Due to a variety of potential barriers to sample acquisition, many of the datasets encountered in important classification applications, ranging from tumor identification to facial recognition, are characterized by small samples of high-dimensional data. In such situations, linear classifiers are popular as they have less risk of overfitting while being faster and more interpretable than non-linear classifiers. They are also easier to understand and implement for the inexperienced practitioner. In this dissertation, several gaps in the literature regarding the analysis and design of linear classifiers for high-dimensional data are addressed using tools from the field of asymptotic Random Matrix Theory (RMT) which facilitate the derivation of limits of relevant quantities or distributions, such as the probability of misclassification of a particular classifier or the asymptotic distribution of its discriminant, in the RMT regime where both the sample size and dimensionality ...

In this dissertation we focus on statistical signal processing for Data Fusion, with a particular focus on wireless sensor networks. Six topics are studied: (i) Data Fusion for classification under model uncertainty; (ii) Decision Fusion over coherent MIMO channels; (iii) Performance analysis of Maximum Ratio Combining in MIMO decision fusion; (iv) Decision Fusion over non-coherent MIMO channels; (v) Decision Fusion for distributed classification of multiple targets; (vi) Data Fusion for inverse localization problems, with application to wideband passive sonar platform estimation. The first topic of this thesis addresses the problem of lack of knowledge of the prior distribution in classification problems that operate on small data sets that may make the application of Bayes' rule questionable. Uniform or arbitrary priors may provide classification answers that, even in simple examples, may end up contradicting our common sense about the problem. Entropic ...

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 ...

This doctoral thesis aims at optimising the floating-point implementations of signal processing algorithms on reconfigurable hardware with respect to accuracy, hardware resource and execution time. It is known that reduced precision in floating-point arithmetic operations on reconfigurable hardware directly translates into increased parallelism and peak performance. As a result, efficient implementations can be obtained by choosing the minimal acceptable precision for floating-point operations. Furthermore, custom-precision floating-point operations allow for trading accuracy with parallelism and performance. We use Affine Arithmetic (AA) for modeling the rounding errors of floating-point computations. The derived rounding error bound by the AA-based error model is then used to determine the smallest mantissa bit width of custom-precision floating-point number formats needed for guaranteeing the desired accuracy of floating-point applications. In this work, we implement the first Matlab-based framework for performing rounding error analysis and numerical range evaluation ...

This dissertation deals with the design of satellite-based navigation receivers. The term Global Navigation Satellite Systems (GNSS) refers to those navigation systems based on a constellation of satellites, which emit ranging signals useful for positioning. Although the american GPS is probably the most popular, the european contribution (Galileo) will be operative soon. Other global and regional systems exist, all with the same objective: aid user's positioning. Initially, the thesis provides the state-of-the-art in GNSS: navigation signals structure and receiver architecture. The design of a GNSS receiver consists of a number of functional blocks. From the antenna to the fi nal position calculation, the design poses challenges in many research areas. Although the Radio Frequency chain of the receiver is commented in the thesis, the main objective of the dissertation is on the signal processing algorithms applied after signal digitation. These ...

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 theory of statistical signal processing finds a wide variety of applications in the fields of data communications, such as in channel estimation, equalization and symbol detection, and sensor array processing, as in beamforming, and radar systems. Indeed, a large number of these applications can be interpreted in terms of a parametric estimation problem, typically approached by a linear filtering operation acting upon a set of multidimensional observations. Moreover, in many cases, the underlying structure of the observable signals is linear in the parameter to be inferred. This dissertation is devoted to the design and evaluation of statistical signal processing methods under realistic implementation conditions encountered in practice. Traditional statistical signal processing techniques intrinsically provide a good performance under the availability of a particularly high number of observations of fixed dimension. Indeed, the original optimality conditions cannot be theoretically guaranteed ...

