No-estacionariedad, multifractalidad y limpieza de ruido en señales reales

Las señales biomédicas, como el electrocardiograma, el electroencefalograma, o la señal de voz, tienen en común características de no estacionariedad y no linealidad. Aunque enmuchas aplicaciones se considera que se trata de señales estacionarias procedentes de sistemas lineales, ésta simplificación constituye una hipótesis de trabajo válida sólo como una aproximación que permite la aplicación de técnicas clásicas deanálisis de señales. Muchos trastornos que afectan a uno o varios órganos pueden ser detectados a través de un correcto análisis de las señales en cuya producción están involucrados. Sin embargo, debe atenderse al hecho de que una señal procedente de un sistema patológico se aleja aún más de las condiciones hipotéticas de estacionariedad y linealidad. Se desprende de esta circunstancia la necesidad de abordar el análisis de las señales biomédicas mediante técnicas no convencionales que permitan su tratamiento en un marco que tenga en cuenta sus características de no estacionariedad y no linealidad. Sobre la base de la experiencia del grupo de trabajo en las áreas del análisis tiempo-frecuencia/escala, análisis y modelado estadístico, análisis multifractal, complejidad y métodos guiados por los datos (adaptativos), a partir de problemas reales se han propuesto y estudiado nuevas técnicas que posibiliten su solución

Blood pressure estimation from photoplethysmogram and electrocardiogram signals using machine learning

Blood pressure measurement is a significant part of preventive healthcare and has been widely used in clinical risk and disease management. However, conventional measurement does not provide continuous monitoring and sometimes is inconvenient with a cuff. In addition to the traditional cuff-based blood pressure measurement methods, some researchers have developed various cuff-less and noninvasive blood pressure monitoring methods based on Pulse Transit Time (PTT). Some emerging methods have employed features of either photoplethysmogram (PPG) or electrocardiogram (ECG) signals, although no studies to our knowledge have employed the combined features from both PPG and ECG signals. Therefore this study aims to investigate the performance of a predictive, machine learning blood pressure monitoring system using both PPG and ECG signals. It validates that the employment of the combination of PPG and ECG signals has improved the accuracy of the blood pressure estimation, compared with previously reported results based on PPG signal only. © 2018 Institution of Engineering and Technology. All rights reserved

Wavelet Image Restoration Using Multifractal Priors

Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this issue by developing a method that performs the image enhancement in an orthogonal space (Fourier space in that case) which effectively transforms the problem from a large multivariate optimization problem to a set of smaller independent univariate optimization problems. The current paper extends these methods to analysis in another orthogonal basis, wavelets. While still providing the computational efficiency obtained with the original method in Fourier space, this extension allows more flexibility in adapting to local properties of the images, as well as capitalizing on the long history of developments for wavelet shrinkage methods. In addition, wavelet methods, including empirical Bayes specific methods, have recently been developed to effectively capture multifractal properties of images. An extension of these methods is utilized to enhance the recovery of textural characteristics of the underlying image. These enhancements should be beneficial in characterizing textural differences such as those occurring in medical images of diseased and healthy tissues. The Bayesian framework defined in the space of wavelets provides a flexible model that is easily extended to a variety of imaging contexts.Comment: 19 pages, 4 figure

Blood pressure estimation with complexity features from electrocardiogram and photoplethysmogram signals

A novel method for the continual, cuff-less estimation of the systolic blood pressure (SBP) and diastolic blood pressure (DBP) values based on signal complexity analysis of the photoplethysmogram (PPG) and the electrocardiogram (ECG) is reported. The proposed framework estimates the blood pressure (BP) values obtained from signals generated from 14 volunteers subjected to a series of exercise routines. Herein, the physiological signals were first pre-processed, followed by the extraction of complexity features from both the PPG and ECG. Subsequently the complexity features were used in regression models (artificial neural network (ANN), support vector machine (SVM) and LASSO) to predict the BP. The performance of the approach was evaluated by calculating the mean absolute error and the standard deviation of the predicted results and compared with the recommendations made by the British Hypertension Society (BHS) and Association for the Advancement of Medical Instrumentation. Complexity features from the ECG and PPG were investigated independently, along with the combined dataset. It was observed that the complexity features obtained from the combination of ECG and PPG signals resulted to an improved estimation accuracy for the BP. The most accurate DBP result of 5.15 ± 6.46 mmHg was obtained from ANN model, and SVM generated the most accurate prediction for the SBP which was estimated as 7.33 ± 9.53 mmHg. Results for DBP fall within recommended performance of the BHS but SBP is outside the range. Although initial results are promising, further improvements are required before the potential of this approach is fully realised

