Accounting for uncertainty in three-dimensional (3D) shapes is important in a large number of scientific and engineering areas, such as biometrics, biomedical imaging, and data mining. It is well known that 3D polar shaped objects can be represented by Fourier descriptors such as spherical harmonics and double Fourier series. However, the statistics of these spectral shape models have not been widely explored. This thesis studies several areas involved in 3D shape modeling, including random field models for statistical shape modeling, optimal shape filtering, parametric active contours for object segmentation and surface reconstruction. It also investigates multi-modal image registration with respect to tumor activity quantification. Spherical harmonic expansions over the unit sphere not only provide a low dimensional polarimetric parameterization of stochastic shape, but also correspond to the Karhunen-Lo´eve (K-L) expansion of any isotropic random field on the unit sphere. Spherical ...

Standard signal processing techniques are implicitly based on the assumption that the signal lies on a regular, homogeneous domain. In practice, however, many signals lie on an irregular or inhomogeneous domain. An application area where data are naturally defined on an irregular or inhomogeneous domain is human brain neuroimaging. The goal in neuroimaging is to map the structure and function of the brain using imaging techniques. In particular, functional magnetic resonance imaging (fMRI) is a technique that is conventionally used in non-invasive probing of human brain function. This doctoral dissertation deals with the development of signal processing schemes that adapt to the domain of the signal. It consists of four papers that in different ways deal with exploiting knowledge of the signal domain to enhance the processing of signals. In each paper, special focus is given to the analysis of ...

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 ...

Facial features segmentation, analysis and recognition of facial expressions by the Transferable Belief Model The aim of this work is the analysis and the classification of facial expressions. Experiments in psychology show that human is able to recognize the emotions based on the visualization of the temporal evolution of some characteristic fiducial points. Thus we firstly propose an automatic system for the extraction of the permanent facial features (eyes, eyebrows and lips). In this work we are interested in the problem of the segmentation of the eyes and the eyebrows. The segmentation of lips contours is based on a previous work developed in the laboratory. The proposed algorithm for eyes and eyebrows contours segmentation consists of three steps: firstly, the definition of parametric models to fit as accurate as possible the contour of each feature; then, a whole set of ...

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 ...

Video signals are sequences of natural images, where images are often modeled as piecewise-smooth signals. Hence, video can be seen as a 3D piecewise-smooth signal made of piecewise-smooth regions that move through time. Based on the piecewise-smooth model and on related theoretical work on rate-distortion performance of wavelet and oracle based coding schemes, one can better analyze the appropriate coding strategies that adaptive video codecs need to implement in order to be efficient. Efficient video representations for coding purposes require the use of adaptive signal decompositions able to capture appropriately the structure and redundancy appearing in video signals. Adaptivity needs to be such that it allows for proper modeling of signals in order to represent these with the lowest possible coding cost. Video is a very structured signal with high geometric content. This includes temporal geometry (normally represented by motion ...

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 ...

In the world of Information and communications technology (ICT), strategies for innovation and development are increasingly focusing on applications that require spatial representation and real-time interaction with and within 3D-media environments. One of the major challenges that such applications have to address is user-centricity, reflecting e.g. on developing complexity-hiding services so that people can personalize their own delivery of services. In these terms, multimodal interfaces represent a key factor for enabling an inclusive use of new technologies by everyone. In order to achieve this, multimodal realistic models that describe our environment are needed, and in particular models that accurately describe the acoustics of the environment and communication through the auditory modality are required. Examples of currently active research directions and application areas include 3DTV and future internet, 3D visual-sound scene coding, transmission and reconstruction and teleconferencing systems, to name but ...

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 ...

Condition monitoring of machines through vibration analysis has been successfully applied on different types of machines for several decades. However, there are still some mechanical systems where its use has not given the same good results. Epicyclic gearboxes (EG) belong to this group of systems. Due to its special characteristics, EG are used in a wide range of applications within the drive technology, mostly when high power transmission is required. Machines dealing with high power transmission are typically critical, which means that a large part of the process in which they are involved depends on their appropriate operation. Hence, there is a high interest on a solution that can effectively detect failures in EG at an early stage, before they evolve and produce major breakdowns. Probably the most important reason for the deficient results of failure detection on EG through ...

Distributed signal or information processing using Internet of Things (IoT), facilitates real-time monitoring of signals, for example, environmental pollutants, health indicators, and electric energy consumption in a smart city. Despite the promising capabilities of IoTs, these distributed deployments often face the challenge of data privacy and communication rate constraints. In traditional machine learning, training data is moved to a data center, which requires massive data movement from distributed IoT devices to a third-party location, thus raising concerns over privacy and inefficient use of communication resources. Moreover, the growing network size, model size, and data volume combined lead to unusual complexity in the design of optimization algorithms beyond the compute capability of a single device. This necessitates novel system architectures to ensure stable and secure operations of such networks. Federated learning (FL) architecture, a novel distributed learning paradigm introduced by McMahan ...

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 ...

The first part of this dissertation considers distributed learning problems over networked agents. The general objective of distributed adaptation and learning is the solution of global, stochastic optimization problems through localized interactions and without information about the statistical properties of the data. Regularization is a useful technique to encourage or enforce structural properties on the resulting solution, such as sparsity or constraints. A substantial number of regularizers are inherently non-smooth, while many cost functions are differentiable. We propose distributed and adaptive strategies that are able to minimize aggregate sums of objectives. In doing so, we exploit the structure of the individual objectives as sums of differentiable costs and non-differentiable regularizers. The resulting algorithms are adaptive in nature and able to continuously track drifts in the problem; their recursions, however, are subject to persistent perturbations arising from the stochastic nature 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 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 ...