Multidimensional Signal Analysis Research Articles

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.

Computation of the nonnegative canonical tensor decomposition with two accelerated proximal gradient algorithms

Multidimensional signal analysis has become an important part of many signal processing problems. This type of analysis allows to take advantage of different diversities of a signal in order to extract useful information. This paper focuses on the design and development of multidimensional data decomposition algorithms called Canonical Polyadic (CP) tensor decomposition, a powerful tool in a variety of real-world applications due to its uniqueness and ease of interpretation of its factor matrices. More precisely, it is desired to compute simultaneously the factor matrices involved in the CP decomposition of a real nonnegative tensor, under nonnegative constraints. For this purpose, two proximal algorithms are proposed, the Monotone Accelerated Proximal Gradient (M-APG) and the Non-monotone Accelerated Proximal Gradient (Nm-APG) algorithms. These algorithms are implemented via a regularization function with a simple control strategy capable of efficiently taking advantage of previous iterations. Simulation results demonstrate better performance of the two proposed algorithms in terms of accuracy when compared to other nonnegative CP algorithms in the literature.

On the Octonion Cross Wigner Distribution of 3-D Signals

This paper introduces definitions of the octonion cross Wigner distribution (OWD) and the octonion ambiguity function, forming a pair of octonion Fourier transforms. The main part is devoted to the study of the basic properties of the OWD. Among them are the properties concerning its nature (nonlinearity, parity, space support conservation, marginals) and some “geometric” transformations (space shift, space scaling) similar to the case of the complex Wigner distribution. This paper also presents specific forms of the modulation property and an extended discussion about the validity of Moyal’s formula and the uncertainty principle, accompanied by new theorems and examples. The paper is illustrated with examples of 3-D separable Gaussian and Gabor signals. The concept of the application of the OWD for the analysis of multidimensional analytic signals is also proposed. The theoretical results presented in the papers are summarized, and the possibility of further research is discussed.

Directional Stockwell transform in L 2(ℝ n )

In the present article, we propose a directionally tuned variant of the continuous Stockwell transform in the context of multi-dimensional signal analysis. Owing to the directional selectivity coupled with a frequency adaptable window, the proposed transform serves as a bridge between the directional short-time Fourier and wavelet transforms. Besides the formulation of all the fundamental results, including the orthogonality relation and reconstruction formula, we also obtain several uncertainty inequalities associated with the directional Stockwell transform.

Serial-EMD: Fast empirical mode decomposition method for multi-dimensional signals based on serialization

Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts forward higher requirements for the capability of real-time signal analysis, it is difficult for existing EMD and its variants to trade off the growth of data dimension and the speed of signal analysis. In order to decompose multi-dimensional signals at a faster speed, we present a novel signal-serialization method (serial-EMD), which concatenates multi-variate or multi-dimensional signals into a one-dimensional signal and uses various one-dimensional EMD algorithms to decompose it. To verify the effects of the proposed method, synthetic multi-variate time series, artificial 2D images with various textures and real-world facial images are tested. Compared with existing multi-EMD algorithms, the decomposition time becomes significantly reduced. In addition, the results of facial recognition with Intrinsic Mode Functions (IMFs) extracted using our method can achieve a higher accuracy than those obtained by existing multi-EMD algorithms, which demonstrates the superior performance of our method in terms of the quality of IMFs. Furthermore, this method can provide a new perspective to optimize the existing EMD algorithms, that is, transforming the structure of the input signal rather than being constrained by developing envelope computation techniques or signal decomposition methods. In summary, the study suggests that the serial-EMD technique is a highly competitive and fast alternative for multi-dimensional signal analysis.