Vers un modèle sous-pixel des images de Soleil calme dans l'extrême ultra-violet

Nous nous intéressons à la modélisation d'images du Soleil acquises dans l'extrême ultraviolet par le télescope Extreme ultraviolet Imaging Telescope (EIT) de la mission Solar and Heliospheric Observatory (SoHO, ESA/NASA). Nous nous intéressons aux régions les moins structurées en apparence, le "Soleil calme". Nous présentons d'abord une analyse multifractale des images de Soleil calme. Au-delà de l'analyse des données, il s'agit d'identifier un modèle stochastique des images étudiées à partir duquel il sera possible de simuler des images similaires mais de résolution arbitrairement fine en exploitant la propriété d'invariance d'échelle. Nous comparons deux familles de modèles (cascades infiniment divisibles et draps stables fractionnaires) permettant de simuler numériquement des images statistiquement similaires aux images de Soleil calme. Cette modélisation permettra la préparation des prochaines observations à haute résolution et d'étudier la variabilité sous-pixel des images du Soleil

Aprendizaje basado en coeficientes de fourier para la identificación de daño en plantas de cultivos

Spectral signature analysis is one of the most widely used diagnostic methods to identify plant diseases. To this end, different information acquisition techniques must be considered to detect the different levels of a particular disease or pest, as in the case of fungal diseases. In this study, cucurbit plants were considered in three stages of levels of a fungal disease were identified which are leaves in the fungal germination stage, leaves with first symptoms, and diseased leaves. A database with spectral signatures of zucchini leaves was used. Then, frequency analysis of spectral features is proposed using Fourier transform to extract features from the obtained coefficients and from classification blocks with support vector machines for damage level estimation. Classification accuracies of 98.3% were demonstrated. Therefore, this method can be used to diagnose the damage levels in different crops.El análisis de firmas espectrales es uno de los métodos de diagnóstico más utilizados para identificar enfermedades en las plantas. Con este fin, se deben considerar diferentes técnicas de adquisición de información para detectar los diferentes niveles de una enfermedades o plaga en particular, como en el caso de las enfermedades fúngicas. En este estudio, se consideraron plantas cucúrbitas en las cuales se identificaron tres etapas de niveles de una enfermedad fúngica que son las hojas en la etapa de germinación del hongo, hojas con primeros síntomas y hojas enfermas. Se utilizó una base de datos con firmas espectrales de hojas de calabacita. A continuación, se propone el análisis de frecuencia de las características espectrales utilizando la transformada de Fourier para extraer características de los coeficientes obtenidos y partir de bloques de clasificación con máquinas de vectores de soporte para la estimación del nivel de daño. Se demostraron precisiones de clasificación del 98.3%. Por lo tanto, este método se puede utilizar para diagnosticar el grado de daño en diferentes cultivos

