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 ...

An important specificity of wireless communication channels are the rapid fluctuations of propagation coefficients. This effect is called fading and is caused by the motion of obstacles, scatterers and reflectors standing along the different paths of electromagnetic wave propagation between the transmitting and the receiving terminal. These changes in the geometry of the wireless channel prompt the attenuation coefficients and the relative phase shifts between the multiple propagation paths to vary. This suggests to model the channel coefficients (the transfer matrix) as random variables. The present thesis studies information rates for reliable transmission of information over fading channels under the realistic assumption that the receiver has only imperfect knowledge of the random fading state. While the over-idealized assumption of perfect channel-state information at the receiver (CSIR) gives rise to many simple expressions and is fairly well understood, the settings with ...

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 ...

In this thesis, signal and image processing algorithms based on sparsity and interval convex programming are developed for inverse problems. Inverse signal processing problems are solved by minimizing the ℓ1 norm or the Total Variation (TV) based cost functions in the literature. A modified entropy functional approximating the absolute value function is defined. This functional is also used to approximate the ℓ1 norm, which is the most widely used cost function in sparse signal processing problems. The modified entropy functional is continuously differentiable, and convex. As a result, it is possible to develop iterative, globally convergent algorithms for compressive sensing, denoising and restoration problems using the modified entropy functional. Iterative interval convex programming algorithms are constructed using Bregman’s D-Projection operator. In sparse signal processing, it is assumed that the signal can be represented using a sparse set of coefficients in ...

As many machine learning and signal processing problems are fundamentally nonconvex and too expensive/difficult to be convexified, my research is focused on understanding the optimization landscapes of their fundamentally nonconvex formulations. After understanding their optimization landscapes, we can develop optimization algorithms to efficiently navigate these optimization landscapes and achieve the global optimality convergence. So, the main theme of this thesis would be optimization, with an emphasis on nonconvex optimization and algorithmic developments for these popular optimization problems. This thesis can be conceptually divided into four parts: Part 1: Convex Optimization. In the first part, we apply convex relaxations to several popular nonconvex problems in signal processing and machine learning (e.g. line spectral estimation problem and tensor decomposition problem) and prove that the solving the new convex relaxation problems is guaranteed to achieve the globally optimal solutions of their original nonconvex ...

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 ...

Next generation search engines will enable query formulations, other than text, relying on visual information encoded in terms of images and shapes. The 3D search technology, in particular, targets specialized application domains ranging from computer aided-design and manufacturing to cultural heritage archival and presentation. Content-based retrieval research aims at developing search engines that would allow users to perform a query by similarity of content. This thesis deals with two fundamentals problems in content-based 3D object retrieval: (1) How to describe a 3D shape to obtain a reliable representative for the subsequent task of similarity search? (2) How to supervise the search process to learn inter-shape similarities for more effective and semantic retrieval? Concerning the first problem, we develop a novel 3D shape description scheme based on probability density of multivariate local surface features. We constructively obtain local characterizations of 3D ...

This Thesis is focused on the use of automatic speaker recognition systems for forensic identification, in what is called forensic automatic speaker recognition. More generally, forensic identification aims at individualization, defined as the certainty of distinguishing an object or person from any other in a given population. This objective is followed by the analysis of the forensic evidence, understood as the comparison between two samples of material, such as glass, blood, speech, etc. An automatic speaker recognition system can be used in order to perform such comparison between some recovered speech material of questioned origin (e.g., an incriminating wire-tapping) and some control speech material coming from a suspect (e.g., recordings acquired in police facilities). However, the evaluation of such evidence is not a trivial issue at all. In fact, the debate about the presentation of forensic evidence in a court ...

Distributed networks comprising a large number of nodes, e.g., Wireless Sensor Networks, Personal Computers (PC’s), laptops, smart phones, etc., which cooperate with each other in order to reach a common goal, constitute a promising technology for several applications. Typical examples include: distributed environmental monitoring, acoustic source localization, power spectrum estimation, etc. Sophisticated cooperation mechanisms can significantly benefit the learning process, through which the nodes achieve their common objective. In this dissertation, the problem of adaptive learning in distributed networks is studied, focusing on the task of distributed estimation. A set of nodes sense information related to certain parameters and the estimation of these parameters constitutes the goal. Towards this direction, nodes exploit locally sensed measurements as well as information springing from interactions with other nodes of the network. Throughout this dissertation, the cooperation among the nodes follows the diffusion optimization ...

In the last few years, wireless devices have evolved to unimaginable heights. Current forecasts suggest that, in the near future, every device that may take advantage of a wireless connection will have one. In addition, there is a gradual migration to smart devices and high-speed connections, and, as a consequence, the overall mobile traffic is expected to experience a tremendous growth in the next years. The multiuser interference will hence become the main limiting factor and the most critical point to address. As instrumental to efficiently manage interference between different systems, this thesis provides a thorough study on cooperative techniques. That is, users share information and exploit it to improve the overall performance. Since multiuser cooperation represents a very broad term, we will focus on algorithm design and transceiver optimization for three cooperative scenarios that capture some of the main ...

We investigate two aspects of multiple-antenna wireless communication systems in this thesis: 1) deployment of an adaptive beamformer array at the receiver; and 2) space-time coding for arrays at the transmitter and the receiver. In the first part of the thesis, we establish sufficient conditions for the convergence of a popular least mean squares (LMS) algorithm known as the sequential Partial Update LMS Algorithm for adaptive beamforming. Partial update LMS (PU-LMS) algorithms are reduced complexity versions of the full update LMS that update a subset of filter coefficients at each iteration. We introduce a new improved algorithm, called Stochastic PU-LMS, which selects the subsets at random at each iteration. We show that the new algorithm converges for a wider class of signals than the existing PU-LMS algorithms. The second part of this thesis deals with the multiple-input multiple-output (MIMO) Shannon ...

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 ...

Fingerprint, is considered one of the most crucial scientific tools in solving criminal cases. This biometric feature is composed of unique and distinctive patterns found on the fingertips of each individual. With advancing technology and progress in forensic sciences, fingerprint analysis plays a vital role in forensic investigations and the analysis of evidence at crime scenes. The fingerprint patterns of each individual start to develop in early stagesof life and never change thereafter. This fact makes fingerprints an exceptional means of identification. In criminal cases, fingerprint analysis is used to decipher traces, evidence, and clues at crime scenes. These analyses not only provide insights into how a crime was committed but also assist in identifying the culprits or individuals involved. Computer-based fingerprint identification systems yield faster and more accurate results compared to traditional methods, making fingerprint comparisons in large databases ...

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 ...

This thesis deals with estimation of states and parameters in nonlinear and non-Gaussian dynamic systems. Sequential Monte Carlo methods are mainly used to this end. These methods rely on models of the underlying system, motivating some developments of the model concept. One of the main reasons for the interest in nonlinear estimation is that problems of this kind arise naturally in many important applications. Several applications of nonlinear estimation are studied. The models most commonly used for estimation are based on stochastic difference equations, referred to as state-space models. This thesis is mainly concerned with models of this kind. However, there will be a brief digression from this, in the treatment of the mathematically more intricate differential-algebraic equations. Here, the purpose is to write these equations in a form suitable for statistical signal processing. The nonlinear state estimation problem is ...