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 ...

Extending the concepts of classical signal processing to graphs, a wide array of methods have come to the fore, including filtering, reconstruction, classification, and sampling. Existing approaches in graph signal processing consider a known and static topology, i.e., fixed number of nodes and a fixed edge support. Two types of tasks stand out, namely, topology inference, where the edge support along with their weights are estimated from signals; and data processing, where existing data and the known topology are used to perform different tasks. However, such tasks become quite challenging when the network size and support changes over time. Particularly, these challenges involve adapting to the changing topology, data distributions and dealing with unknown topological information. The latter manifests for example, when new nodes are available to attach to the graph but their connectivity is uncertain as is the case ...

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 ...

High dimensional time series data are observed in many complex systems. In networked data, some of the time series are influenced by other time series. Identifying these relations encoded in a graph structure or topology among the time series is of paramount interest in certain applications since the identifi ed structure can provide insights about the underlying system and can assist in inference tasks. In practice, the underlying topology is usually sparse, that is, not all the participating time series influence each other. The goal of this dissertation pertains to study the problem of sparse topology identi fication under various settings. Topology identi fication from time series is a challenging task. The first major challenge in topology identi fication is that the assumption of static topology does not hold always in practice since most of the practical systems are evolving ...

The aim of this thesis is to introduce a variety of signal processing methodologies specifically designed to model, interpret, and learn from data structured within topological spaces. These spaces are loosely characterized as a collection of points together with a neighborhood notion among points. The methodologies and tools discussed herein hold particular relevance and utility when applied to signals defined over combinatorial topological spaces, such as cell complexes, or within metric spaces that exhibit non-trivial properties, such as Riemann manifolds with non-flat metrics. One of the primary motivations behind this research is to address and surmount the constraints encountered with traditional graph-based representations when they are employed to depict intricate systems. This thesis emphasizes the necessity to account for sophisticated, multiway, and geometry-sensitive interactions that are not adequately captured by conventional graph models. The contributions of this work include but ...

Inspired by new emerging technologies and networks of devices with high collective computational power, I focus my work on the problematics of distributed algorithms. While each device runs a relatively simple algorithm with low complexity, the group of interconnected units (agents) determines a behavior of high complexity. Typically, such units have their own memory and processing unit, and are interconnected and capable to exchange information with each other. More specifically, this work is focused on the distributed consensus algorithms. Such algorithms allow the agents to coordinate their behaviour and to distributively find a common agreement (consensus). To understand and analyze their behaviour, it is necessary to analyze the convergence of the consensus algorithm, i.e., under which conditions the algorithm reaches a consensus and under which it does not. Naturally, the communication channel can change and the agents may function asynchronously ...

Inference and data analysis over networks have become significant areas of research due to the increasing prevalence of interconnected systems and the growing volume of data they produce. Many of these systems generate data in the form of multivariate time series, which are collections of time series data that are observed simultaneously across multiple variables. For example, EEG measurements of the brain produce multivariate time series data that record the electrical activity of different brain regions over time. Cyber-physical systems generate multivariate time series that capture the behaviour of physical systems in response to cybernetic inputs. Similarly, financial time series reflect the dynamics of multiple financial instruments or market indices over time. Through the analysis of these time series, one can uncover important details about the behavior of the system, detect patterns, and make predictions. Therefore, designing effective methods for ...

The rise of immersive technologies has led to an increase in the number of use cases that adapt this type of technology within the telecommunications area. Some examples are: industrial training, multimedia content consumption and tele-training. Among all the immersive technologies, eXtended Reality through the use of Head-Mounted Displays (HMD) is the one that focuses the majority of current developments. Specifically, the Social XR paradigm frames the use of immersive technologies in a multi-user or social context. Among the decisive factors for using immersive technology in communications use cases, two stand out: the possibility of making the user believe that they has been transported to another place (sensation of presence) and the possibility of increasing interactions by allowing displacements through space (6 degrees of freedom) as well as the possibility of interacting in a more natural way. Such improvements are ...

Every day we share our personal information through digital systems which are constantly exposed to threats. For this reason, security-oriented disciplines of signal processing have received increasing attention in the last decades: multimedia forensics, digital watermarking, biometrics, network monitoring, steganography and steganalysis are just a few examples. Even though each of these elds has its own peculiarities, they all have to deal with a common problem: the presence of one or more adversaries aiming at making the system fail. Adversarial Signal Processing lays the basis of a general theory that takes into account the impact that the presence of an adversary has on the design of effective signal processing tools. By focusing on the application side of Adversarial Signal Processing, namely adversarial information fusion in distributed sensor networks, and adopting a game-theoretic approach, this thesis contributes to the above mission ...

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 localization and tracking of sound sources using microphone arrays is a problem that, even if it has attracted attention from the signal processing research community for decades, remains open. In recent years, deep learning models have surpassed the state-of-the-art that had been established by classic signal processing techniques, but these models still struggle with handling rooms with strong reverberations or tracking multiple sources that dynamically appear and disappear, especially when we cannot apply any criteria to classify or order them. In this thesis, we follow the ideas of the Geometric Deep Learning framework to propose new models and techniques that mean an advance of the state-of-the-art in the aforementioned scenarios. As the input of our models, we use acoustic power maps computed using the SRP-PHAT algorithm, a classic signal processing technique that allows us to estimate the acoustic energy ...

Machine learning and deep learning techniques have emerged as powerful tools for addressing complex challenges across diverse domains. These methodologies are powerful because they extract patterns and insights from large and complex datasets, automate decision-making processes, and continuously improve over time. They enable us to observe and quantify patterns in data that a normal human would not be able to capture, leading to deeper insights and more accurate predictions. This dissertation presents two research papers that leverage these methodologies to tackle distinct yet interconnected problems in neuroimaging and computer vision for the quantification of human health. The first investigation, "Age prediction using resting-state functional MRI," addresses the challenge of understanding brain aging. By employing the Least Absolute Shrinkage and Selection Operator (LASSO) on resting-state functional MRI (rsfMRI) data, we identify the most predictive correlations related to brain age. Our study, ...

Due to significant advances made over the last few decades in the areas of (wireless) networking, communications and microprocessor fabrication, the use of sensor networks to observe physical phenomena is rapidly becoming commonplace. Over this period, many aspects of sensor networks have been explored, yet a thorough understanding of how to analyse and process the vast amounts of sensor data collected remains an open area of research. This work, therefore, aims to provide theoretical, as well as practical, advances this area. In particular, we consider the problem of inferring certain underlying properties of the monitored phenomena, from our sensor measurements. Within mathematics, this is commonly formulated as an inverse problem; whereas in signal processing, it appears as a (multidimensional) sampling and reconstruction problem. Indeed it is well known that inverse problems are notoriously ill-posed and very demanding to solve; meanwhile ...

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 ...

This dissertation studies soft biometrics traits, their applicability in different security and commercial scenarios, as well as related usability aspects. We place the emphasis on human facial soft biometric traits which constitute the set of physical, adhered or behavioral human characteristics that can partially differentiate, classify and identify humans. Such traits, which include characteristics like age, gender, skin and eye color, the presence of glasses, moustache or beard, inherit several advantages such as ease of acquisition, as well as a natural compatibility with how humans perceive their surroundings. Specifically, soft biometric traits are compatible with the human process of classifying and recalling our environment, a process which involves constructions of hierarchical structures of different refined traits. This thesis explores these traits, and their application in soft biometric systems (SBSs), and specifically focuses on how such systems can achieve different goals ...