A Single-Shot Scattering Medium Imaging Method via Bispectrum Truncation.

Imaging using scattering media is a very important yet challenging technology. As one of the most widely used scattering imaging methods, speckle autocorrelation technology has important applications in several fields. However, traditional speckle autocorrelation imaging methods usually use iterative phase recovery algorithms to obtain the Fourier phase of hidden objects, posing issues such as large data calculation volumes and uncertain reconstruction results. Here, we propose a single-shot scattering imaging method based on the bispectrum truncation method. The bispectrum analysis is utilized for hidden object phase recovery, the truncation method is used to avoid the computation of redundant data when calculating the bispectrum data, and the method is experimentally verified. The experimental results show that our method does not require uncertain iterative calculations and can reduce the bispectrum data computation by more than 80% by adjusting the truncation factor without damaging the imaging quality, which greatly improves imaging efficiency. This method paves the way for rapid imaging through scattering media and brings benefits for imaging in dynamic situations.

Higher-Order Spectral Analysis Combined with a Convolution Neural Network for Atrial Fibrillation Detection-Preliminary Study.

The global burden of atrial fibrillation (AFIB) is constantly increasing, and its early detection is still a challenge for public health and motivates researchers to improve methods for automatic AFIB prediction and management. This work proposes higher-order spectra analysis, especially the bispectrum of electrocardiogram (ECG) signals combined with the convolution neural network (CNN) for AFIB detection. Like other biomedical signals, ECG is non-stationary, non-linear, and non-Gaussian in nature, so the spectra of higher-order cumulants, in this case, bispectra, preserve valuable features. The two-dimensional (2D) bispectrum images were applied as input for the two CNN architectures with the output AFIB vs. no-AFIB: the pre-trained modified GoogLeNet and the proposed CNN called AFIB-NET. The MIT-BIH Atrial Fibrillation Database (AFDB) was used to evaluate the performance of the proposed methodology. AFIB-NET detected atrial fibrillation with a sensitivity of 95.3%, a specificity of 93.7%, and an area under the receiver operating characteristic (ROC) of 98.3%, while for GoogLeNet results for sensitivity and specificity were equal to 96.7%, 82%, respectively, and the area under ROC was equal to 96.7%. According to preliminary studies, bispectrum images as input to 2D CNN can be successfully used for AFIB rhythm detection.

Implementation of a Real-Time Brain-to-Brain Synchrony Estimation Algorithm for Neuroeducation Applications.

This study centers on creating a real-time algorithm to estimate brain-to-brain synchronization during social interactions, specifically in collaborative and competitive scenarios. This type of algorithm can provide useful information in the educational context, for instance, during teacher-student or student-student interactions. Positioned within the context of neuroeducation and hyperscanning, this research addresses the need for biomarkers as metrics for feedback, a missing element in current teaching methods. Implementing the bispectrum technique with multiprocessing functions in Python, the algorithm effectively processes electroencephalography signals and estimates brain-to-brain synchronization between pairs of subjects during (competitive and collaborative) activities that imply specific cognitive processes. Noteworthy differences, such as higher bispectrum values in collaborative tasks compared to competitive ones, emerge with reliability, showing a total of 33.75% of significant results validated through a statistical test. While acknowledging progress, this study identifies areas of opportunity, including embedded operations, wider testing, and improved result visualization. Beyond academia, the algorithm's utility extends to classrooms, industries, and any setting involving human interactions. Moreover, the presented algorithm is shared openly, to facilitate implementations by other researchers, and is easily adjustable to other electroencephalography devices. This research not only bridges a technological gap but also contributes insights into the importance of interactions in educational contexts.

Escalator Foundation Bolt Loosening Fault Recognition Based on Empirical Wavelet Transform and Multi-Scale Gray-Gradient Co-Occurrence Matrix.

