Multidimensional Signal Research Articles

Changes in EEG frequency characteristics during sevoflurane general anesthesia: feature extraction by variational mode decomposition.

Mode decomposition is a method for extracting the characteristic intrinsic mode function (IMF) from various multidimensional time-series signals. Variational mode decomposition (VMD) searches for IMFs by optimizing the bandwidth to a narrow band with the [Formula: see text] norm while preserving the online estimated central frequency. In this study, we applied VMD to the analysis of electroencephalogram (EEG) recorded during general anesthesia. Using a bispectral index monitor, EEGs were recorded from 10 adult surgical patients (the median age: 47.0, and the percentile range: 27.0-59.3years) who were anesthetized with sevoflurane. We created an application named EEG Mode Decompositor, which decomposes the recorded EEG into IMFs and displays the Hilbert spectrogram. Over the 30-min recovery from general anesthesia, the median (25-75 percentile range) bispectral index increased from 47.1 (42.2-50.4) to 97.4 (96.5-97.6), and the central frequencies of IMF-1 showed a significant change from 0.4 (0.2-0.5) Hz to 0.2 (0.1-0.3) Hz. IMF-2, IMF-3, IMF-4, IMF-5, and IMF-6 increased significantly from 1.4 (1.2-1.6) Hz to 7.5 (1.5-9.3) Hz, 6.7 (4.1-7.6) Hz to 19.4 (6.9-20.0) Hz, 10.9 (8.8-11.4) Hz to 26.4 (24.2-27.2) Hz, 13.4 (11.3-16.6) Hz to 35.6 (34.9-36.1) Hz, and 12.4 (9.7-18.1) Hz to 43.2 (42.9-43.4) Hz, respectively. The characteristic frequency component changes in specific IMFs during emergence from general anesthesia were visually captured by IMFs derived using VMD. EEG analysis by VMD is useful for extracting distinct changes during general anesthesia.

Multidimensional Signals and Analytic Flexibility: Estimating Degrees of Freedom in Human-Speech Analyses

Recent empirical studies have highlighted the large degree of analytic flexibility in data analysis that can lead to substantially different conclusions based on the same data set. Thus, researchers have expressed their concerns that these researcher degrees of freedom might facilitate bias and can lead to claims that do not stand the test of time. Even greater flexibility is to be expected in fields in which the primary data lend themselves to a variety of possible operationalizations. The multidimensional, temporally extended nature of speech constitutes an ideal testing ground for assessing the variability in analytic approaches, which derives not only from aspects of statistical modeling but also from decisions regarding the quantification of the measured behavior. In this study, we gave the same speech-production data set to 46 teams of researchers and asked them to answer the same research question, resulting in substantial variability in reported effect sizes and their interpretation. Using Bayesian meta-analytic tools, we further found little to no evidence that the observed variability can be explained by analysts’ prior beliefs, expertise, or the perceived quality of their analyses. In light of this idiosyncratic variability, we recommend that researchers more transparently share details of their analysis, strengthen the link between theoretical construct and quantitative system, and calibrate their (un)certainty in their conclusions.

Single-Target Real-Time Passive WiFi Tracking

Device-free human tracking is an essential ingredient for ubiquitous wireless sensing. Recent passive WiFi tracking systems face the challenges of inaccurate separation of dynamic human components and time-consuming estimation of multi-dimensional signal parameters. In this work, we present a scheme named WiFi Doppler Frequency Shift (WiDFS), which can achieve single-target real-time passive tracking using channel state information (CSI) collected from commercial-off-the-shelf (COTS) WiFi devices. We consider the typical system setup including a transmitter with a single antenna and a receiver with three antennas; while our scheme can be readily extended to another setup. To remove the impact of transceiver asynchronization, we first apply CSI cross-correlation between each RX antenna pair. We then combine them to estimate a Doppler frequency shift (DFS) in a short-time window. After that, we leverage the DFS estimate to separate dynamic human components from CSI self-correlation terms of each antenna, thereby separately calculating angle-of-arrival (AoA) and human reflection distance for tracking. In addition, a hardware calibration algorithm is presented to refine the spacing between RX antennas and eliminate the hardware-related phase differences between them. A prototype demonstrates that WiDFS can achieve real-time tracking with a median position error of 72.32 cm in multipath-rich environments.

