopamine. This loss of dopamine is indicative of Parkinson’s disease. The purpose of this research is the introduction of a new method to classify the 3-D magnetic resonance scans of an individual, as an assisting tool for diagnosis of Parkinson’s disease by using the largest MRI dataset (Parkinson’s Progression Markers Initiative) from a population of patients with Parkinson’s disease and control individuals. A contribution is that separate studies are conducted for men and women since gender plays a significant role within Neurobiology, which is demonstrated by the fact that men are more prone to Parkinson’s disease than women are.Methods: Previous to classification, VBM is conducted on magnetic resonance images to detect the regions where features are extracted by using first- and second-order statistics methods. Furthermore, the number of features is considerably reduced by using feature selection techniques. Seven classifiers are used and we are conducting separate experiments for men and women.Results: The best detection performance achieved in men is 99.01% of accuracy, 99.35% of sensitivity, 100% of specificity, and 100% of precision. The best detection performance achieved in women is 96.97% of accuracy, 100% of sensitivity, 96.15% of specificity, and 97.22% of precision. During classification of magnetic resonance images, the corresponding computational complexity is reduced since few features are selected.Conclusions: The proposed method provides high performance as an assisting tool in the diagnosis of Parkinson’s disease, by conducting separate experiments in men and women. While previous works have focused their analysis to the striatum region of the brain (the largest nuclear complex of the basal ganglia), the proposed approach is based on analysis over the whole brain by looking for decreases of tissue thickness, with the consequence of finding other regions of interest such as the cortex.

Image Data-Based Surface Texture Characterization and Prediction Using Machine Learning Approaches for Additive Manufacturing

Abstract The increase in the use of metal additive manufacturing (AM) processes in major industries like aerospace, defense, and electronics indicates the need for maintaining a tight quality control. A quick, low-cost, and reliable online surface texture measurement and verification system are required to improve its industrial adoption. In this paper, a comprehensive investigation of the surface characteristics of Ti-6Al-4V selective laser melted (SLM) parts using image texture parameters is discussed. The image texture parameters extracted from the surface images using first-order and second-order statistical methods, and measured 3D surface roughness parameters are used for characterizing the SLM surfaces. A comparative study of roughness prediction models developed using various machine learning approaches is also presented. Among the models, the Gaussian process regression (GPR) model gives an accurate prediction of roughness values with an R2 value of more than 0.9. The test data results of all models are presented.

Procesamiento de imágenes digitales aplicado al análisis de color y textura del piloncillo de la Huasteca Potosina

The present work demonstrates the implementation of image processing techniques to analyze the color and texture of agroindustrial products, in this case, of the piloncillo or panela in its granular and cone variety. A technological tool based on software was developed, capable of quantifying color and texture and thus implementing quality controls to support the commercialization of this product made in Huasteca Potosina towards global markets. An unsupervised classification method (clustering) is proposed to define the color or colors of the piloncillo, called K-means. In the case of texture analysis, second-order statistical methods derived from the co-occurrence matrix and six Haralick textural descriptors are used: contrast, homogeneity, energy, ASM, correlation and dissimilarity. The developed prototype was validated in 24 producing communities of granulated and cone-shaped piloncillo belonging to the municipalities of Tanlajas and Tancanhuitz, S.L.P. The results of the analysis of color and texture have been related to the manufacturing methods that are currently used, to identify improvements that help standardize the production process.

A second-order statistics method for blind source separation in post-nonlinear mixtures

• Derivation of the conditions and the constraints on the Post-Nonlinear (PNL) model for Second-Order Statistics (SOS)-based separation. • Proposition of an SOS-based method for separation using a time-extended formulation. • Formulation considers the analytical computation of the time-extended covariance matrices. • Promising perspectives for the extension to any polynomial mixing functions in the PNL model. In the context of nonlinear Blind Source Separation (BSS), the Post-Nonlinear (PNL) model is of great importance due to its suitability for practical nonlinear problems. Under certain mild constraints on the model, Independent Component Analysis (ICA) methods are valid for performing source separation, but requires use of Higher-Order Statistics (HOS). Conversely, regarding the sole use of the Second-Order Statistics (SOS), their study is still in an initial stage. In that sense, in this work, the conditions and the constraints on the PNL model for SOS-based separation are investigated. The study encompasses a time-extended formulation of the PNL problem with the objective of extracting the temporal structure of the data in a more extensive manner, considering SOS-based methods for separation, including the proposition of a new one. Based on this, it is shown that, under some constraints on the nonlinearities and if a given number of time delays is considered, source separation can be successfully achieved, at least for polynomial nonlinearities. With the aid of metaheuristics called Differential Evolution and Clonal Selection Algorithm for optimization, the performances of the SOS-based methods are compared in a set of simulation scenarios, in which the proposed method shows to be a promising approach.