Lattice-based multi-channel sampling theorem for linear canonical transform

The multi-channel sampling theorem has flourished as one of the nicest alternatives to the classical Shanon's sampling theorem which relies on non-uniform or multi-channel data acquisition. Although, a primary attempt to study the multi-channel sampling theorem for the multi-dimensional linear canonical transform (LCT) was made by D. Wei and Y. Li (2014) [16], however, it lacks the inherent multi-dimensional nature in the sense that the associated kernel is a product of N-copies of the usual one dimensional kernel, restricting the degrees of freedom only to three. The goal of this paper is to fill this gap by studying the lattice-based multi-channel sampling theorem for the multi-dimensional LCT with N(2N+1) degrees of freedom. The idea is accomplished in two steps: firstly, an elegant convolution structure is presented for constructing the multiplicative filters; secondly, the sampling lattices are constructed via general separable and non-separable matrices which often provide more flexibility and better performance in the context of multi-dimensional signal analysis. In the sequel, the Shanon's sampling theorem for the multi-dimensional LCT is deduced as a particular case of the proposed multi-channel sampling theorem. Finally, some potential applications including signal reconstruction and image super-resolution are presented to validate the obtained results.

Multidimensional Iterative Filtering: a new approach for investigating plasma turbulence in numerical simulations

Turbulent space and astrophysical plasmas exhibit a complex dynamics, which involves nonlinear coupling across different temporal and spatial scales. There is growing evidence that impulsive events, such as magnetic reconnection instabilities, lead to a spatially localized enhancement of energy dissipation, thus speeding up the energy transfer at small scales. Capturing such a diverse dynamics is challenging. Here, we employ the Multidimensional Iterative Filtering (MIF) method, a novel technique for the analysis of non-stationary multidimensional signals. Unlike other traditional methods (e.g. based on Fourier or wavelet decomposition), MIF does not require any previous assumption on the functional form of the signal to be identified. Using MIF, we carry out a multiscale analysis of Hall-magnetohydrodynamic (HMHD) and hybrid particle-in-cell (HPIC) numerical simulations of decaying plasma turbulence. The results assess the ability of MIF to spatially identify and separate the different scales (the MHD inertial range, the sub-ion kinetic and the dissipation scales) of the plasma dynamics. Furthermore, MIF decomposition allows localized current structures to be detected and their contribution to the statistical and spectral properties of turbulence to be characterized. Overall, MIF arises as a very promising technique for the study of turbulent plasma environments.

Denoising High-Field Multi-Dimensional MRI With Local Complex PCA.

Modern high field and ultra high field magnetic resonance imaging (MRI) experiments routinely collect multi-dimensional data with high spatial resolution, whether multi-parametric structural, diffusion or functional MRI. While diffusion and functional imaging have benefited from recent advances in multi-dimensional signal analysis and denoising, structural MRI has remained untouched. In this work, we propose a denoising technique for multi-parametric quantitative MRI, combining a highly popular denoising method from diffusion imaging, over-complete local PCA, with a reconstruction of the complex-valued MR signal in order to define stable estimates of the noise in the decomposition. With this approach, we show signal to noise ratio (SNR) improvements in high resolution MRI without compromising the spatial accuracy or generating spurious perceptual boundaries.

An Improved Minor Component Analysis Algorithm Based on Convergence Analysis of 5G Multi-Dimensional Signals

An Improved Minor Component Analysis Algorithm Based on Convergence Analysis of 5G Multi-Dimensional Signals

An Automatic Procedure for Multidimensional Temperature Signal Analysis of a SCADA System with Application to Belt Conveyor Components

In this paper, a problem of interpretation and analysis of multidimensional temperature data acquired using an online monitoring system is presented. It is highlighted, that apart from the data acquisition system there is a strong need to use automatic decision-making rules. A classical if then else approach i.e. the comparison of a current value of temperature with a priori assumed threshold is not possible due to the cyclic nature of machine operation and the influence of external factors as ventilation system or bulk material stream conveyed on the belt. Moreover, these thresholds are unknown and might themselves depend on the mentioned factors. It should be also noted, that in industrial data acquisition systems, there is a high probability of external disturbances, meaning that the signals should be validated and pre-processed first. Indeed, wenoticed outliers related to the data acquisition system operation. The cyclic variability of temperatures has no diagnostic meaning and makes the interpretation of data and decision making difficult. In this paper, we propose an automatic data processing framework how to extract diagnostic information and present it in a user-friendly manner. The analysed example data comes from a belt conveyor used in underground mining.