Combinatorial Auctions with Interdependent Valuations: SOS to the Rescue

We study combinatorial auctions with interdependent valuations, where each agent i has a private signal si that captures her private information and the valuation function of every agent depends on the entire signal profile, [Formula: see text]. The literature in economics shows that the interdependent model gives rise to strong impossibility results and identifies assumptions under which optimal solutions can be attained. The computer science literature provides approximation results for simple single-parameter settings (mostly single-item auctions or matroid feasibility constraints). Both bodies of literature focus largely on valuations satisfying a technical condition termed single crossing (or variants thereof). We consider the class of submodular over signals (SOS) valuations (without imposing any single crossing-type assumption) and provide the first welfare approximation guarantees for multidimensional combinatorial auctions achieved by universally ex post incentive-compatible, individually rational mechanisms. Our main results are (i) four approximation for any single-parameter downward-closed setting with single-dimensional signals and SOS valuations; (ii) four approximation for any combinatorial auction with multidimensional signals and separable-SOS valuations; and (iii) (k + 3) and (2 log(k) + 4) approximation for any combinatorial auction with single-dimensional signals, with k-sized signal space, for SOS and strong-SOS valuations, respectively. All of our results extend to a parameterized version of SOS, d-approximate SOS, while losing a factor that depends on d. Funding: A. Eden was partially supported by NSF Award IIS-2007887, the European Research Council (ERC) under the European Union's Seventh Framework Programme [FP7/2007-2013]/ERC Grant Agreement 337122, by the Israel Science Foundation [Grant 317/17], and by an Amazon research award. M. Feldman received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program [Grant Agreement 866132], by the Israel Science Foundation [Grant 317/17], by an Amazon research award, and by the NSF-BSF [Grant 2020788]. The work of K. Goldner was supported partially by NSF awards DMS-1903037 and CNS-2228610 and a Shibulal Family Career Development Professorship. A. R. Karlin was supported by the NSF-CCF [Grant 1813135].

Convolution, Correlation, and Uncertainty Principles for the Quaternion Offset Linear Canonical Transform

Quaternion Fourier transform (QFT) has gained significant attention in recent years due to its effectiveness in analyzing multi-dimensional signals and images. This article introduces two-dimensional (2D) right-sided quaternion offset linear canonical transform (QOLCT), which is the most general form of QFT with additional free parameters. We explore the properties of 2D right-sided QOLCT, including inversion and Parseval formulas, besides its relationship with other transforms. We also examine the convolution and correlation theorems of 2D right-sided QOLCT, followed by several uncertainty principles. Additionally, we present an illustrative example of the proposed transform, demonstrating its graphical representation of a given signal and its transformed signal. Finally, we demonstrate an application of QOLCT, where it can be utilized to generalize the treatment of swept-frequency filters.

A Machine Learning Method for the Quality Detection of Base Liquor and Commercial Liquor Using Multidimensional Signals from an Electronic Nose.

Chinese liquor is a world-famous beverage with a long history. Base liquor, a product of liquor brewing, significantly affects the flavor and quality of commercial liquor. In this study, a machine learning method consisting of a deep residual network (ResNet)18 backbone with a light gradient boosting machine (LightGBM) classifier (ResNet-GBM) is proposed for the quality identification of base liquor and commercial liquor using multidimensional signals from an electronic nose (E-Nose). Ablation experiments are conducted to analyze the contribution of the framework's components. Five evaluation metrics (accuracy, sensitivity, precision, F1 score, and kappa score) are used to verify the performance of the proposed method, and six other frameworks (support vector machine (SVM), random forest (RF), k-nearest neighbor (KNN), extreme gradient boosting (XGBoost), multidimensional scaling-support vector machine (MDS-SVM), and back-propagation neural network (BPNN)) on three datasets (base liquor, commercial liquor, and mixed base and commercial liquor datasets). The experimental results demonstrate that the proposed ResNet-GBM model achieves the best performance for identifying base liquor and commercial liquors with different qualities. The proposed framework has the highest F1 score for the identification of commercial liquor in the mixed dataset due to the contribution of similar microconstituents from the base liquor. The proposed method can be used for the quality control of Chinese liquor and promotes the practical application of E-nose devices.

Nonlinear independent component analysis for discrete-time and continuous-time signals

We study the classical problem of recovering a multidimensional source signal from observations of nonlinear mixtures of this signal. We show that this recovery is possible (up to a permutation and monotone scaling of the source’s original component signals) if the mixture is due to a sufficiently differentiable and invertible but otherwise arbitrarily nonlinear function and the component signals of the source are statistically independent with ‘nondegenerate’ second-order statistics. The latter assumption requires the source signal to meet one of three regularity conditions which essentially ensure that the source is sufficiently far away from the nonrecoverable extremes of being deterministic or constant in time. These assumptions, which cover many popular time series models and stochastic processes, allow us to reformulate the initial problem of nonlinear blind source separation as a simple-to-state problem of optimisation-based function approximation. We propose to solve this approximation problem by minimizing a novel type of objective function that efficiently quantifies the mutual statistical dependence between multiple stochastic processes via cumulant-like statistics. This yields a scalable and direct new method for nonlinear Independent Component Analysis with widely applicable theoretical guarantees and for which our experiments indicate good performance.