Robust blind channel estimation algorithm for linear STBC systems using fourth order cumulant matrices

A novel blind channel estimation algorithm, based on fourth-order cumulant matrices, is proposed and applied to linear Space–Time Block Coded (STBC) for Multiple Input Multiple Output systems. Contrary to subspace and Second-Order Statistics (SOS) methods, the presented approach estimates the channel matrix without any modification of the transmitter. It takes advantage of the statistical independence of the signals in front of the space–time encoding. In this paper, the presented algorithm estimates the channel matrix by minimizing a cost function based on the higher cumulant matrices after Zero-Forcing equalization to mitigate the computational complexity and improve the performance. We employ the proposed method to the STBC systems including Spatial Multiplexing, Orthogonal, quasi-Orthogonal and Non-Orthogonal STBC systems. Symbol error rate and Normalized Mean Square Error simulations of the proposed algorithm are shown for a different number of users, signal to noise ratios and different number of symbols per user in comparison with subspace and Second-Order Statistics (SOS) methods. The results show that the presented method performs well and outperforms other methods in estimating the channel matrix from the received data. Moreover, the proposed method presents high convergence speed in estimating the channel matrix.

A second-order blind source separation method for bilinear mixtures

In this paper, we are interested in the problem of Blind Source Separation using a Second-order Statistics (SOS) method in order to separate autocorrelated and mutually independent sources mixed according to a bilinear (BL) model. In this context, we propose a new approach called Bilinear Second-order Blind Source Separation, which is an extension of linear SOS methods, devoted to separate sources present in BL mixtures. These sources, called extended sources, include the actual sources and their products. We first study the statistical properties of the different extended sources, in order to verify the assumption of identifiability when the actual sources are zero-mean and when they are not. Then, we present the different steps performed in order to estimate these actual centred sources and to extract the actual mixing parameters. The obtained results using artificial mixtures of synthetic and real sources confirm the effectiveness of the new proposed approach.

A New Quality Map for 2-D Phase Unwrapping Based on Gray Level Co-Occurrence Matrix

Both in quality-guide phase unwrapping algorithms and weighted minimum-norm phase unwrapping algorithms, quality maps play a crucial role in obtaining the absolute phase from the wrapped ones. In this letter, a new technique for generating quality maps based on the gray level co-occurrence matrix (GLCM) is proposed. GLCM is a classical second-order statistics method for analyzing the texture features of images. Through exploring the second-order statistics of GLCM, much useful information in the image can be exploited. According to the characteristics of the interferogram, the second-order statistic of GLCM called “difference of entropy” is used to generate the quality maps. Besides, we modified the definition of “difference of entropy” to make the statistic more suitable for the problem. Finally, the new algorithm is compared with other conventional algorithms both in the simulated and real data experiments and the results show its better performance.

Characterization of spatiotemporal changes for the classification of dynamic contrast-enhanced magnetic-resonance breast lesions