Discrete shearlet transform on GPU with applications in anomaly detection and denoising

Shearlets have emerged in recent years as one of the most successful methods for the multiscale analysis of multidimensional signals. Unlike wavelets, shearlets form a pyramid of well-localized functions defined not only over a range of scales and locations, but also over a range of orientations and with highly anisotropic supports. As a result, shearlets are much more effective than traditional wavelets in handling the geometry of multidimensional data, and this was exploited in a wide range of applications from image and signal processing. However, despite their desirable properties, the wider applicability of shearlets is limited by the computational complexity of current software implementations. For example, denoising a single 512 × 512 image using a current implementation of the shearlet-based shrinkage algorithm can take between 10 s and 2 min, depending on the number of CPU cores, and much longer processing times are required for video denoising. On the other hand, due to the parallel nature of the shearlet transform, it is possible to use graphics processing units (GPU) to accelerate its implementation. In this paper, we present an open source stand-alone implementation of the 2D discrete shearlet transform using CUDA C++ as well as GPU-accelerated MATLAB implementations of the 2D and 3D shearlet transforms. We have instrumented the code so that we can analyze the running time of each kernel under different GPU hardware. In addition to denoising, we describe a novel application of shearlets for detecting anomalies in textured images. In this application, computation times can be reduced by a factor of 50 or more, compared to multicore CPU implementations.

Numerical simulation and analysis based on multidimensional independent component analysis

By introducing an indicator to evaluate performance of Multidimensional Independent Component Analysis(MICA) algorithm,the separation was studied by numerical simulation.The multidimensional Amari separation error was used as an important indicator of the measurement of MICA algorithm performance.In the comparative separation performance analysis of four algorithms named vkMICA,cfMICA,MSOBI,SJADE,a random distribution of letters signal was used for simulation and testing,and a visual representation of MICA model of separation and uncertainty was got.The results show that MICA is a very effective method for multidimensional source signal analysis.

Special issue on “Multidimensional Signal and Image Analysis on HealthCare Applications”

The rapid approaching of elderly era has caused the impending needs for applying new technology for elderly and disabled people to improve health conditions and increase the quality of life. Under such a situation, novel bioengineering devices and tools are being developed to gain better understanding of human metabolic, anatomy and functions of organs. On the other hand, chronic diseases cause healthcare to be shared by daily health maintenance, triggering the impending need for intelligence of devices in which preliminary decisions need to be built into the system for providing preliminary recommendations. To achieve the development of novel and intelligent bioengineering and healthcare devices, the techniques of multidimensional signal and image processing and analysis can play one of the major roles. Compared with one dimensional signal analysis, the analysis of multidimensional signals and images provides more information. On the other hand, the high dimensionality of data may also cause large computational cost and, therefore, reduce the feasibility. Consequently, how to extract information for best estimation of health situations from the correlated or uncorrelated signals needs to be addressed. The goal of this special issue is to provide most up-to-date and recent advances of multidimensional signal and image analysis techniques for healthcare applications. This special issue serves as a forum and venue for researchers in academia, clinics and industries working in this area to share their experiences with the readers. For this special issue, we received a total of 13 submissions, each of which has gone through rigorous peer review. Based on the review results, six papers are selected for publication in this special issue, with brief description as follows. In “Enhancement of Blood Vessels in Retinal Imaging Using the Nonsubsampled Contourlet Transform”, Lee et al. propose a modified version of the nonsubsampled

Fuzzy Segmentation for the Exploratory Analysis of Multidimensional Signals: Example From a Study on Driver Overtaking Behavior

