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 ...

This dissertation explores the intersection of data fusion, federated learning, and Bayesian methods, with a focus on their applications in indoor localization, GNSS, and image processing. Data fusion involves integrating data and knowledge from multiple sources. It becomes essential when data is only available in a distributed fashion or when different sensors are used to infer a quantity of interest. Data fusion typically includes raw data fusion, feature fusion, and decision fusion. In this thesis, we will concentrate on feature fusion. Distributed data fusion involves merging sensor data from different sources to estimate an unknown process. Bayesian framework is often used because it can provide an optimal and explainable feature by preserving the full distribution of the unknown given the data, called posterior, over the estimated process at each agent. This allows for easy and recursive merging of sensor data ...

Modern technologies have resulted in the production of numerous high-throughput biological datasets. However, the pace of development of capable computational methods does not cope with the pace of generation of new high-throughput datasets. Amongst the most popular biological high-throughput datasets are gene expression datasets (e.g. microarray datasets). This work targets this aspect by proposing a suite of computational methods which can analyse multiple gene expression datasets collectively. The focal method in this suite is the unification of clustering results from multiple datasets using external specifications (UNCLES). This method applies clustering to multiple heterogeneous datasets which measure the expression of the same set of genes separately and then combines the resulting partitions in accordance to one of two types of external specifications; type A identifies the subsets of genes that are consistently co-expressed in all of the given datasets while type ...

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. ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Not Available

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, ...

In this thesis, we consider the problem of decentralized estimation under communication constraints in the context of Collaborative Signal and Information Processing. Motivated by sensor network applications, a high volume of data collected at distinct locations and possibly in diverse modalities together with the spatially distributed nature and the resource limitations of the underlying system are of concern. Designing processing schemes which match the constraints imposed by the system while providing a reasonable accuracy has been a major challenge in which we are particularly interested in the tradeoff between the estimation performance and the utilization of communications subject to energy and bandwidth constraints. One remarkable approach for decentralized inference in sensor networks is to exploit graphical models together with message passing algorithms. In this framework, after the so-called information graph of the problem is constructed, it is mapped onto the ...