An escalator is an essential large-scale public transport equipment; once it fails, this inevitably affects the operation of the escalator and even leads to safety concerns, or perhaps accidents. As an important structural part of the escalator, the foundation of the main engine can cause the operation of the escalator to become abnormal when its fixing bolts become loose. Aiming to reduce the difficulty of extracting the fault features of the footing bolt when it loosens, a fault feature extraction method is proposed in this paper based on empirical wavelet transform (EWT) and the gray-gradient co-occurrence matrix (GGCM). Firstly, the Teager energy operator and multi-scale peak determination are used to improve the spectral partitioning ability of EWT, and the improved EWT is used to decompose the original foundation vibration signal into a series of empirical mode functions (EMFs). Then, the gray-gradient co-occurrence matrix of each EMF is constructed, and six texture features of the gray-gradient co-occurrence matrix are calculated as the fault feature vectors of this EMF. Finally, the fault features of all EMFs are fused, and the degree of the loosening of the escalator foundation bolt is identified using the fused multi-scale feature vector and BiLSTM. The experimental results show that the proposed method based on EWT and GGCM feature extraction can diagnose the loosening degree of foundation bolts more effectively and has a certain engineering application value.

Distribution Characteristics of Ground Echo Amplitude and Recognition of Signal Grazing Angle.

With the continuous advancement of electronic technology, terahertz technology has gradually been applied on radar. Since short wavelength causes severe ground clutter, this paper studies the amplitude distribution statistical characteristics of the terahertz radar clutter based on the measured data, and provides technical support for the radar clutter suppression. Clutter distribution is the function of the radar glancing angle. In order to achieve targeted suppression, in this paper, selected axial integral bispectrum (selected AIB) feature is selected as deep belief network (DBN)input to complete the radar glancing angle recognition and the network structure, network training method, robustness are analyzed also. The ground clutter amplitude distribution can follow normal distribution at 0~45° grazing angles. The Weibull distribution and G0 distribution can describe the amplitude probability density function of ground clutter at grazing angles 85° and 65°. The recognition rate of different signal grazing angles can reach 91% on three different terrains. At the same time, the wide applicability of the selected AIB feature is verified. The analysis results of ground clutter amplitude characteristics play an important role in the suppression of radar ground clutter.

Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack.

A breathing crack is a typical form of structural damage attributed to long-term dynamic loads acting on engineering structures. Traditional linear damage identification methods suffer from the loss of valuable information when structural responses are essentially non-linear. To deal with this issue, bispectrum analysis is employed to study the non-linear dynamic characteristics of a beam structure containing a breathing crack, from the perspective of numerical simulation and experimental validation. A finite element model of a cantilever beam is built with contact elements to simulate a breathing crack. The effects of crack depth and location, excitation frequency and magnitude, and measurement noise on the non-linear behavior of the beam are studied systematically. The result demonstrates that bispectral analysis can effectively identify non-linear damage in different states with strong noise immunity. Compared with existing methods, the bispectral non-linear analysis can efficiently extract non-linear features of a breathing crack, and it can overcome the limitations of existing linear damage detection methods used for non-linear damage detection. This study's outcome provides a theoretical basis and a paradigm for damage identification in cracked structures.

A Novel Block Imaging Technique Using Nine Artificial Intelligence Models for COVID-19 Disease Classification, Characterization and Severity Measurement in Lung Computed Tomography Scans on an Italian Cohort.

