Signal Representation Research Articles

Investigating time-independent and time-dependent diffusion phenomena using steady-state diffusion MRI

Diffusion MRI is a leading method to non-invasively characterise brain tissue microstructure across multiple domains and scales. Diffusion-weighted steady-state free precession (DW-SSFP) is an established imaging sequence for post-mortem MRI, addressing the challenging imaging environment of fixed tissue with short T2 and low diffusivities. However, a current limitation of DW-SSFP is signal interpretation: it is not clear what diffusion ‘regime’ the sequence probes and therefore its potential to characterise tissue microstructure. Building on Extended Phase Graphs (EPG), I establish two alternative representations of the DW-SSFP signal in terms of (1) conventional b-values (time-independent diffusion) and (2) encoding power-spectra (time-dependent diffusion). The proposed representations provide insights into how different parameter regimes and gradient waveforms impact the diffusion sensitivity of DW-SSFP. I subsequently introduce an approach to incorporate existing biophysical models into DW-SSFP without the requirement of extensive derivations, with time dependence estimated via a Gaussian phase approximation representation of the DW-SSFP signal. Investigations incorporating free-diffusion and tissue-relevant microscopic restrictions (cylinder of varying radius) give excellent agreement to complementary analytical models and Monte Carlo simulations. Experimentally, the time-independent representation is used to derive Tensor and proof-of-principle NODDI estimates in a whole human post-mortem brain. A final SNR-efficiency investigation demonstrates the theoretical potential of DW-SSFP for ultra-high field microstructural imaging.

ExoSim 2: the new exoplanet observation simulator applied to the Ariel space mission

ExoSim 2 is the next generation of the Exoplanet Observation Simulator (ExoSim) tailored for spectro-photometric observations of transiting exoplanets from space, ground, and sub-orbital platforms. This software is a complete rewrite implemented in Python 3, embracing object-oriented design principles, which allow users to replace each component with their functions when required. ExoSim 2 is publicly available on GitHub, serving as a valuable resource for the scientific community. ExoSim 2 employs a modular architecture using Task classes, encapsulating simulation algorithms and functions. This flexible design facilitates the extensibility and adaptability of ExoSim 2 to diverse instrument configurations to address the evolving needs of the scientific community. Data management within ExoSim 2 is handled by the Signal class, which represents a structured data cube incorporating time, space, and spectral dimensions. The code execution in ExoSim 2 follows a three-step workflow: the creation of focal planes, the production of Sub-Exposure blocks, and the generation of non-destructive reads (NDRs). Each step can be executed independently, optimizing time and computational resources. ExoSim 2 has been extensively validated against other tools like ArielRad and has demonstrated consistency in estimating photon conversion efficiency, saturation time, and signal generation. The simulator has also been validated independently for instantaneous read-out and jitter simulation, and for astronomical signal representation. In conclusion, ExoSim 2 offers a robust and flexible tool for exoplanet observation simulation, capable of adapting to diverse instrument configurations and evolving scientific needs. Its design principles and validation results underscore its potential as a valuable resource in the field of exoplanet research.

Gait patterns in unstable older patients related with vestibular hypofunction. Preliminary results in assessment with time-frequency analysis

Background Gait instability and falls significantly impact life quality and morbi-mortality in elderly populations. Early diagnosis of gait disorders is one of the most effective approaches to minimize severe injuries. Objective To find a gait instability pattern in older adults through an image representation of data collected by a single sensor. Methods A sample of 13 older adults (71-85 years old) with instability by vestibular hypofunction is compared to a sample of 19 adults (21-75 years old) without instability and normal vestibular function. Image representations of the gait signals acquired on a specific walk path were generated using a continuous wavelet transform and analyzed as a texture using grey level co-occurrence matrix metrics as features. A support vector machine (SVM) algorithm was used to discriminate subjects. Results First results show a good classification performance. According to analysis of extracted features, most information relevant to instability is concentrated in the medio-lateral acceleration (X axis) and the frontal plane angular rotation (Z axis gyroscope). Performing a ten-fold cross-validation through the first ten seconds of the sample dataset, the algorithm achieves a 92,3 F1 score corresponding to 12 true-positives, 1 false positive and 1 false negative. Discussion This preliminary report suggests that the method has potential use in assessing gait disorders in controlled and non-controlled environments. It suggests that deep learning methods could be explored given the availability of a larger population and data samples.