Three‐dimensional generalized analytic signal associated with linear canonical transform in Clifford biquaternion domain

Analytic signal is a useful mathematical tool. It separates qualitative and quantitative information of a signal in form of the local phase and local amplitude. Clifford Fourier transform (CFT) plays a vital role in the representation of multidimensional signals. By generalizing the CFT to Clifford linear canonical transform (CLCT), we present a new type of Clifford biquaternionic analytic signal. Due to the advantages of more freedom, the envelop detection problems of 3D images, with the help of this new analytic signal, can get a better visual appearance. Synthesis examples are presented to demonstrate these advantages.

On the least amount of training data for a machine learning model

Whether the exact amount of training data is enough for a specific task is an important question in machine learning, since it is always very expensive to label many data while insufficient data lead to underfitting. In this paper, the topic that what is the least amount of training data for a model is discussed from the perspective of sampling theorem. If the target function of supervised learning is taken as a multi-dimensional signal and the labeled data as samples, the training process can be regarded as the process of signal recovery. The main result is that the least amount of training data for a bandlimited task signal corresponds to a sampling rate which is larger than the Nyquist rate. Some numerical experiments are carried out to show the comparison between the learning process and the signal recovery, which demonstrates our result. Based on the equivalence between supervised learning and signal recovery, some spectral methods can be used to reveal underlying mechanisms of various supervised learning models, especially those “black-box” neural networks.

Tensor-Based Denoising on Multi-dimensional Diagnostic Signals of Rolling Bearing

Tensor-Based Denoising on Multi-dimensional Diagnostic Signals of Rolling Bearing

The price of independence in a model with unknown dependence

How much does it cost a decisionmaker to base her payoff on interdependent, biased information sources? This question is relevant in economics, statistics, and politics. When there are many information sources, their dependence may be unknown or uncertain, which creates multivariate ambiguity. One approach to answer our leading question involves decoupling inequalities from probability theory. We present new inequalities which hold for any type of dependence. We apply our method to a simple formalization of risky asset investment, and to a voting model where citizens face dependent political signals. For a given set of marginal information, the decoupling bound is the sup over all possible joint distributions connecting the marginals. The bound may therefore be useful in other contexts, when a decisionmaker faces unawareness about the joint distribution of information. Our method highlights a frontier which bounds the maximum value of the decisionmaker’s payoff from dependent multidimensional signals. Beneath the bound lies the set of possible payoffs one could obtain from the signals. In this setting, decoupling performs a somewhat similar function to that of the threshold of acceptance sets, in choice under uncertainty. We show that a conservative decisionmaker’s maximal payoff is approximately 50% more than if the signals were independent.

Physics-Guided Terahertz Computational Imaging: A tutorial on state-of-the-art techniques

Visualizing information inside objects is an everlasting need to bridge the world from physics, chemistry, and biology to computation. Among all tomographic techniques, terahertz (THz) computational imaging has demonstrated its unique sensing features to digitalize multidimensional object information in a nondestructive, nonionizing, and noninvasive way. Applying modern signal processing and physics-guided modalities, THz computational imaging systems have now been launched in various application fields in industrial inspection, security screening, chemical inspection, and nondestructive evaluation. In this article, we review recent advances in THz computational imaging modalities in the aspects of system configuration; wave propagation and interaction models; and physics-guided algorithms for digitalizing interior information of imaged objects. Several image restoration and reconstruction issues based on multidimensional THz signals are further discussed, which provides a crosslink among material digitalization, functional property extraction, and multidimensional imager utilization from a signal processing perspective.

Multidimensional Signal Processing for High Areal Density Heated-Dot Magnetic Recording

In this article, a new multidimensional signal processing scheme for a heated-dot magnetic recording (HDMR) system using double-layered bit-patterned media (BPM) is proposed. This proposed signal processing scheme is capable of simultaneously detecting data sequences recorded on two tracks in each layer sequentially. The effective transmission rate of the HDMR system with two-track simultaneous log-likelihood ratio (LLR) detection and double-layered recording can be increased about four times that of the HDMR system with single-track LLR detection and single-layered recording if the data sequence recorded on each track has the same rate. It is shown that the error rate performance of the HDMR system with two-track simultaneous LLR detection and double-layered recording shows a significant improvement over the HDMR system with single-track LLR detection and single-layered recording by computer simulation.