Computer Tomography (CT) is currently being adapted for visualization of COVID-19 lung damage. Manual classification and characterization of COVID-19 may be biased depending on the expert's opinion. Artificial Intelligence has recently penetrated COVID-19, especially deep learning paradigms. There are nine kinds of classification systems in this study, namely one deep learning-based CNN, five kinds of transfer learning (TL) systems namely VGG16, DenseNet121, DenseNet169, DenseNet201 and MobileNet, three kinds of machine-learning (ML) systems, namely artificial neural network (ANN), decision tree (DT), and random forest (RF) that have been designed for classification of COVID-19 segmented CT lung against Controls. Three kinds of characterization systems were developed namely (a) Block imaging for COVID-19 severity index (CSI); (b) Bispectrum analysis; and (c) Block Entropy. A cohort of Italian patients with 30 controls (990 slices) and 30 COVID-19 patients (705 slices) was used to test the performance of three types of classifiers. Using K10 protocol (90% training and 10% testing), the best accuracy and AUC was for DCNN and RF pairs were 99.41 ± 5.12%, 0.991 (p < 0.0001), and 99.41 ± 0.62%, 0.988 (p < 0.0001), respectively, followed by other ML and TL classifiers. We show that diagnostics odds ratio (DOR) was higher for DL compared to ML, and both, Bispecturm and Block Entropy shows higher values for COVID-19 patients. CSI shows an association with Ground Glass Opacities (0.9146, p < 0.0001). Our hypothesis holds true that deep learning shows superior performance compared to machine learning models. Block imaging is a powerful novel approach for pinpointing COVID-19 severity and is clinically validated.

Fault Diagnosis of Planetary Gearbox Based on Adaptive Order Bispectrum Slice and Fault Characteristics Energy Ratio Analysis.

The vibration of a planetary gearbox (PG) is complex and mutually modulated, which makes the weak features of incipient fault difficult to detect. To target this problem, a novel method, based on an adaptive order bispectrum slice (AOBS) and the fault characteristics energy ratio (FCER), is proposed. The order bispectrum (OB) method has shown its effectiveness in the feature extraction of bearings and fixed-shaft gearboxes. However, the effectiveness of the PG still needs to be explored. The FCER is developed to sum up the fault information, which is scattered by mutual modulation. In this method, the raw vibration signal is firstly converted to that in the angle domain. Secondly, the characteristic slice of AOBS is extracted. Different from the conventional OB method, the AOBS is extracted by searching for a characteristic carrier frequency adaptively in the sensitive range of signal coupling. Finally, the FCER is summed up and calculated from the fault features that were dispersed in the characteristic slice. Experimental data was processed, using both the AOBS-FCER method, and the method that combines order spectrum analysis with sideband energy ratio (OSA-SER), respectively. Results indicated that the new method is effective in incipient fault feature extraction, compared with the methods of OB and OSA-SER.

A Multitask-Aided Transfer Learning-Based Diagnostic Framework for Bearings under Inconsistent Working Conditions.

Rolling element bearings are a vital part of rotating machines and their sudden failure can result in huge economic losses as well as physical causalities. Popular bearing fault diagnosis techniques include statistical feature analysis of time, frequency, or time-frequency domain data. These engineered features are susceptible to variations under inconsistent machine operation due to the non-stationary, non-linear, and complex nature of the recorded vibration signals. To address these issues, numerous deep learning-based frameworks have been proposed in the literature. However, the logical reasoning behind crack severities and the longer training times needed to identify multiple health characteristics at the same time still pose challenges. Therefore, in this work, a diagnosis framework is proposed that uses higher-order spectral analysis and multitask learning (MTL), while also incorporating transfer learning (TL). The idea is to first preprocess the vibration signals recorded from a bearing to look for distinct patterns for a given fault type under inconsistent working conditions, e.g., variable motor speeds and loads, multiple crack severities, compound faults, and ample noise. Later, these bispectra are provided as an input to the proposed MTL-based convolutional neural network (CNN) to identify the speed and the health conditions, simultaneously. Finally, the TL-based approach is adopted to identify bearing faults in the presence of multiple crack severities. The proposed diagnostic framework is evaluated on several datasets and the experimental results are compared with several state-of-the-art diagnostic techniques to validate the superiority of the proposed model under inconsistent working conditions.

Recognizing Non-Collaborative Radio Station Communication Behaviors Using an Ameliorated LeNet.