In this thesis we investigate centralized and distributed variants of sparse Bayesian learning (SBL), an effective probabilistic regression method used in machine learning. Since inference in an SBL model is not tractable in closed form, approximations are needed. We focus on the variational Bayesian approximation, as opposed to others used in the literature, for three reasons: First, it is a flexible general framework for approximate Bayesian inference that estimates probability densities including point estimates as a special case. Second, it has guaranteed convergence properties. And third, it is a deterministic approximation concept that is even applicable for high dimensional problems where non-deterministic sampling methods may be prohibitive. We resolve some inconsistencies in the literature involved in other SBL approximation techniques with regard to a proper Bayesian treatment and the incorporation of a very desired property, namely scale invariance. More specifically, ...

In this thesis, we present a convex optimization approach to address three problems arising in multicomponent image recovery, supervised classification, and image forgery detection. The common thread among these problems is the presence of nonlinear convex constraints difficult to handle with state-of-the-art methods. Therefore, we present a novel splitting technique to simplify the management of such constraints. Relying on this approach, we also propose some contributions that are tailored to the aforementioned applications. The first part of the thesis presents the epigraphical splitting of nonlinear convex constraints. The principle is to decompose the sublevel set of a block-separable function into a collection of epigraphs. So doing, we reduce the complexity of optimization algorithms when the above constraint involves the sum of absolute values, distance functions to a convex set, Euclidean norms, infinity norms, or max functions. We demonstrate through numerical ...

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 ...

The subject of this PhD thesis is the efficient and robust processing and analysis of the audio recordings that are derived from a call center. The thesis is comprised of two parts. The first part is dedicated to dialogue/non-dialogue detection and to speaker segmentation. The systems that are developed are prerequisite for detecting (i) the audio segments that actually contain a dialogue between the system and the call center customer and (ii) the change points between the system and the customer. This way the volume of the audio recordings that need to be processed is significantly reduced, while the system is automated. To detect the presence of a dialogue several systems are developed. This is the first effort found in the international literature that the audio channel is exclusively exploited. Also, it is the first time that the speaker utterance ...

In many modern signal processing applications, traditional machine learning and pattern recognition methods heavily rely on the having a sufficiently large amount of data samples to correctly estimate the underlying structures within complex signals. The main idea is to understand the inherent structural information and relationships embedded within the raw data, thereby enabling a wide variety of inference tasks. Nevertheless, the definition of what constitutes a sufficiently large dataset remains subjective and it is often problem-dependent. In this context, traditional learning approaches often fail to learn meaningful structures in the cases where the number of features closely matches (or even exceeds) the number of observations. These scenarios emphasize the need for tailored strategies that effectively extract meaningful structured information from these high-dimensional settings. In this thesis we address fundamental challenges posed by applying traditional machine learning techniques in large dimensional ...

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 ...

This dissertation details two classes of cooperative localization methods for wireless networks in mixed line-of-sight and non-line-of-sight (LOS/NLOS) environments. The classes of methods depend on the amount of prior knowledge available. The methods used for both classes are based on the assumptions in practical localization environments that neither NLOS identification nor experimental campaigns are affordable. Two major contributions are, first, in methods that provide satisfactory localization accuracy whilst relaxing the requirement on statistical knowledge about the measurement model. Second, in methods that provide significantly improved localization performance without the requirement of good initialization. In the first half of the dissertation, cooperative localization using received signal strength (RSS) measurements in homogeneous mixed LOS/NLOS environments is considered for the case where the key model parameter, the path loss exponent, is unknown. The approach taken is to model the positions and the path ...

Chapter 2 contains a short introduction to the fundamentals of compressed sensing theory, which is the larger context of this thesis. We start with introducing the key concepts of sparsity and sparse representations of signals. We discuss the central problem of compressed sensing, i.e. how to adequately recover sparse signals from a small number of measurements, as well as the multiple formulations of the reconstruction problem. A large part of the chapter is devoted to some of the most important conditions necessary and/or sufficient to guarantee accurate recovery. The aim is to introduce the reader to the basic results, without the burden of detailed proofs. In addition, we also present a few of the popular reconstruction and optimization algorithms that we use throughout the thesis. Chapter 3 presents an alternative sparsity model known as analysis sparsity, that offers similar recovery ...