This paper explains the key role played by windowing in the preliminary analysis of multifactor and multivariate (MFMV) databases. The explanation is based on the general case of a database featuring quantitative or qualitative measurement variables and a hyperparallelepipedic structure in which the directions correspond to the factors. In order to maintain the MFMV aspects of this data structure, the windowing approach as described in this paper does not reduce the information as much as most of the basic non-windowing summarizing procedures using the standard statistical indicators. First, the data in each cell of the hyperparallelepiped are transformed into membership values that can be averaged over factors, such as time or individuals. Then, these membership values may be potentially investigated into with several graphic techniques; for this paper, multiple correspondence analysis (MCA) was chosen. The presentation fall into two parts. First, a didactic example based on a simulated data set describes the approach in comparison with more traditional approaches, and then a real data set, with multidimensional signals recorded for 34 subjects in 15 experimental overtaking situations, is used to demonstrate the power of the “space windowing/MCA” pair on a large real database. Next, the discussion section weighs out the pros and the cons of using space windowing to perform a preliminary analysis of a large MFMV database in studies of human component systems.

On generalized Hilbert transforms and their interaction with the Radon transform in Clifford analysis

AbstractThe present paper deals with the interaction between the multidimensional Hilbert transform and the Radon transform in Clifford analysis, both transforms being protagonists in multidimensional signal analysis theory. In an attempt to complete the picture, we consider in particular the action of the Radon transform on two types of generalized Hilbert operators, which have been constructed in the context of some well‐established families of Clifford distributions. Copyright © 2007 John Wiley & Sons, Ltd.

Automated detection of a preseizure state: non‐linear EEG analysis in epilepsy by Cellular Nonlinear Networks and Volterra systems

AbstractIn this paper we present our work analysing electroencephalographic (EEG) signals for the detection of seizure precursors in epilepsy. Volterra systems and Cellular Nonlinear Networks are considered for a multidimensional signal analysis which is called the feature extraction problem throughout this contribution. Recent results obtained by applying a pattern detection algorithm and a non‐linear prediction of brain electrical activity will be discussed in detail. The aim of this interdisciplinary project is the realization of an implantable seizure warning and preventing system. Copyright © 2006 John Wiley & Sons, Ltd.

Multidimensional Signal Analysis as a Means of Better Understanding Factors Associated with Repetitive Use in Violin Performance

Multidimensional signal analysis (MSA) involves the coordination and correlation of data gathered by multiple analytic techniques. For complex biosystems, MSA provides a means to investigate better aspects of the system that cannot be understood easily using a single method. This is clearly the case for repetitive use injuries, also commonly referred to as overuse syndrome. Injuries from overuse syndrome are the result of deliberate physical behaviors. They typically are investigated through injury-site examinations, statistical or epidemiologic studies, and observation of the behaviors associated with the injury. Diverse methods often must be used to evaluate a patient because individually they provide only partial information relating to the etiology. The use of MSA permits the integration of multiple observational perspectives, generally creating a more holistic view. Using MSA, accurate external description of the movements thought to cause injury can be linked with internal physiologic conditions. Because physical work causes observed damage in overuse syndrome patients, a full examination of internal loading and muscle activity provides one possibility for understanding the evolutionary nature of these pathologies. Kinematic description, internal load analysis, electromyography, and biomechanical modeling are complementary methods used for MSA in this study. In the current study, a nine-camera ViCON v8i system was used to capture three-dimensional body kinematics as input for inverse dynamic modeling. Electromyography (Noraxon; 8-channel, wireless) was measured and synchronized to the model, permitting the correlation of joint moments and selected muscle activity. Results reveal clear relationships between muscle activity and physiologic loading for a variety of bowing speeds, strong interaction among muscles and groups of muscles, and changes in motor control at varying speeds. Additionally, load levels and work patterns are quantitatively established, and evidence is found to support a three-phase division of motor control based on speed: (1) increasing physical effort, (2) optimization, and (3) approaching physiologic limits. Combined with previous kinematic, kinetic, and statistical studies, the current study illuminates the relative risks of static versus dynamic loading, and provides perspective on the working patterns of muscles throughout the kinematic chain of the arms and torso during violin performance. Most importantly, this study begins the process of establishing MSA as a means of gleaning a greater overall view from the separate observational perspectives provided by multiple assessment methods used to examine performing artists’ injuries. This is the first such study for violin performance; an activity highly correlated with overuse syndrome.