A reproducible representation of healthy tibiofemoral kinematics during stair descent using REFRAME – part I: REFRAME foundations and validation

In clinical movement biomechanics, kinematic measurements are collected to characterise the motion of articulating joints and investigate how different factors influence movement patterns. Representative time-series signals are calculated to encapsulate (complex and multidimensional) kinematic datasets succinctly. Exacerbated by numerous difficulties to consistently define joint coordinate frames, the influence of local frame orientation and position on the characteristics of the resultant kinematic signals has been previously proven to be a major limitation. Consequently, for consistent interpretation of joint motion (especially direct comparison) to be possible, differences in local frame position and orientation must first be addressed. Here, building on previous work that introduced a frame orientation optimisation method and demonstrated its potential to induce convergence towards a consistent kinematic signal, we present the REference FRame Alignment MEthod (REFRAME) that addresses both rotational and translational kinematics, is validated here for a healthy tibiofemoral joint, and allows flexible selection of optimisation criteria to fittingly address specific research questions. While not claiming to improve the accuracy of joint kinematics or reference frame axes, REFRAME does enable a representation of knee kinematic signals that accounts for differences in local frames (regardless of how these differences were introduced, e.g. anatomical heterogeneity, use of different data capture modalities or joint axis approaches, intra- and inter-rater reliability, etc.), as evidenced by peak root-mean-square errors of 0.24° ± 0.17° and 0.03 mm ± 0.01 mm after its implementation. By using a self-contained optimisation approach to systematically re-align the position and orientation of reference frames, REFRAME allows researchers to better assess whether two kinematic signals represent fundamentally similar or different underlying knee motion. The openly available implementation of REFRAME could therefore allow the consistent interpretation and comparison of knee kinematic signals across trials, subjects, examiners, or even research institutes.

Multilayer regulation underlies the functional precision and evolvability of the olfactory system.

Sensory neurons must be reproducibly specified to permit accurate neural representation of external signals but also able to change during evolution. We studied this paradox in the Drosophila olfactory system by establishing a single-cell transcriptomic atlas of all developing antennal sensory lineages, including latent neural populations that normally undergo programmed cell death (PCD). This atlas reveals that transcriptional control is robust, but imperfect, in defining selective sensory receptor expression. A second layer of precision is afforded by the intersection of expression of functionally-interacting receptor subunits. A third layer is defined by stereotyped PCD patterning, which masks promiscuous receptor expression in neurons fated to die and removes "empty" neurons lacking receptors. Like receptor choice, PCD is under lineage-specific transcriptional control; promiscuity in this regulation leads to previously-unappreciated heterogeneity in neuronal numbers. Thus functional precision in the mature olfactory system belies developmental noise that might facilitate the evolution of sensory pathways.

Age-Trajectories of Higher-Order Diffusion Properties of Major Brain Metabolites in Cerebral and Cerebellar Gray Matter Using InVivo Diffusion-Weighted MR Spectroscopy at 3T.

Healthy brain aging involves changes in both brain structure and function, including alterations in cellular composition and microstructure across brain regions. Unlike diffusion-weighted MRI (dMRI), diffusion-weighted MR spectroscopy (dMRS) can assess cell-type specific microstructural changes, providing indirect information on both cell composition and microstructure through the quantification and interpretation of metabolites' diffusion properties. This work investigates age-related changes in the higher-order diffusion properties of total N-Acetyl-aspartate (neuronal biomarker), total choline (glial biomarker), and total creatine (both neuronal and glial biomarker) beyond the classical apparent diffusion coefficient in cerebral and cerebellar gray matter of healthy human brain. Twenty-five subjects were recruited and scanned using a diffusion-weighted semi-LASER sequence in two brain regions-of-interest (ROI) at 3T: posterior-cingulate (PCC) and cerebellar cortices. Metabolites' diffusion was characterized by quantifying metrics from both Gaussian and non-Gaussian signal representations and biophysical models. All studied metabolites exhibited lower apparent diffusivities and higher apparent kurtosis values in the cerebellum compared to the PCC, likely stemming from the higher microstructural complexity of cellular composition in the cerebellum. Multivariate regression analysis (accounting for ROI tissue composition as a covariate) showed slight decrease (or no change) of all metabolites' diffusivities and slight increase of all metabolites' kurtosis with age, none of which statistically significant (p > 0.05). The proposed age-trajectories provide benchmarks for identifying anomalies in the diffusion properties of major brain metabolites which could be related to pathological mechanisms altering both the brain microstructure and cellular composition.

