Multifractal analysis for multivariate data with application to remote sensing

Texture characterization is a central element in many image processing applications. Texture analysis can be embedded in the mathematical framework of multifractal analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, the coefficients or wavelet leaders. Although successfully applied in various contexts, multi fractal analysis suffers at present from two major limitations. First, the accurate estimation of multifractal parameters for image texture remains a challenge, notably for small sample sizes. Second, multifractal analysis has so far been limited to the analysis of a single image, while the data available in applications are increasingly multivariate. The main goal of this thesis is to develop practical contributions to overcome these limitations. The first limitation is tackled by introducing a generic statistical model for the logarithm of wavelet leaders, parametrized by multifractal parameters of interest. This statistical model enables us to counterbalance the variability induced by small sample sizes and to embed the estimation in a Bayesian framework. This yields robust and accurate estimation procedures, effective both for small and large images. The multifractal analysis of multivariate images is then addressed by generalizing this Bayesian framework to hierarchical models able to account for the assumption that multifractal properties evolve smoothly in the dataset. This is achieved via the design of suitable priors relating the dynamical properties of the multifractal parameters of the different components composing the dataset. Different priors are investigated and compared in this thesis by means of numerical simulations conducted on synthetic multivariate multifractal images. This work is further completed by the investigation of the potential benefit of multifractal analysis and the proposed Bayesian methodology for remote sensing via the example of hyperspectral imaging

Bayesian estimation of the parameters of the joint multifractal spectrum of signals and images

Multifractal analysis has become a reference tool for signal and image processing. Grounded in the quantification of local regularity fluctuations, it has proven useful in an increasing range of applications, yet so far involving only univariate data (scalar-valued time series or single channel images). Recently the theoretical ground for multivariate multifractal analysis has been devised, showing potential for quantifying transient higher-order dependence beyond linear correlation among collections of data. However, the accurate estimation of the parameters associated with a multivariate multifractal model remains challenging, severely limiting their actual use in applications. The main goal of this thesis is to propose and study practical contributions on multivariate multifractal analysis of signals and images. Specifically, the proposed approach relies on a novel and original joint Gaussian model for the logarithm of wavelet leaders and leverages on a Whittle-based likelihood approximation and data augmentation for the matrix-valued parameters of interest. This careful design enables efficient estimation procedures to be constructed for two relevant choices of priors using Bayesian inference. Algorithms based on Monte Carlo Markov Chain and Expectation Maximization strategies are designed and used to approximate the Bayesian estimators. Monte Carlo simulations, conducted on synthetic multivariate signals and images with various sample sizes, numbers of components and multifractal parameter settings, demonstrate significant performance improvements over the state of the art. In addition, theoretical lower bounds on the variance of the estimators are designed to study their asymptotic behavior. Finally, the relevance of the proposed multivariate multifractal estimation framework is shown for two real-world data examples: drowsiness detection from multichannel physiological signals and potential remote sensing applications in multispectral satellite imagery

Modellierung des hydrologischen Kreislaufs und der Interaktion mit Vegetation im Zusammenhang mit dem Klimawandel