Separability and Axial Symmetry of>tex<$M$>/tex<-D Polynomials and Maximum-Entropy>tex<$M$>/tex<-D Random Processes

In multidimensional system and signal analysis it is often assumed that an M-dimensional (M-D) polynomial is separable. The following properties are presented to show rationales of the separability assumption. First, if an M-D polynomial is separable, it is axially symmetric. Second, if the autocorrelation generating function of an M-D deterministic sequence with the support in the first 2/sup M/-rant is axially symmetric, it is separable. Third, if a wide-sense stationary and 2/sup M/-rant causal M-D stochastic process has the maximum entropy subject to marginal autocovariance constraints, it is separable.

A Family of Two-Dimensional Nonseparable Malvar Wavelets

Malvar wavelets or lapped orthogonal transform (LOT) has been recognized as a useful tool in eliminating blocking effects in transform coding. Recently, it has been also extended to more general forms, which enable one to construct an orthonormal basis from arbitrary local orthonormal bases on different intervals. In this paper, we study two-dimensional cases and construct nonseparable Malvar wavelets, which are potentially important in multidimensional signal analysis. With nonseparable Malvar wavelets, we then construct nonseparable Lemarié–Meyer wavelets which are band-limited. We discuss the implementation and applications of nonseparable Malvar wavelets in image processing. Finally, we present several numerical examples.

Analysis and recovery of multidimensional signals from irregular samples using nonlinear and iterative techniques

A recurring problem in signal processing is reconstruction based upon imperfect information. In this paper we offer two methods. The first one is a simple nonlinear method, based upon spectral analysis, to reconstruct two-dimensional (2-D) band-limited signals from nonuniform samples. The second method is an iterative technique; by using an intelligent initial condition, we get faster convergence than a simple successive approximation. These methods and analyses are extendable to n-dimensional signals. The feasibility of this procedure is demonstrated through examples of both black-and-white and colour image restoration when some of the pixels are lost. Ein häufig wiederkehrendes Problem in der Signalverarbeitung ist die Rekonstruktion anhand von nicht perfekter Information. In dieser Arbeit werden zwei Methoden angegeben. Die erste ist eine einfache nichtlineare Methode basierend auf einer Spektralanalyse zur Rekonstruktion von zweidimensionalen (2-D) bandbegrenzten Signalen aus nicht gleichförmigen Abtastwerten. Die zweite Methode ist eine iterative Technik: Durch die Verwendung einer intelligenten Initialbedingung bekommen wir eine schnellere Konvergenz als bei einfacher sukzessiver Approximation. Diese Methoden und Analysen werden auf n-dimensionale Signale erweitert. Die Wirksamkeit dieser Prozedur wird durch Beispiele von Schwarz-weiß- und Farbbild-Rekonstruktionen demonstriert, wenn einige Pixel verlorengegangen sind. Un problème fréquent en traitment du signal est la reconstruction basée sur une information imparfaite. Dans cet article, nous proposons deux méthodes. La première est une méthode non-linéaire simple basée sur l'analyse du spectre pour reconstruire des signaux bi-dimensionnels à bandes limités à partir d'échantillons non uniformes. La seconde méthode est une technique itérative; en utilisant une condition initiale intelligente, nous obtenons une convergence plus rapide qu'avec une simple approximation successive. Ces méthodes et ces analyses peuvent être étendues aux signaux à n dimensions. La faisabilité de cette procédure est démontrée par des exemples de restoration d'images noir et blanc ou couleur lorsque des pixels sont perdus.