The abundance of large and heterogeneous systems is rendering contemporary data more pervasive, intricate, and with a non-regular structure. With classical techniques facing troubles to deal with the irregular (non-Euclidean) domain where the signals are defined, a popular approach at the heart of graph signal processing (GSP) is to: (i) represent the underlying support via a graph and (ii) exploit the topology of this graph to process the signals at hand. In addition to the irregular structure of the signals, another critical limitation is that the observed data is prone to the presence of perturbations, which, in the context of GSP, may affect not only the observed signals but also the topology of the supporting graph. Ignoring the presence of perturbations, along with the couplings between the errors in the signal and the errors in their support, can drastically hinder ...

Multisensor data fusion technology combines data and information from multiple sensors to achieve improved accuracies and better inference about the environment than could be achieved by the use of a single sensor alone. In this dissertation, we propose parametric and nonparametric multisensor data fusion algorithms with a broad range of applications. Image registration is a vital first step in fusing sensor data. Among the wide range of registration techniques that have been developed for various applications, mutual information based registration algorithms have been accepted as one of the most accurate and robust methods. Inspired by the mutual information based approaches, we propose to use the joint R´enyi entropy as the dissimilarity metric between images. Since the R´enyi entropy of an image can be estimated with the length of the minimum spanning tree over the corresponding graph, the proposed information-theoretic registration ...

This dissertation deals with the distributed processing techniques for parameter estimation and efficient data-gathering in wireless communication and sensor networks. The estimation problem consists in inferring a set of parameters from temporal and spatial noisy observations collected by different nodes that monitor an area or field. The objective is to derive an estimate that is as accurate as the one that would be obtained if each node had access to the information across the entire network. With the aim of enabling an energy aware and low-complexity distributed implementation of the estimation task, several useful optimization techniques that generally yield linear estimators were derived in the literature. Up to now, most of the works considered that the nodes are interested in estimating the same vector of global parameters. This scenario can be viewed as a special case of a more general ...

The necessity to process signals living in non-Euclidean domains, such as signals de- fined on the top of a graph, has led to the extension of signal processing techniques to the graph setting. Among different approaches, graph signal processing distinguishes it- self by providing a Fourier analysis of these signals. Analogously to the Fourier transform for time and image signals, the graph Fourier transform decomposes the graph signals in terms of the harmonics provided by the underlying topology. For instance, a graph signal characterized by a slow variation between adjacent nodes has a low frequency content. Along with the graph Fourier transform, graph filters are the key tool to alter the graph frequency content of a graph signal. This thesis focuses on graph filters that are performed distributively in the node domain–that is, each node needs to exchange in- formation ...

Image segmentation through deformable models is a method that localizes object boundaries. When difficult segmentation context are proposed because of noise or a lack of information, the use of prior knowledge in the deformation process increases segmentation accuracy. Medical imaging is often concerned by these context. Moreover, medical applications deal with large amounts of data. Then it is mandatory to use a robust and fast processing. This question lead us to a local regularisation of the deformable model. Highly based on the active contour framework, also known as \emph{snake}, we propose a new regularization scheme. This is done by filtering the displacements at each iteration. The filter is based on a smoothing spline kernel whose aim was to approximate a set of points rather than interpolating it. We point out the consistency of the regularization parameter in such a method. ...

In recent years, advances in signal processing have led the wireless sensor networks to be capable of mobility. The signal processing in a wireless sensor network differs from that of a traditional wireless network mainly in two important aspects. Unlike traditional wireless networks, in a sensor network the signal processing is performed in a fully distributed manner as the sensor measurements in a distributed fashion across the network collected. Additionally, due to the limited onboard resource of a sensor network it is essential to develop energy and bandwidth efficient signal processing algorithms. The thesis is devoted to discuss the state of the arte of algorithms commonly known as tracking algorithms. Although tracking algorithms have only been attracting research and development attention recently, already a wide literature and great variety of proposed approaches regarding the topic exist. The dissertation focus on ...

Wireless networks and power distribution grids are experiencing increasing demands on their efficiency and reliability. Judicious methods for allocating scarce resources such as power and bandwidth are of paramount importance. As a result, nonlinear optimization and signal processing tools have been incorporated into the design of contemporary networks. This thesis develops schemes for efficient resource allocation (RA) in such dynamic networks, with an emphasis in stochasticity, which is accounted for in the problem formulation as well as in the algorithms and schemes to solve those problems. Stochastic optimization and decomposition techniques are investigated to develop low-complexity algorithms with specific applications in cross-layer design of wireless communications, cognitive radio (CR) networks and smart power distribution systems. The costs and constraints on the availability of network resources, together with diverse quality of service (QoS) requirements, render network design, management, and operation challenging ...