Leveraging deep learning for robust EEG analysis in mental health monitoring.

Mental health monitoring utilizing EEG analysis has garnered notable interest due to the non-invasive characteristics and rich temporal information encoded in EEG signals, which are indicative of cognitive and emotional conditions. Conventional methods for EEG-based mental health evaluation often depend on manually crafted features or basic machine learning approaches, like support vector classifiers or superficial neural networks. Despite the potential of these approaches, they often fall short in capturing the intricate spatiotemporal relationships within EEG data, leading to lower classification accuracy and poor adaptability across various populations and mental health scenarios. To overcome these limitations, we introduce the EEG Mind-Transformer, an innovative deep learning architecture composed of a Dynamic Temporal Graph Attention Mechanism (DT-GAM), a Hierarchical Graph Representation and Analysis (HGRA) module, and a Spatial-Temporal Fusion Module (STFM). The DT-GAM is designed to dynamically extract temporal dependencies within EEG data, while the HGRA models the brain's hierarchical structure to capture both localized and global interactions among different brain regions. The STFM synthesizes spatial and temporal elements, generating a comprehensive representation of EEG signals. Our empirical results confirm that the EEG Mind-Transformer significantly surpasses conventional approaches, achieving an accuracy of 92.5%, a recall of 91.3%, an F1-score of 90.8%, and an AUC of 94.2% across several datasets. These findings underline the model's robustness and its generalizability to diverse mental health conditions. Moreover, the EEG Mind-Transformer not only pushes the boundaries of state-of-the-art EEG-based mental health monitoring but also offers meaningful insights into the underlying brain functions associated with mental disorders, solidifying its value for both research and clinical settings.

Novel cylindrical representation of the STFT for signal analysis

AbstractThe proposal of new signal representation techniques in time‐frequency domain can improve the visualization and acquisition of frequency components in various applications. In this sense, this article presents a novel and different representation of the short‐time Fourier transform (STFT) spectrogram for signal analysis, based on changing the visualization from a linear to a cylindrical representation by means of a linear transformation. Simulations show that this new representation focuses on the accuracy of the frequency components rather according to the angular position in which they occur; on the other hand it is easier to analyze high‐frequency components than those of low frequency. Finally, it is visually easier to identify fixed components along the test in this representation in a wide window STFT analysis.

Arrhythmia Classification Using CNN-SVM from ECG Spectrogram Representation

Arrhythmia, a critical subset of cardiovascular diseases and a leading cause of morbidity and mortality, is caused by irregular heartbeats that disrupt the normal rhythm of the heart. Detecting arrhythmias accurately is essential for timely diagnosis and treatment, which can be achieved through electrocardiogram (ECG) signals. This study presents a hybrid Convolutional Neural Network (CNN) and Support Vector Machine (SVM) model for arrhythmia classification, leveraging spectrogram representations of ECG signals. The CNN extracts spatial and temporal features from the spectrograms, while the SVM classifies five arrhythmia classes: Normal (N), Supra-ventricular premature (S), Ventricular escape (V), Fusion of ventricular and normal (F), and Unclassified (Q). Preprocessing techniques such as wavelet denoising and Short-Time Fourier Transform (STFT) were applied to improve signal quality and facilitate robust feature extraction. The proposed model was trained and evaluated on the MIT-BIH Arrhythmia Database, achieving a weighted F1-score of 0.985, demonstrating its ability to handle the imbalanced dataset effectively. Class-wise metrics highlighted high precision, recall, and F1-scores for majority classes and commendable performance for underrepresented classes, despite the inherent imbalance. These findings underscore the hybrid model's potential for arrhythmia classification by integrating the feature extraction strengths of CNNs with the precise classification capabilities of SVMs. Future research could address dataset imbalance through augmentation techniques and explore the model’s generalizability by testing on larger and more diverse datasets, paving the way for its application in real-world clinical scenarios.

