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 ...

In this thesis, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral drive by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.

The overriding aim of this thesis is to investigate the benefits of focusing time-frequency analysis on particular regions of the time-frequency plane. The thesis examines aspects of such a regionalisation in the analysis of both deterministic signals and stochastic processes. The majority of deterministic energetic time-frequency representations are non-parametric indicating the distribution of the energy of a signal in the time-frequency plane but providing no further information about the time-frequency structure. This thesis develops a semi-parametric time-frequency model to simultaneously describe the time-frequency energetic structure of a signal and provide an indication of its time-frequency complexity. The model aims to identify ‘timefrequency components’ within the signal to indicate how their energy is distributed in the time-frequency plane and thereby to probabilistically associate every location in the plane with each identified component. The thesis investigates a number of applications of the ...

In this thesis we focus on the development of energy-efficient adaptive algorithms for Wireless Sensor Networks. Its contributions can be arranged in two main lines. Firstly, we focus on the efficient management of energy resources in WSNs equipped with finite-size batteries and energy-harvesting devices. To that end, we propose a censoring scheme by which the nodes are able to decide if a message transmission is worthy or not given their energetic condition. In order to do so, we model the system using a Markov Decision Process and use this model to derive optimal policies. Later, these policies are analyzed in simplified scenarios in order to get insights of their features. Finally, using Stochastic Approximation, we develop low-complexity censoring algorithms that approximate the optimal policy, with less computational complexity and faster convergence speed than other approaches such as Q-learning. Secondly, we ...

Recent advances in many fields ranging from engineering to natural science, require increasingly complicated optimization tasks in the experiment design, for which the target objectives are generally in the form of black-box functions that are expensive to evaluate. In a common formulation of this problem, a designer is expected to solve the black-box optimization tasks via sequentially attempting candidate solutions and receiving feedback from the system. This thesis considers Bayesian optimization (BO) as the black-box optimization framework, and investigates the enhancements on BO from the aspects of efficiency, adaptation and reliability. Generally, BO consists of a surrogate model for providing probabilistic inference and an acquisition function which leverages the probabilistic inference for selecting the next candidate solution. Gaussian process (GP) is a prominent non-parametric surrogate model, and the quality of its inference is a critical factor on the optimality performance ...

Advanced mobile communication systems are characterized by a dense deployment of different types of wireless access points. Since these systems are primarily limited by interference, multiple-input multiple-output (MIMO) techniques as well as coordinated transmission and detection schemes are necessary to mitigate this limitation. Thus, mobile communication systems become more complex which requires that also the mathematical tools for their theoretical analysis must evolve. These must be able to take the most important system characteristics into account, such as fading, path loss, and interference. The aim of this thesis is to develop such tools based on large random matrix theory and to demonstrate their usefulness with the help of several practical applications, such as the performance analysis of network MIMO and large-scale MIMO systems, the design of low-complexity polynomial expansion detectors, and the study of random beamforming techniques as well as ...

The modern power grid is facing major challenges in the transition to a low-carbon energy sector. The growing energy demand and environmental concerns require carefully revisiting how electricity is generated, transmitted, and consumed, with an eye to the integration of renewable energy sources. The envisioned smart grid is expected to address such issues by introducing advanced information, control, and communication technologies into the energy infrastructure. In this context, demand-side management (DSM) makes the end users responsible for improving the efficiency, reliability and sustainability of the power system: this opens up unprecedented possibilities for optimizing the energy usage and cost at different levels of the network. The design of DSM techniques has been extensively discussed in the literature in the last decade, although the performance of these methods has been scarcely investigated from the analytical point of view. In this thesis, ...

Visual information, in the form of digital images and videos, has become so omnipresent in computer databases and repositories, that it can no longer be considered a “second class citizen”, eclipsed by textual information. In that scenario, image classification has become a critical task. In particular, the pursuit of automatic identification of complex semantical concepts represented in images, such as scenes or objects, has motivated researchers in areas as diverse as Information Retrieval, Computer Vision, Image Processing and Artificial Intelligence. Nevertheless, in contrast to text documents, whose words carry semantic, images consist of pixels that have no semanticinformation by themselves, making the task very challenging. In this dissertation, we have addressed the problem of representing images based on their visual information. Our aim is content-based concept detection in images and videos, with a novel representation that enriches the Bag-of-Words model. ...