This work improves a LeNet model algorithm based on a signal's bispectral features to recognize the communication behaviors of a non-collaborative short-wave radio station. At first, the mapping relationships between the burst waveforms and the communication behaviors of a radio station are analyzed. Then, bispectral features of simulated behavior signals are obtained as the input of the network. With regard to the recognition neural network, the structure of LeNet and the size of the convolutional kernel in LeNet are optimized. Finally, the five types of communication behavior are recognized by using the improved bispectral estimation matrix of signals and the ameliorated LeNet. The experimental results show that when the signal-to-noise ratio (SNR) values are 8, 10, or 15 dB, the recognition accuracy values of the improved algorithm reach 81.5%, 94.5%, and 99.3%, respectively. Compared with other algorithms, the training time cost and recognition accuracy of the proposed algorithm are lower and higher, respectively; thus, the proposed algorithm is of great practical value.

A Novel Fault Detection Method for Rolling Bearings Based on Non-Stationary Vibration Signature Analysis.

To realize the accurate fault detection of rolling element bearings, a novel fault detection method based on non-stationary vibration signal analysis using weighted average ensemble empirical mode decomposition (WAEEMD) and modulation signal bispectrum (MSB) is proposed in this paper. Bispectrum is a third-order statistic, which can not only effectively suppress Gaussian noise, but also help identify phase coupling. However, it cannot effectively decompose the modulation components which are inherent in vibration signals. To alleviate this issue, MSB based on the modulation characteristics of the signals is developed for demodulation and noise reduction. Still, the direct application of MSB has some interfering frequency components when extracting fault features from non-stationary signals. Ensemble empirical mode decomposition (EEMD) is an advanced nonlinear and non-stationary signal processing approach that can decompose the signal into a list of stationary intrinsic mode functions (IMFs). The proposed method takes advantage of WAEEMD and MSB for bearing fault diagnosis based on vibration signature analysis. Firstly, the vibration signal is decomposed into IMFs with a different frequency band using EEMD. Then, the IMFs are reconstructed into a new signal by the weighted average method, called WAEEMD, based on Teager energy kurtosis (TEK). Finally, MSB is applied to decompose the modulated components in the reconstructed signal and extract the fault characteristic frequencies for fault detection. Furthermore, the efficiency and performance of the proposed WAEEMD-MSB approach is demonstrated on the fault diagnosis for a motor bearing outer race fault and a gearbox bearing inner race fault. The experimental results verify that the WAEEMD-MSB has superior performance over conventional MSB and EEMD-MSB in extracting fault features and has precise and effective advantages for rolling element bearing fault detection.

Continuous wavelet transform and higher-order spectrum: combinatory potentialities in breath sound analysis and electroencephalogram-based pain characterization.

The combination of the continuous wavelet transform (CWT) with a higher-order spectrum (HOS) merges two worlds into one that conveys information regarding the non-stationarity, non-Gaussianity and nonlinearity of the systems and/or signals under examination. In the current work, the third-order spectrum (TOS), which is used to detect the nonlinearity and deviation from Gaussianity of two types of biomedical signals, that is, wheezes and electroencephalogram (EEG), is combined with the CWT to offer a time-scale representation of the examined signals. As a result, a CWT/TOS field is formed and a time axis is introduced, creating a time-bifrequency domain, which provides a new means for wheeze nonlinear analysis and dynamic EEG-based pain characterization. A detailed description and examples are provided and discussed to showcase the combinatory potential of CWT/TOS in the field of advanced signal processing.This article is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Bispectrum Inversion with Application to Multireference Alignment.

We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the signal by aligning and averaging the data. In contrast, we consider a method based on estimating the signal directly, using features of the signal that are invariant under translations. Specifically, we estimate the power spectrum and the bispectrum of the signal from the observations. Under mild assumptions, these invariant features contain enough information to infer the signal. In particular, the bispectrum can be used to estimate the Fourier phases. To this end, we propose and analyze a few algorithms. Our main methods consist of non-convex optimization over the smooth manifold of phases. Empirically, in the absence of noise, these non-convex algorithms appear to converge to the target signal with random initialization. The algorithms are also robust to noise. We then suggest three additional methods. These methods are based on frequency marching, semidefinite relaxation and integer programming. The first two methods provably recover the phases exactly in the absence of noise. In the high noise level regime, the invariant features approach for MRA results in stable estimation if the number of measurements scales like the cube of the noise variance, which is the information-theoretic rate. Additionally, it requires only one pass over the data which is important at low signal-to-noise ratio when the number of observations must be large.