There is a growing interest to extend climate change predictions to smaller, catchment-size scales and identify their implications on hydrological and ecological processes. This thesis presents a blueprint methodology for studying climate change impacts on eco-hydrological dynamics at the plot and catchment scales. A weather generator, AWE-GEN, is developed to produce input meteorological variables to eco-hydrological models. The weather generator is also used for the simulation of future climate scenarios, as inferred from climate models. Using a Bayesian technique, a stochastic downscaling procedure derives the distributions of factors of change for several climate statistics from a multi-model ensemble of outputs of General Circulation Models. The factors of change are subsequently applied to the statistics derived from observations to re-evaluate the parameters of the weather generator. The time series obtained for present and future climates serve as input to a newly developed eco-hydrological model Tethys-Chloris. The methodology is applied to simulate the present (1961-2000) and future (2081-2100) hydrological regimes for the area of Tucson (AZ, U.S.A.). A general reduction of precipitation and a significant increase of air temperature are inferred with the downscaling procedure. The eco-hydrological model is successively used to detect changes in the surface water partition and vegetation dynamics for a desert shrub ecosystem, typical of the semi-arid climate of southern Arizona. An appreciable effect of climate change can be observed in metrics of vegetation performance. The negative impact on vegetation due to amplification of water stress in a warmer and dryer climate is partially offset by the effect of the augment of carbon dioxide concentration. Additionally, an increase of runoff and a depletion of soil moisture with consequence in deep recharge are detected. Such an outcome might affect water availability and risk management in semi-arid systems.Es besteht derzeit ein wachsendes wissenschaftliches Interesse daran, Vorhersagen zum Klimawandel auch auf eine kleinere Skala zu übertragen. Diese Arbeit präsentiert eine Vorgehensweise um Einflüsse des Klimawandels auf ökologisch-hydrologische Dynamiken auf der Einzugsgebietskala nachzuvollziehen. Dazu wurde ein Wettergenerator, AWEGEN, entwickelt, der meteorologische Variablen ausgibt. Der Wettergenerator wird darüber hinaus für die Simulation zukünftiger Klimaszenarien genutzt, die aus den Klimamodellen hervorgehen. Mittels einer Bayes-Technik werden stochastische Downscaling-Prozeduren zur Verteilung der Wechselfaktoren für verschiedene Klimastatistiken aus einem Multimodell-Ensemble ermittelt, die auf Daten des Globalen Klimamodells beruhen. Die Wechselfaktoren werden danach auf die aus Beobachtungen erhaltenen Statistiken angewendet, um die Parameter des Wettergenerators zu überprüfen. Die Zeitreihen dienen als Ausgangsdaten für das neu entwickelte öko-hydrologische Modell Tethys-Chloris. Diese Methode wird angewendet, um die momentanen (1961-2000) sowie zukünftigen (2081-2100) hydrologischen Regime im Gebiet von Tucson (Arizona, U.S.A.) zu simulieren. Dabei ließen sich eine generelle Reduzierung des Niederschlags und eine Zunahme der Lufttemperatur feststellen. Das öko-hydrologische Modell wurde im Anschluss genutzt, um Änderungen in der Verteilung der Oberflächengewässer und der Vegetationsdynamik für ein Wüsten-Buschland Ökosystems nachzuweisen, wie es für das semi-aride Klima typisch ist. Ein nennenswerter Effekt des Klimawandels kann in den Metriken der Vegetationsleistung beobachtet werden. Der negative Einfluss auf die Vegetation aufgrund von Wassermangel in einem wärmeren und trockeneren Klima wird teilweise ausgeglichen durch den Effekt einer verbesserten Kohlendioxidversorgung. Zusätzlich wird eine Erhöhung des (Oberflächen-)Abflusses beobachtet. Diese Ergebnisse beeinflussen die Wasserverfügbarkeit und das Risikomanagement im semi-ariden System

Quantitative Methods for Economics and Finance

This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice

Bayesian joint estimation of the multifractality parameter of image patches using gamma Markov Random Field priors

International audienceTexture analysis can be embedded in the mathematical framework of multifractal (MF) analysis, enabling the study of the fluctuations in regularity of image intensity and providing practical tools for their assessment, wavelet leaders. A statistical model for leaders was proposed permitting Bayesian estimation of MF parameters for images yielding improved estimation quality over linear regression based estimation. This present work proposes an extension of this Bayesian model for patch-wise MF analysis of images. Classical MF analysis assumes space homogeneity of the MF properties whereas here we assume MF properties may change between texture elements and we do not know where the changes are located. This paper proposes a joint Bayesian model for patches formulated using spatially smoothing gamma Markov Random Field priors to counterbalance the increased statistical variability of estimates caused by small patch sizes. Numerical simulations based on synthetic multi-fractal images demonstrate that the proposed algorithm outperforms previous formulations and standard estimators

Complexity Science in Human Change

This reprint encompasses fourteen contributions that offer avenues towards a better understanding of complex systems in human behavior. The phenomena studied here are generally pattern formation processes that originate in social interaction and psychotherapy. Several accounts are also given of the coordination in body movements and in physiological, neuronal and linguistic processes. A common denominator of such pattern formation is that complexity and entropy of the respective systems become reduced spontaneously, which is the hallmark of self-organization. The various methodological approaches of how to model such processes are presented in some detail. Results from the various methods are systematically compared and discussed. Among these approaches are algorithms for the quantification of synchrony by cross-correlational statistics, surrogate control procedures, recurrence mapping and network models.This volume offers an informative and sophisticated resource for scholars of human change, and as well for students at advanced levels, from graduate to post-doctoral. The reprint is multidisciplinary in nature, binding together the fields of medicine, psychology, physics, and neuroscience