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 ...

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 ...

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 ...

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 ...

The effectiveness of machine learning (ML) in today's applications largely depends on the goodness of the representation of data used within the ML algorithms. While the massiveness in dimension of modern day data often requires lower-dimensional data representations in many applications for efficient use of available computational resources, the use of uncorrelated features is also known to enhance the performance of ML algorithms. Thus, an efficient representation learning solution should focus on dimension reduction as well as uncorrelated feature extraction. Even though Principal Component Analysis (PCA) and linear autoencoders are fundamental data preprocessing tools that are largely used for dimension reduction, when engineered properly they can also be used to extract uncorrelated features. At the same time, factors like ever-increasing volume of data or inherently distributed data generation impede the use of existing centralized solutions for representation learning that require ...

The level of automation in our society is ever increasing. Technologies like self-driving cars, virtual reality, and fully autonomous robots, which all were unimaginable a few decades ago, are realizable today, and will become standard consumer products in the future. These technologies depend upon autonomous localization and situation awareness where careful processing of sensory data is required. To increase efficiency, robustness and reliability, appropriate models for these data are needed. In this thesis, such models are analyzed within three different application areas, namely (1) magnetic localization, (2) extended target tracking, and (3) autonomous learning from raw pixel information. Magnetic localization is based on one or more magnetometers measuring the induced magnetic field from magnetic objects. In this thesis we present a model for determining the position and the orientation of small magnets with an accuracy of a few millimeters. This ...

In many modern signal processing applications, traditional machine learning and pattern recognition methods heavily rely on the having a sufficiently large amount of data samples to correctly estimate the underlying structures within complex signals. The main idea is to understand the inherent structural information and relationships embedded within the raw data, thereby enabling a wide variety of inference tasks. Nevertheless, the definition of what constitutes a sufficiently large dataset remains subjective and it is often problem-dependent. In this context, traditional learning approaches often fail to learn meaningful structures in the cases where the number of features closely matches (or even exceeds) the number of observations. These scenarios emphasize the need for tailored strategies that effectively extract meaningful structured information from these high-dimensional settings. In this thesis we address fundamental challenges posed by applying traditional machine learning techniques in large dimensional ...

Due to a variety of potential barriers to sample acquisition, many of the datasets encountered in important classification applications, ranging from tumor identification to facial recognition, are characterized by small samples of high-dimensional data. In such situations, linear classifiers are popular as they have less risk of overfitting while being faster and more interpretable than non-linear classifiers. They are also easier to understand and implement for the inexperienced practitioner. In this dissertation, several gaps in the literature regarding the analysis and design of linear classifiers for high-dimensional data are addressed using tools from the field of asymptotic Random Matrix Theory (RMT) which facilitate the derivation of limits of relevant quantities or distributions, such as the probability of misclassification of a particular classifier or the asymptotic distribution of its discriminant, in the RMT regime where both the sample size and dimensionality ...

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 ...

A new approach to robust filtering, prediction, smoothing and open-loop control of discrete-time signal vectors is presented. Linear time-invariant filters are designed to be insensitive to spectral uncertainty in signal models. The goal is to obtain a simple design method, leading to filters which are not overly conservative. Modelling errors are described by sets of time-invariant models, parameterized by random variables with known covariances. These covariances could either be estimated from data, or be used as robustness ``tuning knobs". A robust design is obtained by minimizing the H-2 norm, averaged with respect to the assumed model errors. A polynomial matrix solution, based on an averaged spectral factorization and a Diophantine equation, is derived. The robust filters are referred to as cautious filters. The filters turn out to be not more complicated to design than the ordinary filters. The main effort ...

Localizing the bioelectric phenomena originating from the cerebral cortex and evoked by auditory and somatosensory stimuli are clear objectives to both understand how the brain works and to recognize different pathologies. Diseases such as Parkinson's, Alzheimer's, schizophrenia and epilepsy are intensively studied to find a cure or accurate diagnosis. Epilepsy is considered the disease with major prevalence within disorders with neurological origin. The recurrent and sudden incidence of seizures can lead to dangerous and possibly life-threatening situations. Since disturbance of consciousness and sudden loss of motor control often occur without any warning, the ability to predict epileptic seizures would reduce patients' anxiety, thus considerably improving quality of life and safety. The common procedure for epilepsy seizure detection is based on brain activity monitorization via electroencephalogram (EEG) data. This process consumes a lot of time, especially in the case of long ...

This thesis introduces new learning algorithms for Radial Basis Function (RBF) networks. RBF networks is a feed-forward two-layer neural network used for functional approximation or pattern classification applications. The proposed training algorithms are based on robust statistics. Their theoretical performance has been assessed and compared with that of classical algorithms for training RBF networks. The applications of RBF networks described in this thesis consist of simultaneously modeling moving object segmentation and optical flow estimation in image sequences and 3-D image modeling and segmentation. A Bayesian classifier model is used for the representation of the image sequence and 3-D images. This employs an energy based description of the probability functions involved. The energy functions are represented by RBF networks whose inputs are various features drawn from the images and whose outputs are objects. The hidden units embed kernel functions. Each kernel ...

This Ph.D. thesis focuses on developing a system for high-quality speech synthesis and voice conversion. Vocoder-based speech analysis, manipulation, and synthesis plays a crucial role in various kinds of statistical parametric speech research. Although there are vocoding methods which yield close to natural synthesized speech, they are typically computationally expensive, and are thus not suitable for real-time implementation, especially in embedded environments. Therefore, there is a need for simple and computationally feasible digital signal processing algorithms for generating high-quality and natural-sounding synthesized speech. In this dissertation, I propose a solution to extract optimal acoustic features and a new waveform generator to achieve higher sound quality and conversion accuracy by applying advances in deep learning. The approach remains computationally efficient. This challenge resulted in five thesis groups, which are briefly summarized below. I introduce firstly a new method to shape the ...

In this dissertation we focus on statistical signal processing for Data Fusion, with a particular focus on wireless sensor networks. Six topics are studied: (i) Data Fusion for classification under model uncertainty; (ii) Decision Fusion over coherent MIMO channels; (iii) Performance analysis of Maximum Ratio Combining in MIMO decision fusion; (iv) Decision Fusion over non-coherent MIMO channels; (v) Decision Fusion for distributed classification of multiple targets; (vi) Data Fusion for inverse localization problems, with application to wideband passive sonar platform estimation. The first topic of this thesis addresses the problem of lack of knowledge of the prior distribution in classification problems that operate on small data sets that may make the application of Bayes' rule questionable. Uniform or arbitrary priors may provide classification answers that, even in simple examples, may end up contradicting our common sense about the problem. Entropic ...

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 ...