Seismic Reflection Imaging of Fluid‐Filled Sills in the West Eifel Volcanic Field, Germany

AbstractWe applied state‐of‐the‐art seismic processing and imaging techniques to crustal‐scale seismic reflection data from the BELCORP/DEKORP87 lines 1A and 1B. The aim of the presented work was to identify structural evidence in the Earth's crust and upper mantle related to the ongoing magmatic activity in the Quaternary West Eifel Volcanic Field (WEVF) in Central Europe where ca. 70 eruptions happened since 65 ka. Following careful signal‐processing, Fresnel volume migration was applied and yielded images with exceptionally strong lithospheric reflectors in the SE of the WEVF. Sparse signal representation revealed numerous reversed polarities. Using petrophysical relations, the corresponding reflections can be interpreted as reflections from melt and/or volatile‐bearing (supercritical CO2) zones which appear as horizontally elongated lens‐shaped sills. Furthermore, we observed reflections with similarly inverted polarities from structural features located around the Moho at of 31 km depth, indicating fluids or melts from the uppermost mantle and supporting magmatic underplating models.

DCSENets: Interpretable deep learning for patient-independent seizure classification using enhanced EEG-based spectrogram visualization.

Neurologists often face challenges in identifying epileptic activities within multichannel EEG recordings, requiring extensive hours of analysis. Computer-aided diagnosis systems have been proposed to reduce manual inspection of EEG signals by neurologists. However, direct analysis of EEG signals is difficult due to their complex and dynamic nature, with variation across multiple patients. Therefore, researchers have proposed the short-time Fourier transform (STFT) to capture dynamic events indicative of seizures through time-varying frequency representation of EEG signals. However, tradeoffs between time and frequency resolution limited the spectrogram's interpretability and affected clinical deployment. Hence, this study proposes extracting high-resolution channels via a novel STFT spectrogram construction algorithm encompassing taper functions for seizure diagnosis. Initially, we extracted seizure and non-seizure segments from each channel of selected patients in the CHB-MIT dataset. Next, we systematically apply taper functions like Hann and Gaussian windows to minimize the edge effect during the construction of spectrogram images. Finally, we employ Dilated Convolutional Squeeze and Excitation Networks (DCSENets) through leave-one-patient-out cross-validation (LOPOCV) to perform patient-independent seizure classification. The proposed DCSENets achieve an average accuracy of 87.20±11.48% and 87.29±10.48% with Hann and Gaussian taper functions, respectively, and 86.85±11.56% without the taper function. Most patients with high performances indicate similarity in train-test sample distribution using the Kolmogorov-Smirnov test at 0.01<p≤0.05 or p>0.05. Furthermore, the Grad CAM deep visual explainer integration enhances the interpretability of the deep learning model's decision-making process. Consequently, neurologists are provided not only with enhanced visualized spectrograms but also a transparent model for improved seizure diagnosis.

Arrhythmia Detection by Data Fusion of ECG Scalograms and Phasograms.

