This PhD thesis considers the problem of locating some target nodes in different wireless infrastructures such as wireless cellular radio networks and wireless sensor networks. To be as realistic as possible, mixed line-of-sight and non-line-of-sight (LOS/NLOS) localization environment is introduced. Both the conventional non-cooperative localization and the new emerging cooperative localization have been studied thoroughly. Owing to the random nature of the measurements, probabilistic methods are more advanced as compared to the old-fashioned geometric methods. The gist behind the probabilistic methods is to infer the unknown positions of the target nodes in an estimation process, given a set of noisy position related measurements, a probabilistic measurement model, and a few known reference positions. In contrast to the majority of the existing methods, harsh but practical constraints are taken into account: neither offline calibration nor non-line-of-sight state identification is equipped in ...

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 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 ...

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 ...

Inverse problems related to physical processes are of great importance in practically every field related to signal processing, such as tomography, acoustics, wireless communications, medical and radar imaging, to name only a few. At the same time, many of these problems are quite challenging due to their ill-posed nature. On the other hand, signals originating from physical phenomena are often governed by laws expressible through linear Partial Differential Equations (PDE), or equivalently, integral equations and the associated Green’s functions. In addition, these phenomena are usually induced by sparse singularities, appearing as sources or sinks of a vector field. In this thesis we primarily investigate the coupling of such physical laws with a prior assumption on the sparse origin of a physical process. This gives rise to a “dual” regularization concept, formulated either as sparse analysis (cosparse), yielded by a PDE ...

Reverberation consists of a complex acoustic phenomenon that occurs inside rooms. Many audio signal processing methods, addressing source localization, signal enhancement and other tasks, often assume absence of reverberation. Consequently, reverberant environments are considered challenging as state-ofthe-art methods can perform poorly. The acoustics of a room can be described using a variety of mathematical models, among which, physical models are the most complete and accurate. The use of physical models in audio signal processing methods is often non-trivial since it can lead to ill-posed inverse problems. These inverse problems require proper regularization to achieve meaningful results and involve the solution of computationally intensive large-scale optimization problems. Recently, however, sparse regularization has been applied successfully to inverse problems arising in different scientific areas. The increased computational power of modern computers and the development of new efficient optimization algorithms makes it possible ...

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 ...

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 ...

Indoor location has experienced a major boost in recent years. location based services (LBS), which until recently were restricted to outdoor scenarios and the use of GPS, have also been extended into buildings. From large public structures such as airports or hospitals to a multitude of industrial scenarios, LBS has become increasingly present in indoor scenarios. Of the various technologies that can be used to achieve this indoor location, the ones based on ultra- wideband (UWB) signals have become ones of the most demanded due primarily to their accuracy in position estimation. Additionally, the appearance in the market of more and more manufacturers and products has lowered the prices of these devices to levels that allow to think about their use for large deployments with a contained budget. By their nature, UWB signals are very resistant to the multi-path phenomenon, ...

In many hands-free speech communication applications such as teleconferencing or voice-controlled applications, the recorded microphone signals do not only contain the desired speech signal, but also attenuated and delayed copies of the desired speech signal due to reverberation as well as additive background noise. Reverberation and background noise cause a signal degradation which can impair speech intelligibility and decrease the performance for many signal processing techniques. Acoustic multi-channel equalization techniques, which aim at inverting or reshaping the measured or estimated room impulse responses between the speech source and the microphone array, comprise an attractive approach to speech dereverberation since in theory perfect dereverberation can be achieved. However in practice, such techniques suffer from several drawbacks, such as uncontrolled perceptual effects, sensitivity to perturbations in the measured or estimated room impulse responses, and background noise amplification. The aim of this thesis ...

In multiuser ultra-wideband (UWB) systems, a large number of multipath components (MPCs) are introduced by the channel. One of the main challenges for the receiver is to effectively suppress the interference with affordable complexity. In this thesis, we focus on the linear adaptive interference suppression algorithms for the direct-sequence ultrawideband (DS-UWB) systems in both time-domain and frequency-domain. In the time-domain, symbol by symbol transmission multiuser DS-UWB systems are considered. We first investigate a generic reduced-rank scheme based on the concept of joint and iterative optimization (JIO) that jointly optimizes a projection vector and a reduced-rank filter by using the minimum mean-squared error (MMSE) criterion. A low-complexity scheme, named Switched Approximations of Adaptive Basis Functions (SAABF), is proposed as a modification of the generic scheme, in which the complexity reduction is achieved by using a multi-branch framework to simplify the structure ...

Efficient decoding techniques for LDPC codes are in demand, since these codes are included in many standards nowadays. Although the theoretical performance of LDPC codes is impressive, their practical implementation leads to problems like numerical inaccuracy, limited memory resources, etc. We investigate methods that are suited to reduce the decoding complexity while still keeping the loss in performance small. We aim to reduce the complexity using three approaches: simplification of the component decoders, restricting the message passing algorithm to binary variables and combining the LDPC decoder with other receiver tasks like demapping or multi-user detection. For the simplification of the component decoders, we analyze the min-sum algorithm and derive a theoretical framework which is used to explain previous heuristic approaches to improve the performance of this algorithm. Using this framework, we are able to modify the algorithm in order to ...

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 ...

Image segmentation through deformable models is a method that localizes object boundaries. When difficult segmentation context are proposed because of noise or a lack of information, the use of prior knowledge in the deformation process increases segmentation accuracy. Medical imaging is often concerned by these context. Moreover, medical applications deal with large amounts of data. Then it is mandatory to use a robust and fast processing. This question lead us to a local regularisation of the deformable model. Highly based on the active contour framework, also known as \emph{snake}, we propose a new regularization scheme. This is done by filtering the displacements at each iteration. The filter is based on a smoothing spline kernel whose aim was to approximate a set of points rather than interpolating it. We point out the consistency of the regularization parameter in such a method. ...

We consider fitting data by linear and nonlinear models. The specific problems that we aim at, although they encompass classic formulations, have as common ground the fact that we attack a special situation: the ill-posed problems. In the linear case, we consider the total least squares problem. There exist special methods to approach the so-called nongeneric cases, but we propose extensions for the more commonly encountered close-to-nongeneric problems. Several methods of introducing regularization in the context of total least squares are analyzed. They are based on truncation methods or on penalty optimization. The obtained problems might not have closed form solutions. We discuss numerical linear algebra and local optimization methods. Data fitting by nonlinear or nonparametric models is the second subject of the thesis. We extend the nonlinear regression theory to the case when we have to deal with supplementary ...