Multifractal Analysis for Images : The wavelet Leaders contribution

1. Motivation Scale invariance has been observed in numerous applications involving data of various and very different natures. It can be operationally defined as the power law behavior with respect to scale of the structure functions, which are given by the empirical moments of the absolute value of the multiresolution coefficients of the data at a given scale (cf. Eq. (1)). The estimation of the exponents characterizing these power laws – termed scaling exponents – constitutes the ultimate goal of the practical analysis of scale invariance (also called scaling analysis). These scaling exponents are then commonly involved in standard signal processing tasks, such as detection, identification, or classification. In practice, scaling analysis is often conducted within the theoretical framework of multifractal analysis. In a nutshell, multifractal analysis aims at characterizing the fluctuation (in time or space) of the local regularity of the process under analysis through analysis of the (power law) behavior of the structure functions in the limit of fine scales. Though multifractal analysis can theoretically be extended to dimensions higher than 1 without technical difficulties, most practical implementations remain restricted to one dimensional signals. This is mainly due to the fact that multifractal analysis requires the use of a range of both positive and negative empirical moments, hence demanding for multiresolution quantities with adequate properties. To date, the only practically available procedure for the multifractal analysis of 2D signals, hence images, is the so called Wavelet Transform Modulus Maxima (WTMM) procedure (based on the skeleton of a continuous wavelet transform (CWT)). Yet, the WTMM procedure suffers from a number of theoretical and practical drawbacks: It has a high computational cost; The calculation of the 2D CWT skeleton requires involved theoretical definitions as well as a cumbersome practical procedure; It is still lacking a theoretical support. Therefore, in numerous applications where the data are naturally images, multifractal analysis remains restricted to 1D slices of the data and hence incomplete. In the present contribution, elaborating on previous results obtained for (1D) signals, we propose a practical multifractal analysis method for (2D) images based on two key features: The use of a 2D Discrete Wavelet Transform (DWT) (instead of a 2D CWT); The replacement of wavelet coefficients with wavelet Leaders. This yields two major benefits: The computation cost is very low; Wavelet Leaders have been shown to yield a complete and rigorous analysis of the multifractal analysis of bounded functions. This is because wavelet Leaders consist of monotonous increasing quantities that finely account for the irregularities of the analyzed function. The aims of the present contribution are twofold: First, studying the necessary theoretical elements, validity and limitations of a wavelet Leader based multifractal analysis of images, and second, the evaluation of its practical statistical performance....Nous nous intéressons à la réalisation pratique d’une procédure permettant d’effectuer une analyse multifractale, c’est-à-dire des fluctuations de régularité locale, de champs scalaires bidimensionnels, d’images notamment. L’originalité de la procédure réside dans la construction, à partir des coefficients d’une transformée discrète bidimensionnelle en ondelettes, de coefficients dominants, impliqués ensuite dans l’estimation des attributs multifractals. Nous donnons des éléments mathématiques relatifs aux problèmes théoriques liés à la validité du formalisme multifractal ainsi construit, et à son application à des images réelles. Nous indiquons comment l’utiliser pour détecter la présence éventuelle de singularités oscillantes. Pour étudier les performances des procédures construites, ces estimateurs sont mis en oeuvre sur un grand nombre de réalisations de processus synthétiques, dont les propriétés multifractales sont connues théoriquement. Nous validons le fait que l’analyse multifractale 2D, construite sur les coefficients dominants, permet une mesure effective et complète des propriétés multifractales des images analysées. De plus, comparant les résultats obtenus d’images mono-fractales à ceux produits sur des images multi-fractales, nous commentons de façon détaillée l’apport des coefficients dominants par rapport à l’usage des coefficients d’ondelettes. Les attributs multifractals ainsi estimés peuvent ensuite être impliqués dans des tâches de classification, par exemple

Multifractional Brownian Motion and Its Applications to Factor Analysis on Consumer Confidence Index

This thesis aims at introducing a new way to model time series objects in statistics using multifractional processes. It provides a detailed review of Brownian motion, fractional Brownian motion and extends the above 2 models to multifractional processes. To demonstrate a successful application to the real world, we perform pattern analysis on consumer confidence and household spending behavior. The analysis is conducted through investigating the local Holder regularity of the consumer confidence index and household expenditure. In the analysis, we first model consumer confidence index and household expenditure with a multifractional stochastic processes. We then use the index, pointwise Holder exponent (PHE), to measure the local Holder regularity of their paths. Next, several estimators of the PHE have been derived and compared using the data. Finally, we detect which household consumption factors share similar patterns of local Holder regularity to the CCI using K-means clustering