The automatic detection of arrhythmia is of primary importance due to the huge number of victims caused worldwide by cardiovascular diseases. To this aim, several deep learning approaches have been recently proposed to automatically classify heartbeats in a small number of classes. Most of these approaches use convolutional neural networks (CNNs), exploiting some bi-dimensional representation of the ECG signal, such as spectrograms, scalograms, or similar. However, by adopting such representations, state-of-the-art approaches usually rely on the magnitude information alone, while the important phase information is often neglected. Motivated by these considerations, the focus of this paper is aimed at investigating the effect of fusing the magnitude and phase of the continuous wavelet transform (CWT), known as the scalogram and phasogram, respectively. Scalograms and phasograms are fused in a simple CNN-based architecture by using several fusion strategies, which fuse the information in the input layer, some intermediate layers, or in the output layer. Numerical results evaluated on the PhysioNet MIT-BIH Arrhythmia database show the effectiveness of the proposed ideas. Although a simple architecture is used, their competitiveness is high compared to other state-of-the-art approaches, by obtaining an overall accuracy of about 98.5% and sensitivity and specificity of 98.5% and 95.6%, respectively.

A Comprehensive Survey on Emerging Techniques and Technologies in Spatio-Temporal EEG Data Analysis

In recent years, the field of electroencephalography (EEG) analysis has witnessed remarkable advancements, driven by the integration of machine learning and artificial intelligence. This survey aims to encapsulate the latest developments, focusing on emerging methods and technologies that are poised to transform our comprehension and interpretation of brain activity. The structure of this paper is organized according to the categorization within the machine learning community, with representation learning as the foundational concept that encompasses both discriminative and generative approaches. We delve into self-supervised learning methods that enable the robust representation of brain signals, which are fundamental for a variety of downstream applications. Within the realm of discriminative methods, we explore advanced techniques such as graph neural networks (GNN), foundation models, and approaches based on large language models (LLMs). On the generative front, we examine technologies that leverage EEG data to produce images or text, offering novel perspectives on brain activity visualization and interpretation. This survey provides an extensive overview of these cutting-edge techniques, their current applications, and the profound implications they hold for future research and clinical practice. The relevant literature and open-source materials have been compiled and are consistently updated at https://github.com/wpf535236337/LLMs4TS.

Spectral Representation of Non-vanishing Signals and the Prediction Problem

Spectral Representation of Non-vanishing Signals and the Prediction Problem

NUMERICAL-ANALYTICAL METHOD OF DECOMPOSITION-AUTOCOMPENSATION FOR SOLVING THE SIGNAL RECOGNITION PROBLEM BASED ON INACCURATE OBSERVATIONS

A numerical-analytical method is developed to solve the problem of optimal recognition of a set of possible signals observed as an additive mixture containing not only a fluctuation observation error (with an unknown statistical distribution) but also a singular interference (with parametric uncertainty). The method allows for both the detection of signals present in the mixture and the estimation of their parameters within a specified quality criterion and associated constraints. The proposed method, based on the idea of generalized invariant-unbiased estimation of linear functional values, enables decomposition of the computational procedure and autocompensation of singular interference without resorting to the traditional expansion of the state space. Linear spectral decompositions in specified functional bases are used for the parametric finite-dimensional representation of signals and interference, while knowledge of the correlation matrix of the observation error is sufficient for error description. Random and systematic errors are analyzed, and an illustrative example is provided.

Investigation of the Effect of Diverse Dictionaries and Sparse Decomposition Techniques for Power Quality Disturbances

The quality of power signals is strongly influenced by nonlinear loads in Electrical Power systems. Representation of electrical signals using different Sparse techniques is an interesting area of research as it moderates the volume of data to be stored. The storage of signals in Sparse form will make data storage easier and more efficient. Earlier studies concentrated on blindly choosing Overcomplete Hybrid Dictionaries (OHDs) for Sparse representation. The effect of different dictionaries in representing electrical signals has also not been reviewed in them. This paper presents an investigation of the effect of various dictionaries and the sparsity constant on the representation of electrical signals. The validation for statements presented in this paper is carried out by representing power signals with diverse power line disturbances like Swell, DC offset, and random oscillation, with the help of various dictionaries in the simulation platform. The Sparse representation of the power signals was generated using the Orthogonal Matching Pursuit algorithm. The resultant Sparse representation was then compared with the original signal. The difference between them was found to be negligible with the help of different metrics. The ratio of the obtained signal from Sparse representation, the original signal (A/R ratio), and the Mean Squared Error were taken as the metrics. The MATLAB platform was used for performing the simulation study.

