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 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 ...

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 ...

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 ...

Localization, separation and tracking of acoustic sources are ancient challenges that lots of animals and human beings are doing intuitively and sometimes with an impressive accuracy. Artificial methods have been developed for various applications and conditions. The majority of those methods are centralized, meaning that all signals are processed together to produce the estimation results. The concept of distributed sensor networks is becoming more realistic as technology advances in the fields of nano-technology, micro electro-mechanic systems (MEMS) and communication. A distributed sensor network comprises scattered nodes which are autonomous, self-powered modules consisting of sensors, actuators and communication capabilities. A variety of layout and connectivity graphs are usually used. Distributed sensor networks have a broad range of applications, which can be categorized in ecology, military, environment monitoring, medical, security and surveillance. In this dissertation we develop algorithms for distributed sensor networks ...

To the surprise of most of us, complexity in nature spawns from simplicity. No matter how simple a basic unit is, when many of them work together, the interactions among these units lead to complexity. This complexity is present in the spreading of diseases, where slightly different policies, or conditions,might lead to very different results; or in biological systems where the interactions between elements maintain the delicate balance that keep life running. Fortunately, despite their complexity, current advances in technology have allowed us to have more than just a sneak-peak at these systems. With new views on how to observe such systems and gather data, we aimto understand the complexity within. One of these new views comes from the field of graph signal processing which provides models and tools to understand and process data coming from such complex systems. With ...

Reverberation is the sum of reflected sound waves and is present in any conventional room. Speech communication devices such as mobile phones in hands-free mode, tablets, smart TVs, teleconferencing systems, hearing aids, voice-controlled systems, etc. use one or more microphones to pick up the desired speech signals. When the microphones are not in the proximity of the desired source, strong reverberation and noise can degrade the signal quality at the microphones and can impair the intelligibility and the performance of automatic speech recognizers. Therefore, it is a highly demanded task to process the microphone signals such that reverberation and noise are reduced. The process of reducing or removing reverberation from recorded signals is called dereverberation. As dereverberation is usually a completely blind problem, where the only available information are the microphone signals, and as the acoustic scenario can be non-stationary, ...

In modern devices which provide hands-free speech capturing functionality, such as hands-free communication kits and voice-controlled devices, the received speech signal at the microphones is corrupted by background noise, interfering speech signals, and room reverberation. In many practical situations, the microphones are not necessarily located near the desired source, and hence, the ratio of the desired speech power to the power of the background noise, the interfering speech, and the reverberation at the microphones can be very low, often around or even below 0 dB. In such situations, the comfort of human-to-human communication, as well as the accuracy of automatic speech recognisers for voice-controlled applications can be signi cantly degraded. Therefore, e ffective speech enhancement algorithms are required to process the microphone signals before transmitting them to the far-end side for communication, or before feeding them into a speech recognition ...

This thesis presents a unified theory for the design and analysis of recursive algorithms for the adaptation of transversal digital filters. First, the widely used error minimization approach to algorithm design is investigated and it is shown not to allow a coherent derivation of practical algorithms from an optimality criterion. The reason is found in the incompatibility of the assumption of a time-invariant application environment for the optimality definition and of the practical demand on the adaptive filter for tracking in time-varying environments. The present proposal for a deterministic approach to algorithm design goes beyond mere error minimization in that the time variation of the coefficients of the adaptive filter is included as well. In the sequel a wealth of algorithms is shown to fulfil this novel unified description and several algorithm modifications, which often appear ad hoc, are derived ...

Human action recognition problem is one of the most challenging problems in the computer vision domain, and plays an emerging role in various fields of study. In this thesis, we investigate structured and sequential representations of spatio-temporal data for recognizing human actions and for measuring action performance quality. In video sequences, we characterize each action with a graphical structure of its spatio-temporal interest points and each such interest point is qualified by its cuboid descriptors. In the case of depth data, an action is represented by the sequence of skeleton joints. Given such descriptors, we solve the human action recognition problem through a hyper-graph matching formulation. As is known, hyper-graph matching problem is NP-complete. We simplify the problem in two stages to enable a fast solution: In the first stage, we take into consideration the physical constraints such as time ...

