This work is concerned with two image-processing problems, image deconvolution with incomplete observations and data fusion of spectral images, and with some of the algorithms that are used to solve these and related problems. In image-deconvolution problems, the diagonalization of the blurring operator by means of the discrete Fourier transform usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather slow methods, or, otherwise, use inexact convolution models, resulting in the occurrence of artifacts in the enhanced images. We propose a new deconvolution framework for images with incomplete observations that allows one to work with diagonalizable convolution operators, and therefore is very fast. The framework is also an efficient, high-quality alternative to existing methods of dealing with the image boundaries, such as edge ...

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, ...

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 deals with problems of Pattern Recognition in the framework of Machine Learning (ML) and, specifically, Statistical Learning Theory (SLT), using Support Vector Machines (SVMs). The focus of this work is on the geometric interpretation of SVMs, which is accomplished through the notion of Reduced Convex Hulls (RCHs), and its impact on the derivation of new, efficient algorithms for the solution of the general SVM optimization task. The contributions of this work is the extension of the mathematical framework of RCHs, the derivation of novel geometric algorithms for SVMs and, finally, the application of the SVM algorithms to the field of Medical Image Analysis and Diagnosis (Mammography). Geometric SVM Framework's extensions: The geometric interpretation of SVMs is based on the notion of Reduced Convex Hulls. Although the geometric approach to SVMs is very intuitive, its usefulness was restricted by ...

In this doctoral dissertation, we principally explore the use of the temporal information available in video sequences for person and gender recognition; in particular, we focus on the analysis of head and facial motion, and their potential application as biometric identifiers. We also investigate how to exploit as much video information as possible for the automatic recognition; more precisely, we examine the possibility of integrating the head and mouth motion information with facial appearance into a multimodal biometric system, and we study the extraction of novel spatio-temporal facial features for recognition. We initially present a person recognition system that exploits the unconstrained head motion information, extracted by tracking a few facial landmarks in the image plane. In particular, we detail how each video sequence is firstly pre-processed by semiautomatically detecting the face, and then automatically tracking the facial landmarks over ...

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. Furthermore, new challenges arise from modern database architectures, such as the requirements for learning methods to be amenable to streaming, parallel and distributed computing. In this context, an increasingly popular approach is to first compress the database into a representation called a linear sketch, that satisfies all the mentioned requirements, then learn the desired information using only this sketch, which can be significantly faster than using the full data if the sketch is small. In this thesis, we introduce a generic methodology to fit a mixture of probability distributions on the data, using only a sketch of the database. The sketch is defined by combining two notions from the reproducing kernel literature, namely kernel mean embedding and Random Features expansions. It is seen to correspond ...

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 nowadays communication systems, error correction provides robust data transmission through imperfect (noisy) channels. Error correcting codes are a crucial component in most storage and communication systems – wired or wireless –, e.g. GSM, UMTS, xDSL, CD/DVD. At least as important as the data integrity issue is the recent realization that error correcting codes fundamentally change the trade-offs in system design. High-integrity, low redundancy coding can be applied to increase data rate, or battery life time or by reducing hardware costs, making it possible to enter mass market. When it comes to the design of error correcting codes and their properties, there are two main theories that play an important role in this work. Classical coding theory aims at finding the best code given an available block length. This thesis focuses on the ubiquitous Reed-Solomon codes, one of the major ...

A fundamental theorem in information theory – the data processing inequality – states that deterministic processing cannot increase the amount of information contained in a random variable or a stochastic process. The task of signal processing is to operate on the physical representation of information such that the intended user can access this information with little effort. In the light of the data processing inequality, this can be viewed as the task of removing irrelevant information, while preserving as much relevant information as possible. This thesis defines information loss for memoryless systems processing random variables or stochastic processes, both with and without a notion of relevance. These definitions are the basis of an information-theoretic systems theory, which complements the currently prevailing energy-centered approaches. The results thus developed are used to analyze various systems in the signal processor’s toolbox: polynomials, quantizers, ...

The main objective of this thesis is to suggest a general Bayesian framework for model selection based on the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. In particular, we aim to reveal the undiscovered potentials of RJMCMC in model selection applications by exploiting the original formulation to explore spaces of di erent classes or structures and thus, to show that RJMCMC o ers a wider interpretation than just being a trans-dimensional model selection algorithm. The general practice is to use RJMCMC in a trans-dimensional framework e.g. in model estimation studies of linear time series, such as AR and ARMA and mixture processes, etc. In this thesis, we propose a new interpretation on RJMCMC which reveals the undiscovered potentials of the algorithm. This new interpretation, firstly, extends the classical trans-dimensional approach to a much wider meaning by exploring the spaces ...

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 ...

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 ...

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 ...

The large number of practical applications involving digital images has motivated a significant interest towards restoration solutions that improve the visual quality of the data under the presence of various acquisition and compression artifacts. Digital images are the results of an acquisition process based on the measurement of a physical quantity of interest incident upon an imaging sensor over a specified period of time. The quantity of interest depends on the targeted imaging application. Common imaging sensors measure the number of photons impinging over a dense grid of photodetectors in order to produce an image similar to what is perceived by the human visual system. Different applications focus on the part of the electromagnetic spectrum not visible by the human visual system, and thus require different sensing technologies to form the image. In all cases, even with the advance of ...

Independent component analysis (ICA) and blind source separation (BSS) deal with extracting a number of mutually independent elements from a set of observed linear mixtures. Motivated by various applications, this work considers a more general and more flexible model: the sources can be partitioned into groups exhibiting dependence within a given group but independence between two different groups. We argue that this is tantamount to considering multidimensional components, as opposed to the standard ICA case which is restricted to one-dimensional components. In this work, we focus on second-order methods to separate statistically-independent multidimensional components from their linear instantaneous mixture. The purpose of this work is to provide theoretical answers to questions which so far have been discussed mainly in the empirical domain. Namely, we provide a closed-form expression for the figure of merit, the mean square error (MSE), for multidimensional ...