Recent academic developments have initiated a paradigm shift in the way spatial sensor data can be acquired. Traditional localized and regularly arranged sensor arrays are replaced by sensor nodes that are randomly distributed over the entire spatial field, and which communicate with each other or with a master node through wireless communication links. Together, these nodes form a so-called ‘wireless sensor network’ (WSN). Each node of a WSN has a local sensor array and a signal processing unit to perform computations on the acquired data. The advantage of WSNs compared to traditional (wired) sensor arrays, is that many more sensors can be used that physically cover the full spatial field, which typically yields more variety (and thus more information) in the signals. It is likely that future data acquisition, control and physical monitoring, will heavily rely on this type of ...

In this doctoral thesis several scale-free texture segmentation procedures based on two fractal attributes, the Hölder exponent, measuring the local regularity of a texture, and local variance, are proposed.A piecewise homogeneous fractal texture model is built, along with a synthesis procedure, providing images composed of the aggregation of fractal texture patches with known attributes and segmentation. This synthesis procedure is used to evaluate the proposed methods performance.A first method, based on the Total Variation regularization of a noisy estimate of local regularity, is illustrated and refined thanks to a post-processing step consisting in an iterative thresholding and resulting in a segmentation.After evidencing the limitations of this first approach, deux segmentation methods, with either "free" or "co-located" contours, are built, taking in account jointly the local regularity and the local variance.These two procedures are formulated as convex nonsmooth functional minimization problems.We ...

Wireless Sensor Networks (WSNs) aim for accurate data gathering and representation of one or multiple physical variables from the environment, by means of sensor reading and wireless data packets transmission to a Data Fusion Center (DFC). There is no comprehensive common set of requirements for all WSN, as they are application dependent. Moreover, due to specific node capabilities or energy consumption constraints several tradeoffs have to be considered during the design, and particularly, the price of the sensor nodes is a determining factor. The distinction between small and large scale WSNs does not only refers to the quantity of sensor nodes, but also establishes the main design challenges in each case. For example, the node organization is a key issue in large scale WSNs, where many inexpensive nodes have to properly work in a coordinated manner. Regarding the amount of ...

During the last decades, information is being gathered and processed at an explosive rate. This fact gives rise to a very important issue, that is, how to effectively and precisely describe the information content of a given source signal or an ensemble of source signals, such that it can be stored, processed or transmitted by taking into consideration the limitations and capabilities of the several digital devices. One of the fundamental principles of signal processing for decades is the Nyquist-Shannon sampling theorem, which states that the minimum number of samples needed to reconstruct a signal without error is dictated by its bandwidth. However, there are many cases in our everyday life in which sampling at the Nyquist rate results in too many data and thus, demanding an increased processing power, as well as storage requirements. A mathematical theory that emerged ...

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In Wireless Sensor Networks (WSN), the ability of sensor nodes to know its position is an enabler for a wide variety of applications for monitoring, control, and automation. Often, sensor data is meaningful only if its position can be determined. Many WSN are deployed indoors or in areas where Global Navigation Satellite System (GNSS) signal coverage is not available, and thus GNSS positioning cannot be guaranteed. In these scenarios, WSN may be relied upon to achieve a satisfactory degree of positioning accuracy. Typically, batteries power sensor nodes in WSN. These batteries are costly to replace. Therefore, power consumption is an important aspect, being performance and lifetime ofWSN strongly relying on the ability to reduce it. It is crucial to design effective strategies to maximize battery lifetime. Optimization of power consumption can be made at different layers. For example, at the ...

The first part of this dissertation considers distributed learning problems over networked agents. The general objective of distributed adaptation and learning is the solution of global, stochastic optimization problems through localized interactions and without information about the statistical properties of the data. Regularization is a useful technique to encourage or enforce structural properties on the resulting solution, such as sparsity or constraints. A substantial number of regularizers are inherently non-smooth, while many cost functions are differentiable. We propose distributed and adaptive strategies that are able to minimize aggregate sums of objectives. In doing so, we exploit the structure of the individual objectives as sums of differentiable costs and non-differentiable regularizers. The resulting algorithms are adaptive in nature and able to continuously track drifts in the problem; their recursions, however, are subject to persistent perturbations arising from the stochastic nature of ...

In this thesis we investigate centralized and distributed variants of sparse Bayesian learning (SBL), an effective probabilistic regression method used in machine learning. Since inference in an SBL model is not tractable in closed form, approximations are needed. We focus on the variational Bayesian approximation, as opposed to others used in the literature, for three reasons: First, it is a flexible general framework for approximate Bayesian inference that estimates probability densities including point estimates as a special case. Second, it has guaranteed convergence properties. And third, it is a deterministic approximation concept that is even applicable for high dimensional problems where non-deterministic sampling methods may be prohibitive. We resolve some inconsistencies in the literature involved in other SBL approximation techniques with regard to a proper Bayesian treatment and the incorporation of a very desired property, namely scale invariance. More specifically, ...