The early detection of breast cancer is one of the most important predictors in determining the prognosis for women with malignant tumours. Dynamic contrast-enhanced magnetic-resonance imaging (DCE-MRI) is an important imaging modality for detecting and interpreting the different breast lesions from a time sequence of images and has proved to be a very sensitive modality for breast-cancer diagnosis. However, DCE-MRI exhibits only a moderate specificity, thus leading to a high rate of false positives, resulting in unnecessary biopsies that are stressful and physically painful for the patient and lead to an increase in the cost of treatment. There is a strong medical need for a DCE-MRI computer-aided diagnosis tool that would offer a reliable support to the physician's decision providing a high level of sensitivity and specificity. In our study we investigated the possibility of increasing differentiation between the malignant and the benign lesions with respect to the spatial variation of the temporal enhancements of three parametric maps, i.e., the initial enhancement (IE) map, the post-initial enhancement (PIE) map and the signal enhancement ratio (SER) map, by introducing additional methods along with the grey-level co-occurrence matrix, i.e., a second-order statistical method already applied for quantifying the spatiotemporal variations. We introduced the grey-level run-length matrix and the grey-level difference matrix, representing two additional, second-order statistical methods, and the circular Gabor as a frequency-domain-based method. Each of the additional methods is for the first time applied to the DCE-MRI data to differentiate between the malignant and the benign breast lesions. We applied the least-square minimum-distance classifier (LSMD), logistic regression and least-squares support vector machine (LS-SVM) classifiers on a total of 115 (78 malignant and 37 benign) breast DCE-MRI cases. The performances were evaluated using ten experiments of a ten-fold cross-validation. Our experimental analysis revealed the PIE map, together with the feature subset in which the discriminating ability of the co-occurrence features was increased by adding the newly introduced features, to be the most significant for differentiation between the malignant and the benign lesions. That diagnostic test - the aforementioned combination of parametric map and the feature subset achieved the sensitivity of 0.9193 which is statistically significantly higher compared to other diagnostic tests after ten-experiments of a ten-fold cross-validation and gave a statistically significantly higher specificity of 0.7819 for the fixed 95% sensitivity after the receiver operating characteristic (ROC) curve analysis. Combining the information from all the three parametric maps significantly increased the area under the ROC curve (AUC) of the aforementioned diagnostic test for the LSMD and logistic regression; however, not for the LS-SVM. The LSMD classifier yielded the highest area under the ROC curve when using the combined information, increasing the AUC from 0.9651 to 0.9755. Introducing new features to those of the grey-level co-occurrence matrix significantly increased the differentiation between the malignant and the benign breast lesions, thus resulting in a high sensitivity and improved specificity.

A General Framework to Perform the MAX/MIN Operations in Parameterized Statistical Timing Analysis Using Information Theoretic Concepts

As integrated circuit technologies are scaled down to the nanometer regime, process variations have increasing impact on circuit timing. To address this issue, parameterized statistical static timing analysis (SSTA) has been recently developed. In parameterized SSTA, process variations are represented as random variables (RVs) and timing quantities (delays and others) are expressed as functions of these variables. Most of the existing algorithms to compute the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> operations in parameterized SSTA model spatial and path-based statistical dependencies of variation sources using the second-order statistical methods. Unfortunately, such methods have limited capabilities to determine statistical relations between RVs. This results in decreasing the accuracy of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> algorithms, especially when process parameters follow non-Gaussian probability density functions (PDFs) and/or affect timing quantities nonlinearly. In contrast, information theory (IT) provides powerful techniques that allow a natural PDF-based analysis of probabilistic relations between RVs. So, in this paper, we propose a new framework to perform the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> operations based on IT concepts. The key ideas behind our framework are: 1) exploiting information entropy to measure unconditional equivalence between an actual <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> output and its approximate parameterized representation, and 2) using mutual information to measure equivalence of actual and parameterized <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> outputs from the viewpoint of their statistical relations to process variations. We construct a general IT-based <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> algorithm that allows a number of particular realizations accounting for statistical properties of parameterized RVs. The experimental results validate the correctness and demonstrate a high accuracy of the new IT-based approach to compute the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MAX</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIN</i> .

A second-order statistical method for spectrum sensingin correlated shadowing and fading environments

Abstract Spectrum sensing is one of the most important tasks of cognitive radios (CRs) in future wireless systems and of user equipment (UE) in next generation wireless networks (NGWNs). Therefore, deciding whether a specific portion of radio frequency (RF) spectrum is occupied or not is of paramount importance for all sorts of future wireless communications systems. In this study, a spectrum sensing method that employs a second–order statistical approach is proposed for detecting fast fading signals in spatially correlated shadowing environments. Analysis and performance results are presented along with the discussion related to the performance comparison of the energy detection method.

