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

Data assimilation for precipitation nowcasting using Bayesian inference

This work introduces a new variational Bayes data assimilation method for the stochastic estimation of precipitation dynamics using radar observations for short term probabilistic forecasting (nowcasting). A previously developed spatial rainfall model based on the decomposition of the observed precipitation field using a basis function expansion captures the precipitation intensity from radar images as a set of ‘rain cells’. The prior distributions for the basis function parameters are carefully chosen to have a conjugate structure for the precipitation field model to allow a novel variational Bayes method to be applied to estimate the posterior distributions in closed form, based on solving an optimisation problem, in a spirit similar to 3D VAR analysis, but seeking approximations to the posterior distribution rather than simply the most probable state. A hierarchical Kalman filter is used to estimate the advection field based on the assimilated precipitation fields at two times. The model is applied to tracking precipitation dynamics in a realistic setting, using UK Met Office radar data from both a summer convective event and a winter frontal event. The performance of the model is assessed both traditionally and using probabilistic measures of fit based on ROC curves. The model is shown to provide very good assimilation characteristics, and promising forecast skill. Improvements to the forecasting scheme are discusse

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field

Capturing the role of the co-play of land use and rainfall on water and sediment flux dynamics across different spatiotemporal scales in intensively managed landscapes

Anthropogenic activities in intensively managed landscapes (IMLs) have significantly modified material travel times and delivery, and have led to more pronounced event-based dynamics compared to undisturbed conditions. Understanding and mitigating human impacts requires the use of both field-based observations and physically-based numerical models to tease out causal relationships and feedbacks between the relevant processes across the cascade of scales, from the plot to the watershed. Unfortunately, there are no event-based numerical models capable of adequately simulating sediment fluxes across scales in IMLs, thus hampering our ability to understand and mitigate anthropogenic impacts.The goal of this study was to develop a conceptual modeling framework for IMLs that considered all the connections and interactions between terrestrial and in-stream sources on an event basis, and to use the framework to identify a characteristic scale unit (CSU) representative of sediment flux laws within the drainage network. The CSU was considered to be a scale at which local-scale variability in landscape properties ceased to have an effect on mean trends in sediment fluxes and, thus, an appropriate scale for simulating/monitoring sediment fluxes for watershed management purposes.The framework was developed and tested in the South Amana sub-watershed (SASW), IA. An upland erosion model was coupled with an instream sediment transport model to simulate material fluxes along different pathways in SASW. A sediment fingerprinting model was also utilized to constrain the predicted contributions of terrestrial and instream sources. Modeling advances made included the incorporation of a surface roughness evolution threshold, space/time variant flow resistance representations of landscape attributes, and the stochastic representation of material origins, travel times, and delivery to the watershed outlet. The developed model was validated via an extensive field campaign performed at scales ranging from the plot to the sub-watershed.The study results revealed thresholds of influence of landscape roughness attributes, and highlighted important intra-seasonal trends in source contributions driven by the co-play of land use and rainfall. A CSU for sediment fluxes and the factors affecting it were identified. Future studies must examine the CSU as dictated by the interplay between event-based and seasonal dynamics, and the implications for watershed management

Computational Modeling for Abnormal Brain Tissue Segmentation, Brain Tumor Tracking, and Grading

This dissertation proposes novel texture feature-based computational models for quantitative analysis of abnormal tissues in two neurological disorders: brain tumor and stroke. Brain tumors are the cells with uncontrolled growth in the brain tissues and one of the major causes of death due to cancer. On the other hand, brain strokes occur due to the sudden interruption of the blood supply which damages the normal brain tissues and frequently causes death or persistent disability. Clinical management of these brain tumors and stroke lesions critically depends on robust quantitative analysis using different imaging modalities including Magnetic Resonance (MR) and Digital Pathology (DP) images. Due to uncontrolled growth and infiltration into the surrounding tissues, the tumor regions appear with a significant texture variation in the static MRI volume and also in the longitudinal imaging study. Consequently, this study developed computational models using novel texture features to segment abnormal brain tissues (tumor, and stroke lesions), tracking the change of tumor volume in longitudinal images, and tumor grading in MR images. Manual delineation and analysis of these abnormal tissues in large scale is tedious, error-prone, and often suffers from inter-observer variability. Therefore, efficient computational models for robust segmentation of different abnormal tissues is required to support the diagnosis and analysis processes. In this study, brain tissues are characterized with novel computational modeling of multi-fractal texture features for multi-class brain tumor tissue segmentation (BTS) and extend the method for ischemic stroke lesions in MRI. The robustness of the proposed segmentation methods is evaluated using a huge amount of private and public domain clinical data that offers competitive performance when compared with that of the state-of-the-art methods. Further, I analyze the dynamic texture behavior of tumor volume in longitudinal imaging and develop post-processing frame-work using three-dimensional (3D) texture features. These post-processing methods are shown to reduce the false positives in the BTS results and improve the overall segmentation result in longitudinal imaging. Furthermore, using this improved segmentation results the change of tumor volume has been quantified in three types such as stable, progress, and shrinkage as observed by the volumetric changes of different tumor tissues in longitudinal images. This study also investigates a novel non-invasive glioma grading, for the first time in literature, that uses structural MRI only. Such non-invasive glioma grading may be useful before an invasive biopsy is recommended. This study further developed an automatic glioma grading scheme using the invasive cell nuclei morphology in DP images for cross-validation with the same patients. In summary, the texture-based computational models proposed in this study are expected to facilitate the clinical management of patients with the brain tumors and strokes by automating large scale imaging data analysis, reducing human error, inter-observer variability, and producing repeatable brain tumor quantitation and grading

Power laws and inverse motion modeling: application to turbulence measurements from satellite images

International audienceIn the context of tackling the ill-posed inverse problem of motion estimation from image sequences, we propose to introduce prior knowledge on flow regularity given by turbulence statistical models. Prior regularity is formalized using turbulence power laws describing statistically self-similar structure of motion increments across scales. The motion estimation method minimizes the error of an image observation model while constraining second order structure function to behave as a power law within a prescribed range. Thanks to a Bayesian modeling framework, the motion estimation method is able to jointly infer the most likely power law directly from image data. The method is assessed on velocity fields of 2D or quasi-2D flows. Estimation accuracy is first evaluated on a synthetic image sequence of homogeneous and isotropic 2D turbulence. Results obtained with the approach based on physics of fluids outperforms state-of-the-art. Then, the method analyzes atmospheric turbulence using a real meteorological image sequence. Selecting the most likely power law model enables the recovery of physical quantities which are of major interest for turbulence atmospheric characterization. In particular, from meteorological images we are able to estimate energy and enstrophy fluxes of turbulent cascades, which are in agreement with previous in situ measurements