Feature Extraction and Similarity of Movement Detection during Sleep, Based on Higher Order Spectra and Entropy of the Actigraphy Signal: Results of the Hispanic Community Health Study/Study of Latinos.

The aim of this work was to develop a new unsupervised exploratory method of characterizing feature extraction and detecting similarity of movement during sleep through actigraphy signals. We here propose some algorithms, based on signal bispectrum and bispectral entropy, to determine the unique features of independent actigraphy signals. Experiments were carried out on 20 randomly chosen actigraphy samples of the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) database, with no information other than their aperiodicity. The Pearson correlation coefficient matrix and the histogram correlation matrix were computed to study the similarity of movements during sleep. The results obtained allowed us to explore the connections between certain sleep actigraphy patterns and certain pathologies.

Early Fault Diagnosis for Planetary Gearbox Based Wavelet Packet Energy and Modulation Signal Bispectrum Analysis.

The planetary gearbox is at the heart of most rotating machinery. The premature failure and subsequent downtime of a planetary gearbox not only seriously affects the reliability and safety of the entire rotating machinery but also results in severe accidents and economic losses in industrial applications. It is an important and challenging task to accurately detect failures in a planetary gearbox at an early stage to ensure the safety and reliability of the mechanical transmission system. In this paper, a novel method based on wavelet packet energy (WPE) and modulation signal bispectrum (MSB) analysis is proposed for planetary gearbox early fault diagnostics. First, the vibration signal is decomposed into different time-frequency subspaces using wavelet packet decomposition (WPD). The WPE is calculated in each time-frequency subspace. Secondly, the relatively high energy vectors are selected from a WPE matrix to obtain a reconstructed signal. The reconstructed signal is then subjected to MSB analysis to obtain the fault characteristic frequency for fault diagnosis of the planetary gearbox. The validity of the proposed method is carried out through analyzing the vibration signals of the test planetary gearbox in two fault cases. One fault is a chipped sun gear tooth and the other is an inner-race fault in the planet gear bearing. The results show that the proposed method is feasible and effective for early fault diagnosis in planetary gearboxes.

Non-Gaussian Resistance Fluctuations in Gold-Nanoparticle-Based Gas Sensors: An Appraisal of Different Evaluation Techniques.

Volatile organic compounds, such as formaldehyde, can be used as biomarkers in human exhaled breath in order to non-invasively detect various diseases, and the same compounds are of much interest also in the context of environmental monitoring and protection. Here, we report on a recently-developed gas sensor, based on surface-functionalized gold nanoparticles, which is able to generate voltage noise with a distinctly non-Gaussian component upon exposure to formaldehyde with concentrations on the ppm level, whereas this component is absent, or at least much weaker, when the sensor is exposed to ethanol or to pure air. We survey four different statistical methods to elucidate a non-Gaussian component and assess their pros and cons with regard to efficient gas detection. Specifically, the non-Gaussian component was clearly exposed in analysis using level-crossing parameters, which require nothing but a modest computational effort and simple electronic circuitry, and analogous results could be reached through the bispectrum function, albeit with more intense computation. Useful information could be obtained also via the Lévy-stable distribution and, possibly, the second spectrum.

An Automatic Prediction of Epileptic Seizures Using Cloud Computing and Wireless Sensor Networks.