During the past years wireless communications have been exhibiting an increased growth rendering them the most common way for communication. The continuously increasing demand for wireless services resulted in limited availability of the wireless spectrum. To this end, Cognitive Radio (CR) techniques have been proposed in literature during the past years. The concept of CR approach is to utilize advanced radio and signal-processing technology along with novel spectrum allocation policies to enable new unlicensed wireless users to operate in the existing occupied spectrum areas without degrading the performance of the existing licensed ones. Moreover, the broadcast and fading nature of the wireless channel results in severe degradation on the performance of wireless transmissions. A solution to the problem is the use of multiple-antenna systems so as to achieve spatial diversity. However, in many cases, the communication devices' nature permit the ...

Statistical robustness and collaborative inference in a distributed sensor network are two challenging requirements posed on many modern signal processing applications. This dissertation aims at solving these tasks jointly by providing generic algorithms that are applicable to a wide variety of real-world problems. The first part of the thesis is concerned with sequential detection---a branch of detection theory that is focused on decision-making based on as few measurements as possible. After reviewing some fundamental concepts of statistical hypothesis testing, a general formulation of the Consensus+Innovations Sequential Probability Ratio Test for sequential binary hypothesis testing in distributed networks is derived. In a next step, multiple robust versions of the algorithm based on two different robustification paradigms are developed. The functionality of the proposed detectors is verified in simulations, and their performance is examined under different network conditions and outlier concentrations. Subsequently, ...

The multi-frequency Global Navigation Satellite System (GNSS) signals are designed to overcome the inherent performance limitations of single-frequency receivers. However, the processing of multiple frequency signals in a time-varying GNSS signal environment which are potentially affected by multipath, ionosphere scintillation, blockage, and interference is quite challenging, as each signal is influenced differently by channel effects according to its Radio Frequency (RF). In order to get the benefit of synchronously/coherently generated multiple frequency signals, advanced receiver signal processing techniques need to be developed. The aim of this research thesis is to extract the best performance benefits out of multifrequency GNSS signals in a time-varying GNSS signal environment. To accomplish this objective, it is necessary to analyze the multi-frequency signal characteristics and to investigate suitable signal processing algorithms in order to enable the best performance of each signal. The GNSS receiver position ...

Time-varying systems are encountered in various fields of engineering. If the time-varying behavior of a system is undesired, it produces a distorted output signal. Dedicated time-varying systems can be cascaded with the original system to correct the impact of the undesired time-varying behavior on the output signal. In applications where a high reconstruction accuracy is important, the computational cost of designing and employing flexible digital correction systems remains challenging. In particular, the computational load becomes a major challenge if the digital correction system needs to be redesigned for each time instant. In this thesis, low complexity correction methods for the design of linear time-varying correction filters are presented. These filters can be applied to postcorrect or precorrect linear time-varying systems. In order to mitigate the computational complexity of the filter design, a low complexity filter design algorithm for the least-squares ...

The problem of signal separation is a very broad and fundamental one. A powerful paradigm within which signal separation can be achieved is the assumption that the signals/sources are statistically independent of one another. This is known as Independent Component Analysis (ICA). In this thesis, the theoretical aspects and derivation of ICA are examined, from which disparate approaches to signal separation are drawn together in a unifying framework. This is followed by a review of signal separation techniques based on ICA. Second order statistics based output decorrelation methods are employed to try to solve the challenging problem of separating convolutively mixed signals, in the context of mainly audio source separation and the Cocktail Party Problem. Various optimisation techniques are devised to implement second order signal separation of both artificially mixed signals and real mixtures. A study of the advantages and ...