An enhanced deep intelligent model with feature fusion and ensemble learning for the fault diagnosis of rotating machinery

Vibration signals, serving as critical sources of information for monitoring the status of rotating machinery, demand effective extraction and rational utilization of its features to significantly enhance the accuracy and reliability of fault diagnosis. However, vibration signal features typically manifest as nonlinear and nonstationary, posing a significant challenge in industrial settings. To tackle this challenge, this article proposes an enhanced deep intelligent model based on feature fusion and ensemble learning for practical fault diagnosis of rotating machinery. First, a parallel network structure is introduced to comprehensively and accurately explore the fault characteristics of rotating machinery. This network comprises two branches: the first branch designs an improved one-dimensional convolutional neural network to extract locally robust features from raw signals; the second branch adopts variational mode decomposition to decompose raw signals into a set of intrinsic mode functions and extract comprehensive statistical features in both the time and frequency domains, significantly enhancing the signal representation capability. Subsequently, a deep neural network is used to extract more stable feature information. The features from the two branches are then fused, and the final network output is generated through a softmax regression function. Finally, ensemble learning uses a majority voting scheme to obtain more stable final outputs. To confirm the effectiveness of the proposed method, experiments are conducted on two laboratory cases and one industrial case. The experimental results demonstrate that the proposed method significantly improves fault diagnosis accuracy and reliability in controlled laboratory environments and real-world industrial applications, making it highly applicable for real-time monitoring and predictive maintenance of industrial machinery. These improvements can reduce maintenance costs and downtime, thus enhancing operational efficiency in various industrial settings.

Electrocardiography Denoising via Sparse Dictionary Learning from Small Datasets

Abstract Wearable electrocardiography monitors, e.g. embedded in textile shirts, offer new approaches in diagnosis but suffers upon limited computational capacities. Hence, we propose and evaluate a lightweight algorithm for electrocardiography denoising via sparse dictionary learning, targeting two types of noise: baseline wander and muscle artifacts. For each type of noise a dictionary is built using K-singular value decomposition. This iterative method alternates between finding a sparse representation for every training signal and then updating every atom of the dictionary on its own. A sparse representation is found using the orthogonal matching pursuit algorithm. The atoms are updated exploiting the properties of the singular value decomposition. For further sparse approximation, we use the basis pursuit denoising algorithm. Electrocardiography data stems from synthetically-generated signals as well as the freely-available Brno University of Technology ECG Quality Database. Noise is added to the signals using the MIT-BIH Noise Stress Database. Our results regarding baseline wander demonstrate that the algorithm outperforms the American Heart Association-recommended bandpass filter w.r.t. signal-to-noise ratio. Moreover, a small number of training data is sufficient for satisfying results which indicates the suitability of the method for wearable hardware with low memory and power specifications.

On Linear Operators in Hilbert Spaces and Their Applications in OFDM Wireless Networks

This paper explores the application of Hilbert topological spaces and linear operator algebra in the modelling and analysis of OFDM signals and wireless channels, where the channel is considered as a linear time-invariant (LTI) system. The wireless channel, when subjected to an input OFDM signal, can be described as a mapping from an input Hilbert space to an output Hilbert space, with the system response governed by linear operator theory. By employing the mathematical framework of Hilbert spaces, we formalise the representation of OFDM signals, which are interpreted as elements of an infinite-dimensional vector space endowed with an inner product. The LTI wireless channel is characterised by using bounded linear operators on these spaces, allowing for the decomposition of complex channel behaviour into a series of linear transformations. The channel’s impulse response is treated as a kernel operator, facilitating a functional analysis approach to understanding the signal transmission process. This representation enables a more profound understanding of channel effects, such as fading and interference, through the eigenfunction expansion of the operator, leading to a spectral characterization of the channel. The algebraic properties of linear operators are leveraged to develop optimal solutions for mitigating channel distortion effects.

Time–frequency representation of adjacent multi-component signals driven by IVKF-MPRTF and its application for mechanical equipment fault diagnosis

Time–frequency representation of adjacent multi-component signals driven by IVKF-MPRTF and its application for mechanical equipment fault diagnosis