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 ...

Nowadays, many disciplines in science and engineering deal with problems for which a solution relies on knowledge about the characteristics of one or more given systems that can only be ascertained based on restricted observations. This requires the fitting of an adequately chosen model, such that it “best” conforms to a set of measured data. Depending on the context, this fitting procedure may resort to a huge amount of recorded data and abundant numerical power, or contrarily, to only a few streams of samples, which have to be processed on the fly at low computational cost. This thesis, exclusively focuses on the latter scenario. It specifically studies unexpected behaviour and reliability of the widely spread and computationally highly efficient class of gradient type algorithms. Additionally, special attention is paid to systems that combine several of them. Chapter 3 is dedicated ...

Recent academic developments have initiated a paradigm shift in the way spatial sensor data can be acquired. Traditional localized and regularly arranged sensor arrays are replaced by sensor nodes that are randomly distributed over the entire spatial field, and which communicate with each other or with a master node through wireless communication links. Together, these nodes form a so-called ‘wireless sensor network’ (WSN). Each node of a WSN has a local sensor array and a signal processing unit to perform computations on the acquired data. The advantage of WSNs compared to traditional (wired) sensor arrays, is that many more sensors can be used that physically cover the full spatial field, which typically yields more variety (and thus more information) in the signals. It is likely that future data acquisition, control and physical monitoring, will heavily rely on this type of ...

This thesis deals with several open problems in acoustic echo cancellation and acoustic feedback control. Our main goal has been to develop solutions that provide a high performance and sound quality, and behave in a robust way in realistic conditions. This can be achieved by departing from the traditional ad-hoc methods, and instead deriving theoretically well-founded solutions, based on results from parameter estimation and system identification. In the development of these solutions, the computational efficiency has permanently been taken into account as a design constraint, in that the complexity increase compared to the state-of-the-art solutions should not exceed 50 % of the original complexity. In the context of acoustic echo cancellation, we have investigated the problems of double-talk robustness, acoustic echo path undermodeling, and poor excitation. The two former problems have been tackled by including adaptive decorrelation filters in the ...

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 ...

Compressed sensing (CS) is a recently introduced signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are developed assuming a Gaussian (light-tailed) model for the corrupting noise. However, when the underlying signal and/or the measurements are corrupted by impulsive noise, commonly employed linear sampling operators, coupled with Gaussian-derived reconstruction algorithms, fail to recover a close approximation of the signal. This dissertation develops robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. To achieve this objective, we make use of robust statistics theory to develop appropriate methods addressing the problem of impulsive noise in CS systems. We develop a generalized Cauchy distribution (GCD) ...

Noise or interference is often assumed to be a random process. Conventional linear filtering, control or prediction techniques are used to cancel or reduce the noise. However, some noise processes have been shown to be nonlinear and deterministic. These nonlinear deterministic noise processes appear to be random when analysed with second order statistics. As nonlinear processes are widespread in nature it may be beneficial to exploit the coherence of the nonlinear deterministic noise with nonlinear filtering techniques. The nonlinear deterministic noise processes used in this thesis are generated from nonlinear difference or differential equations which are derived from real world scenarios. Analysis tools from the theory of nonlinear dynamics are used to determine an appropriate sampling rate of the nonlinear deterministic noise processes and their embedding dimensions. Nonlinear models, such as the Volterra series filter and the radial basis function ...

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 ...

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 ...

Wireless communications and networking are gradually permeating our life and substantially influencing every corner of this world. Wireless devices, particularly those of small size, will take part in this trend more widely, efficiently, seamlessly and smartly. Techniques requiring only limited resources, especially in terms of hardware, are becoming more important and urgently needed. That is why we focus this thesis around analyzing wireless communications and networking based on signal strength (SS) measurements, since these are easy and convenient to gather. SS-based techniques can be incorporated into any device that is equipped with a wireless chip. More specifically, this thesis studies \textbf{SS-based localization} and \textbf{path-loss exponent (PLE) self-estimation}. Although these two research lines might seem unrelated, they are actually marching towards the same goal. The former can easily enable a very simple wireless chip to infer its location. But to solve ...

This thesis is based on nine papers, all concerned with parameter estimation. The thesis aims at solving problems related to real-world applications such as spectroscopy, DNA sequencing, and audio processing, using sparse modeling heuristics. For the problems considered in this thesis, one is not only concerned with finding the parameters in the signal model, but also to determine the number of signal components present in the measurements. In recent years, developments in sparse modeling have allowed for methods that jointly estimate the parameters in the model and the model order. Based on these achievements, the approach often taken in this thesis is as follows. First, a parametric model of the considered signal is derived, containing different parameters that capture the important characteristics of the signal. When the signal model has been determined, an optimization problem is formed aimed at finding ...

Multimedia consumer electronics are nowadays everywhere from teleconferencing, hands-free communications, in-car communications to smart TV applications and more. We are living in a world of telecommunication where ideal scenarios for implementing these applications are hard to find. Instead, practical implementations typically bring many problems associated to each real-life scenario. This thesis mainly focuses on two of these problems, namely, acoustic echo and acoustic feedback. On the one hand, acoustic echo cancellation (AEC) is widely used in mobile and hands-free telephony where the existence of echoes degrades the intelligibility and listening comfort. On the other hand, acoustic feedback limits the maximum amplification that can be applied in, e.g., in-car communications or in conferencing systems, before howling due to instability, appears. Even though AEC and acoustic feedback cancellation (AFC) are functional in many applications, there are still open issues. This means that ...

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 ...

This work considers a Broadcast Channel (BC) system, where the transmitter is equipped with multiple antennas and each user at the receiver side could have one or more antennas. Depending on the number of antennas at the receiver side, such a system is known as Multiple-User Multiple-Input Single-Output (MU-MISO), for single antenna users, or Multiple-UserMultiple-InputMultiple-Output (MU-MIMO), for several antenna users. This model is suitable for current wireless communication systems. Regarding the direction of the data flow, we differentiate between downlink channel or BC, and uplink channel or Multiple Access Channel (MAC). In the BC the signals are sent from the Base Station (BS) to the users, whereas the information from the users is sent to the BS in the MAC. In this work we focus on the BC where the BS applies linear precoding taking advantage of multiple antennas. The ...

Sparsity-based estimation techniques deal with the problem of retrieving a data vector from an undercomplete set of linear observations, when the data vector is known to have few nonzero elements with unknown positions. It is also known as the atomic decomposition problem, and has been carefully studied in the field of compressed sensing. Recent findings have led to a method called basis pursuit, also known as Least Absolute Shrinkage and Selection Operator (LASSO), as a numerically reliable sparsity-based approach. Although the atomic decomposition problem is generally NP-hard, it has been shown that basis pursuit may provide exact solutions under certain assumptions. This has led to an extensive study of signals with sparse representation in different domains, providing a new general insight into signal processing. This thesis further investigates the role of sparsity-based techniques, especially basis pursuit, for solving parameter estimation ...