In the current heterogeneous communication environments, the great variety of multimedia systems and applications combined with fast evolution of networking architectures and topologies, give rise to new research problems related to the various elements of the communication chain. This includes, the ever present problem in video communications, which results from the need for coping with transmission errors and losses. In this context, video streaming with path diversity appeared as a novel communication framework, involving different technological fields and posing several research challenges. The research work carried out in this thesis is a contribution to robust video coding and adaptation techniques in the field of Multiple Description Coding (MDC) for multipath video streaming. The thesis starts with a thorough study of MDC and its theoretical basis followed by a description of the most important practical implementation aspects currently available in literature. ...

This thesis addresses a number of issues concerned with the restoration of one type of image sequence namely archived black and white motion pictures. These are often a valuable historical record but because of the physical nature of the film they can suffer from a variety of degradations which reduce their usefulness. The main visual defects are ‘dirt and sparkle’ due to dust and dirt becoming attached to the film or abrasion removing the emulsion and ‘line scratches’ due to the film running against foreign bodies in the camera or projector. For an image restoration algorithm to be successful it must be based on a mathematical model of the image. A number of models have been proposed and here we explore the use of a general class of model known as Markov Random Fields (MRFs) based on Gibbs distributions by ...

The increasing use of technological devices and biometric recognition systems in people daily lives has motivated a great deal of research interest in the development of effective and robust systems. However, there are still some challenges to be solved in these systems when Deep Neural Networks (DNNs) are employed. For this reason, this thesis proposes different approaches to address these issues. First of all, we have analyzed the effect of introducing the most widespread DNN architectures to develop systems for face and text-dependent speaker verification tasks. In this analysis, we observed that state-of-the-art DNNs established for many tasks, including face verification, did not perform efficiently for text-dependent speaker verification. Therefore, we have conducted a study to find the cause of this poor performance and we have noted that under certain circumstances this problem is due to the use of a ...

This dissertation develops false discovery rate (FDR) controlling machine learning algorithms for large-scale high-dimensional data. Ensuring the reproducibility of discoveries based on high-dimensional data is pivotal in numerous applications. The developed algorithms perform fast variable selection tasks in large-scale high-dimensional settings where the number of variables may be much larger than the number of samples. This includes large-scale data with up to millions of variables such as genome-wide association studies (GWAS). Theoretical finite sample FDR-control guarantees based on martingale theory have been established proving the trustworthiness of the developed methods. The practical open-source R software packages TRexSelector and tlars, which implement the proposed algorithms, have been published on the Comprehensive R Archive Network (CRAN). Extensive numerical experiments and real-world problems in biomedical and financial engineering demonstrate the performance in challenging use-cases. The first three main parts of this dissertation present ...

Multiple antennas at the base station side can be used to enhance the spectral efficiency and energy efficiency of the next generation wireless technologies. Indeed, massive multi-input multi-output (MIMO) is seen as one promising technology to bring the aforementioned benefits for fifth generation wireless standard, commonly known as 5G New Radio (5G NR). In this monograph, we will explore a wide range of potential topics in multi-user MIMO (MU-MIMO) relevant to 5G NR, • Sum rate maximizing beamforming (BF) design and robustness to partial channel state information at the transmitter (CSIT) • Asymptotic analysis of the various BF techniques in massiveMIMO and • Bayesian channel estimationmethods using sparse Bayesian learning. While massive MIMO has the aforementioned benefits, it makes the acquisition of the channel state information at the transmitter (CSIT) very challenging. Since it requires large amount of uplink (UL) ...

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 ...

This thesis develops new mathematical theory and presents novel recovery algorithms for discrete linear dynamical systems (LDS) with sparsity constraints on either control inputs or initial state. The recovery problems in this framework manifest as the problem of reconstructing one or more sparse signals from a set of noisy underdetermined linear measurements. The goal of our work is to design algorithms for sparse signal recovery which can exploit the underlying structure in the measurement matrix and the unknown sparse vectors, and to analyze the impact of these structures on the efficacy of the recovery. We answer three fundamental and interconnected questions on sparse signal recovery problems that arise in the context of LDS. First, what are necessary and sufficient conditions for the existence of a sparse solution? Second, given that a sparse solution exists, what are good low-complexity algorithms that ...