Cations make a difference: Soil nutrient patches and fine‐scale root abundance of individual species in a mountain grassland

Abstract Root densities in the field vary at the centimetre scale, but we have no information on whether this variation is linked to the variation in nutrient concentrations and availability. Roots of many species are able to proliferate in nutrient‐rich patches in controlled conditions in culture, but because data on nutrient concentrations and, in particular, on their temporal stability in the field are scarce, we do not know to what extent root distribution in the soil bears traces of such a response. Here, we linked centimetre‐scale measurements of soil nutrient concentrations over 6 weeks with estimation of root biomass and its species composition at the same points to determine whether there is any association between the two. In addition to phosphorus, nitrate and ammonium, we determined the concentrations of metal cations (magnesium, calcium and potassium). We used qPCR to determine the quantities of individual species in the root biomass samples. We found that calcium and magnesium (and to a lesser degree phosphorus and potassium) showed fine‐scale patchiness that was stable throughout the study (6 weeks) and was consistent over all these elements. Nutrient patches were associated with high root biomass and the occurrence of roots of several species. Such patches are formed primarily by elements with known low mobility in soil (cations, phosphorus). In contrast, nitrogen ions showed overwhelmingly high temporal variation with no relationship between root density and nitrogen concentration. Soil nutrient concentrations, thus, constitute a multidimensional signal. Some elements strongly vary in time, while some are much more stable and, thus, form stable patches that permit root response over periods of weeks or months. Among them, calcium and magnesium play an important role in forming soil heterogeneity at a scale comparable with the scale at which fine root densities also vary. As these cations affect a number of plant functions, their association with higher root densities confirms their role in the growth dynamics of terrestrial ecosystems. Read the free Plain Language Summary for this article on the Journal blog.

Trends in EEG signal feature extraction applications.

This paper will focus on electroencephalogram (EEG) signal analysis with an emphasis on common feature extraction techniques mentioned in the research literature, as well as a variety of applications that this can be applied to. In this review, we cover single and multi-dimensional EEG signal processing and feature extraction techniques in the time domain, frequency domain, decomposition domain, time-frequency domain, and spatial domain. We also provide pseudocode for the methods discussed so that they can be replicated by practitioners and researchers in their specific areas of biomedical work. Furthermore, we discuss artificial intelligence applications such as assistive technology, neurological disease classification, brain-computer interface systems, as well as their machine learning integration counterparts, to complete the overall pipeline design for EEG signal analysis. Finally, we discuss future work that can be innovated in the feature extraction domain for EEG signal analysis.

Ultrastretchable, Self-Healing Conductive Hydrogel-Based Triboelectric Nanogenerators for Human–Computer Interaction

The rapid development of wearable electronic devices and virtual reality technology has revived interest in flexible sensing and control devices. Here, we report an ionic hydrogel (PTSM) prepared from polypropylene amine (PAM), tannic acid (TA), sodium alginate (SA), and MXene. Based on the multiple weak H-bonds, this hydrogel exhibits excellent stretchability (strain >4600%), adhesion, and self-healing. The introduction of MXene nanosheets endows the hydrogel sensor with a high gauge factor (GF) of 6.6. Meanwhile, it also enables triboelectric nanogenerators (PTSM-TENGs) fabricated from silicone rubber-encapsulated hydrogels to have excellent energy harvesting efficiency, with an instantaneous output power density of 54.24 mW/m2. We build a glove-based human-computer interaction (HMI) system using PTSM-TENGs. The multidimensional signal features of PTSM-TENG are extracted and analyzed by the HMI system, and the functions of gesture visualization and robot hand control are realized. In addition, triboelectric signals can be used for object recognition with the help of machine learning techniques. The glove based on PTSM-TENG achieves the classification and recognition of five objects through contact, with an accuracy rate of 98.7%. Therefore, strain sensors and triboelectric nanogenerators based on hydrogels have broad application prospects in man-machine interface, intelligent recognition systems, auxiliary control systems, and other fields due to their excellent stretchable and high self-healing performance.