A robust structural design method using the Kriging model to define the probability of design success

In this study, a robust optimization method is proposed by introducing the Kriging approximation model and defining the probability of design-success. A key problem in robust optimization is that the mean and the variation of a response cannot be calculated easily. This research presents an implementation of the approximate statistical moment method based on the Kriging metamodel. Furthermore, the statistics using the second-order statistical approximation method are adopted to avoid the local robust optimum. Thus, the probability of design-success, which is defined as the probability of satisfying the imposed design requirements, is represented as a function of approximate mean and variance. The formulation for the robust optimization can be defined as the probability of design-success of each response. The mathematical problem and the design problems of a two-bar structure and microgyroscope are investigated for the validation of the proposed method.

Noise-insensitive image optimal flow estimation using higher-order statistics

A new algorithm is presented that estimates the displacement vector field from two successive image frames. In the case where the sequence is severely corrupted by additive (Gaussian or not, colored) noise of unknown covariance, then second-order statistics methods do not work well. However, we have studied this topic from a viewpoint different from the above to explore the fundamental limits in image optimal flow estimation. Our scheme is based on subpixel optimal flow estimation using the bispectrum in the parametric domain. The displacement vector of a moving object is estimated by solving linear equations involving third-order holograms and the matrix containing the Dirac delta function. To prove the feasibility of the proposed method, we compared it with a phase correlation technique and the nonparametric bispectrum method described in Res. Lett. Signal Process., ID 417915 (2008). Our results show that our method is considerably more immune to the presence of noise.

A framework for blind modal identification using joint approximate diagonalization

In this paper, a second-order statistical method employed in blind source separation (BSS) is adapted for use in modal parameter identification. Modal responses and mode shapes are estimated by the use of second-order blind identification (SOBI) on an expanded and pre-treated dataset. Frequency and damping can be obtained from the modal responses by simple single degree of freedom methods. Using this approach, a class of new non-parametric output-only modal identification algorithms is proposed and examples of its use are provided. It is demonstrated that the proposed methodology provides a novel and robust approach to modal identification. For the example shown, it is deduced that quality of the modal parameters produced by the method is competitive with the state of the art parametric methods.

A robust optimization using the statistics based on kriging metamodel

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.

Remote sensing methods and techniques as a tool for the implementation of environmental legislation. The Greek Forest Law case study

Implementation of environmental legislation can be supported by the production of maps with two information levels, one which identifies areas where a legal rule is enforced and another which identifies areas where there is an infringement of that rule. This paper investigates the efficiency of remote sensing methods and techniques for the production of such a map regarding a specific law case, the Greek Forest Law. To do this, we identified, with the use of KVR-1000 very high resolution imagery, potential illegal buildings in forests and forest areas, which were mapped at a scale of 1:5000. For this purpose, an image processing method was developed which integrates spectral and first-order texture signatures, detects disturbances in forest environment, and classifies them in order for the buildings to be identified among other disturbances. The texture signatures were selected after an investigation of the performance of first- and second-order statistical texture methods in detecting disturbances in forest environment. By the method developed, buildings are mapped by segmented parts of their edges. Based on a sample of 163 buildings, the accuracy of the method was calculated at approximately 89%, i.e. 11% of the buildings included in the sample were not detected. The map produced would probably not be acceptable in court, however it can adequately support administrative procedures in ministries, forest services, etc., regarding identification of illegal building, incorporation of forest areas in an existing city plan, organization of the forest and forest area register book, etc.

Equalization and interference cancellation in linear multiuser systems based on second-order statistics

Potential applications of blind channel identification and equalization in data communication systems have recently been explored. For multiuser systems that are irreducible and column-reduced, second-order statistical methods normally can identify channel dynamics up to a unitary mixing matrix. Additional user separation (equalization) can rely on higher order statistics and other prior information. In this paper, we investigate the equalizability of user signals and the cancellation of unwanted interfering signals based only on second-order output statistics. We show that a user channel can be equalized if it has the longest memory. Furthermore, interfering user signals can be cancelled under a more relaxed multiuser channel condition.