Epilepsy is one of the most common neurological disorders which is characterized by the spontaneous and unforeseeable occurrence of seizures. An automatic prediction of seizure can protect the patients from accidents and save their life. In this article, we proposed a mobile-based framework that automatically predict seizures using the information contained in electroencephalography (EEG) signals. The wireless sensor technology is used to capture the EEG signals of patients. The cloud-based services are used to collect and analyze the EEG data from the patient's mobile phone. The features from the EEG signal are extracted using the fast Walsh-Hadamard transform (FWHT). The Higher Order Spectral Analysis (HOSA) is applied to FWHT coefficients in order to select the features set relevant to normal, preictal and ictal states of seizure. We subsequently exploit the selected features as input to a k-means classifier to detect epileptic seizure states in a reasonable time. The performance of the proposed model is tested on Amazon EC2 cloud and compared in terms of execution time and accuracy. The findings show that with selected HOS based features, we were able to achieve a classification accuracy of 94.6 %.

Third order spectral analysis robust to mixing artifacts for mapping cross-frequency interactions in EEG/MEG.

We present a novel approach to the third order spectral analysis, commonly called bispectral analysis, of electroencephalographic (EEG) and magnetoencephalographic (MEG) data for studying cross-frequency functional brain connectivity. The main obstacle in estimating functional connectivity from EEG and MEG measurements lies in the signals being a largely unknown mixture of the activities of the underlying brain sources. This often constitutes a severe confounder and heavily affects the detection of brain source interactions. To overcome this problem, we previously developed metrics based on the properties of the imaginary part of coherency. Here, we generalize these properties from the linear to the nonlinear case. Specifically, we propose a metric based on an antisymmetric combination of cross-bispectra, which we demonstrate to be robust to mixing artifacts. Moreover, our metric provides complex-valued quantities that give the opportunity to study phase relationships between brain sources. The effectiveness of the method is first demonstrated on simulated EEG data. The proposed approach shows a reduced sensitivity to mixing artifacts when compared with a traditional bispectral metric. It also exhibits a better performance in extracting phase relationships between sources than the imaginary part of the cross-spectrum for delayed interactions. The method is then applied to real EEG data recorded during resting state. A cross-frequency interaction is observed between brain sources at 10Hz and 20Hz, i.e., for alpha and beta rhythms. This interaction is then projected from signal to source level by using a fit-based procedure. This approach highlights a 10-20Hz dominant interaction localized in an occipito-parieto-central network.

Transformations between rotational and translational invariants formulated in reciprocal spaces.

Correlation functions play an important role in the theoretical underpinnings of many disparate areas of the physical sciences: in particular, scattering theory. More recently, they have become useful in the classification of objects in areas such as computer vision and our area of cryoEM. Our primary classification scheme in the cryoEM image processing system, EMAN2, is now based on third order invariants formulated in Fourier space. This allows a factor of 8 speed up in the two classification procedures inherent in our software pipeline, because it allows for classification without the need for computationally costly alignment procedures. In this work, we address several formal and practical aspects of such multispectral invariants. We show that we can formulate such invariants in the representation in which the original signal is most compact. We explicitly construct transformations between invariants in different orientations for arbitrary order of correlation functions and dimension. We demonstrate that third order invariants distinguish 2D mirrored patterns (unlike the radial power spectrum), which is a fundamental aspects of its classification efficacy. We show the limitations of 3rd order invariants also, by giving an example of a wide family of patterns with identical (vanishing) set of 3rd order invariants. For sufficiently rich patterns, the third order invariants should distinguish typical images, textures and patterns.

Accumulated bispectral image-based respiratory sound signal classification using deep learning.

The COVID-19 virus is increasingly crucial to human health since new variants appear frequently. Detection of COVID-19 through respiratory sound has been an important area of research. This study analyzes respiratory sounds using novel accumulated bi-spectral features. The principal domain bispectrum is used for computing accumulated bispectrum. The resulting magnitude bispectrum is used in forming the bispectral image. In this work, a convolutional neural network (CNN) and ResNet-50 algorithms are designed to classify respiratory sounds as either COVID-19 or healthy. The performance of the proposed method is compared with the state-of-the-art methods. The proposed CNN-based method achieves the highest accuracy of 87.68% for shallow breath sounds, and ResNet-50 achieves the highest accuracy of 87.62% for deep breath sounds. Similarly, proposed methods gives the improved performance for other respiratory sounds.