Application of Machine Learning Methods for an Analysis of E-Nose Multidimensional Signals in Wastewater Treatment

The work represents a successful attempt to combine a gas sensors array with instrumentation (hardware), and machine learning methods as the basis for creating numerical codes (software), together constituting an electronic nose, to correct the classification of the various stages of the wastewater treatment process. To evaluate the multidimensional measurement derived from the gas sensors array, dimensionality reduction was performed using the t-SNE method, which (unlike the commonly used PCA method) preserves the local structure of the data by minimizing the Kullback-Leibler divergence between the two distributions with respect to the location of points on the map. The k-median method was used to evaluate the discretization potential of the collected multidimensional data. It showed that observations from different stages of the wastewater treatment process have varying chemical fingerprints. In the final stage of data analysis, a supervised machine learning method, in the form of a random forest, was used to classify observations based on the measurements from the sensors array. The quality of the resulting model was assessed based on several measures commonly used in classification tasks. All the measures used confirmed that the classification model perfectly assigned classes to the observations from the test set, which also confirmed the absence of model overfitting.

Frequency Domain Filtering Method for SSVEP-EEG Preprocessing

Steady-state visual evoked potential (SSVEP) signal collected from the scalp typically contains other types of electric signals, and it is important to remove these noise components from the actual signal by application of a pre-processing step for accurate analysis. High-pass or bandpass filtering of the SSVEP signal in the time domain is the most common pre-processing method. Because frequency is the most important feature information contained in the SSVEP signal, a technique for frequency-domain filtering of SSVEP was proposed here. In this method, the time-domain signal is extended to multi-dimensional signal by empirical mode decomposition (EMD), where each dimension represents a intrinsic mode function (IMF). The multi-dimensional signal is transformed to a frequency-domain signal by 2-D Fourier transform, the Gaussian high-pass filter function is constructed to perform high-pass filtering, and then the filtered signal is transformed to time domain by 2-D inverse Fourier transform. Finally, the filtered multi-dimensional intrinsic mode function is superimposed and averaged as the frequency-domain filtered signal. Compared with the time-domain filtering method, the experimental results revealed that frequency-domain filtering method effectively removed the baseline drift in signal and effectively suppressed the low-frequency interference component. This method was tested using data from public datasets and the results show that the proposed frequency-domain filtering method can significantly improve the feature recognition performance of canonical correlation analysis (CCA), filter bank canonical correlation analysis (FBCCA), and task-related component analysis (TRCA) methods. Thus, the results suggest that the application of frequency-domain filtering in the pre-processing stage allows improved noise removal. The proposed method extends SSVEP signal filtering from time-domain to frequency-domain, and the results suggest that this analysis tool significantly promotes the practical application of SSVEP systems.

Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation.

The efforts in compressive sensing (CS) literature can be divided into two groups: finding a measurement matrix that preserves the compressed information at its maximum level, and finding a robust reconstruction algorithm. In the traditional CS setup, the measurement matrices are selected as random matrices, and optimization-based iterative solutions are used to recover the signals. Using random matrices when handling large or multi-dimensional signals is cumbersome especially when it comes to iterative optimizations. Recent deep learning-based solutions increase reconstruction accuracy while speeding up recovery, but jointly learning the whole measurement matrix remains challenging. For this reason, state-of-the-art deep learning CS solutions such as convolutional compressive sensing network (CSNET) use block-wise CS schemes to facilitate learning. In this work, we introduce a separable multi-linear learning of the CS matrix by representing the measurement signal as the summation of the arbitrary number of tensors. As compared to block-wise CS, tensorial learning eases blocking artifacts and improves performance, especially at low measurement rates (MRs), such as [Formula: see text]. The software implementation of the proposed network is publicly shared at https://github.com/mehmetyamac/GTSNET.

Motion Analysis Using Global Navigation Satellite System and Physiological Data

Motion analysis by wearable sensors forms a very important research topic with a general mathematical background and applications in different areas including engineering, robotics, and neurology. This paper presents the use of the global navigation satellite system (GNSS) for detecting and recording the position of a moving body and the simultaneous acquisition of signals from further sensors. The application is related to the monitoring of physical activity and the analysis of the heart rate dynamics during the run at route segments of different slopes with changing speed, forming an alternative to the heart monitoring on the treadmill ergometer. The proposed computational method includes digital methods of data preprocessing, time synchronization, and data resampling to enable their correlation, feature extraction both in time and frequency domains, and classification. The datasets include signals acquired during ten experimental runs in the selected area. The detection of the patterns of motion includes segmenting the signals by analysing the GNSS data, evaluating the patterns, and classifying the motion signals under different terrain conditions. This method of classification provides a comparison of neural networks, support vector machine, Bayesian, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -nearest neighbour methods. The highest accuracy of 93.3 % was achieved by using combined features and a two-layer neural network for classification into three classes with different slopes. The proposed method and graphical user interface suggest the efficiency of multi-channel and multi-dimensional signal processing with applications in rehabilitation, fitness movement monitoring, neurology, cardiology, engineering, and robotic systems as well.