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 ...

This doctorate thesis focuses on sparse regression, a statistical modeling tool for selecting valuable predictors in underdetermined linear models. By imposing different constraints on the structure of the variable vector in the regression problem, one obtains estimates which have sparse supports, i.e., where only a few of the elements in the response variable have non-zero values. The thesis collects six papers which, to a varying extent, deals with the applications, implementations, modifications, translations, and other analysis of such problems. Sparse regression is often used to approximate additive models with intricate, non-linear, non-smooth or otherwise problematic functions, by creating an underdetermined model consisting of candidate values for these functions, and linear response variables which selects among the candidates. Sparse regression is therefore a widely used tool in applications such as, e.g., image processing, audio processing, seismological and biomedical modeling, but is ...

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 ...

The unprecedented processing demand, posed by the explosion of big data, challenges researchers to design efficient and adaptive machine learning algorithms that do not require persistent retraining and avoid learning redundant information. Inspired from learning techniques of intelligent biological agents, identifying transferable knowledge across learning problems has been a significant research focus to improve machine learning algorithms. In this thesis, we address the challenges of knowledge transfer through embedding spaces that capture and store hierarchical knowledge. In the first part of the thesis, we focus on the problem of cross-domain knowledge transfer. We first address zero-shot image classification, where the goal is to identify images from unseen classes using semantic descriptions of these classes. We train two coupled dictionaries which align visual and semantic domains via an intermediate embedding space. We then extend this idea by training deep networks that ...

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 ...

This dissertation deals with the distributed processing techniques for parameter estimation and efficient data-gathering in wireless communication and sensor networks. The estimation problem consists in inferring a set of parameters from temporal and spatial noisy observations collected by different nodes that monitor an area or field. The objective is to derive an estimate that is as accurate as the one that would be obtained if each node had access to the information across the entire network. With the aim of enabling an energy aware and low-complexity distributed implementation of the estimation task, several useful optimization techniques that generally yield linear estimators were derived in the literature. Up to now, most of the works considered that the nodes are interested in estimating the same vector of global parameters. This scenario can be viewed as a special case of a more general ...

Resistivity distribution estimation, widely known as Electrical Impedance Tomography (EIT), is a non linear ill-posed inverse problem. However, the partial derivative equation ruling this experiment yields no analytical solution for arbitrary conductivity distribution. Thus, solving the forward problem requires an approximation. The Finite Element Method (FEM) provides us with a computationally cheap forward model which preserves the non linear image-data relation and also reveals sufficiently accurate for the inversion. Within the Bayesian approach, Markovian priors on the log-conductivity distribution are introduced for regularization. The neighborhood system is directly derived from the FEM triangular mesh structure. We first propose a maximum a posteriori (MAP) estimation with a Huber-Markov prior which favours smooth distributions while preserving locally discontinuous features. The resulting criterion is minimized with the pseudo-conjugate gradient method. Simulation results reveal significant improvements in terms of robustness to noise, computation rapidity ...

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 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 ...

Ill-posed inverse problems appear in many signal and image processing applications, such as deblurring, super-resolution and compressed sensing. The common approach to address them is to design a specific algorithm, or recently, a specific deep neural network, for each problem. Both signal processing and machine learning tactics have drawbacks: traditional reconstruction strategies exhibit limited performance for complex signals, such as natural images, due to the hardness of their mathematical modeling; while modern works that circumvent signal modeling by training deep convolutional neural networks (CNNs) suffer from a huge performance drop when the observation model used in training is inexact. In this work, we develop and analyze reconstruction algorithms that are not restricted to a specific signal model and are able to handle different observation models. Our main contributions include: (a) We generalize the popular sparsity-based CoSaMP algorithm to any signal ...

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 ...

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 analysis and design of new non-centralized learning algorithms for potential application in distributed adaptive estimation is the focus of this thesis. Such algorithms should be designed to have low processing requirement and to need minimal communication between the nodes which would form a distributed network. They ought, moreover, to have acceptable performance when the nodal input measurements are coloured and the environment is dynamic. Least mean square (LMS) and recursive least squares (RLS) type incremental distributed adaptive learning algorithms are first introduced on the basis of a Hamiltonian cycle through all of the nodes of a distributed network. These schemes require each node to communicate only with one of its neighbours during the learning process. An original steady-steady performance analysis of the incremental LMS algorithm is performed by exploiting a weighted spatial-temporal energy conservation formulation. This analysis confirms that ...

In this doctoral thesis several scale-free texture segmentation procedures based on two fractal attributes, the Hölder exponent, measuring the local regularity of a texture, and local variance, are proposed.A piecewise homogeneous fractal texture model is built, along with a synthesis procedure, providing images composed of the aggregation of fractal texture patches with known attributes and segmentation. This synthesis procedure is used to evaluate the proposed methods performance.A first method, based on the Total Variation regularization of a noisy estimate of local regularity, is illustrated and refined thanks to a post-processing step consisting in an iterative thresholding and resulting in a segmentation.After evidencing the limitations of this first approach, deux segmentation methods, with either "free" or "co-located" contours, are built, taking in account jointly the local regularity and the local variance.These two procedures are formulated as convex nonsmooth functional minimization problems.We ...

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 ...