Spectral unmixing is one the major issues arising when analysing hyperspectral images. It consists of identifying the macroscopic materials present in a hyperspectral image and quantifying the proportions of these materials in the image pixels. Most unmixing techniques rely on a linear mixing model which is often considered as a first approximation of the actual mixtures. However, the linear model can be inaccurate for some specific images (for instance images of scenes involving multiple reflections) and more complex nonlinear models must then be considered to analyse such images. The aim of this thesis is to study new nonlinear mixing models and to propose associated algorithms to analyse hyperspectral images. First, a post-nonlinear model is investigated and efficient unmixing algorithms based on this model are proposed. The prior knowledge about the components present in the observed image, their proportions and the ...

This dissertation investigates robust signal processing and machine learning techniques, with the objective of improving the robustness of two applications against various threats, namely Global Navigation Satellite System (GNSS) based positioning and satellite imaging. GNSS technology is widely used in different fields, such as autonomous navigation, asset tracking, or smartphone positioning, while the satellite imaging plays a central role in monitoring, detecting and estimating the intensity of key natural phenomena, such as flooding prediction and earthquake detection. Considering the use of both GNSS positioning and satellite imaging in critical and safety-of-life applications, it is necessary to protect those two technologies from either intentional or unintentional threats. In the real world, the common threats to GNSS technology include multipath propagation and intentional/unintentional interferences. This thesis investigates methods to mitigate the influence of such sources of error, with the final objective of ...

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 ...

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 ...

Hyperspectral (HS) imaging, which consists of acquiring a same scene in several hundreds of contiguous spectral bands (a three dimensional data cube), has opened a new range of relevant applications, such as target detection [MS02], classification [C.-03] and spectral unmixing [BDPD+12]. However, while HS sensors provide abundant spectral information, their spatial resolution is generally more limited. Thus, fusing the HS image with other highly resolved images of the same scene, such as multispectral (MS) or panchromatic (PAN) images is an interesting problem. The problem of fusing a high spectral and low spatial resolution image with an auxiliary image of higher spatial but lower spectral resolution, also known as multi-resolution image fusion, has been explored for many years [AMV+11]. From an application point of view, this problem is also important as motivated by recent national programs, e.g., the Japanese next-generation space-borne ...

A complex physical system like the human brain can only be comprehended by the use of a combination of various medical imaging techniques, each of which shed light on only a specific aspect of the neural processes that take place beneath the skull. Electroencephalography (EEG) and functional magnetic resonance (fMRI) are two such modalities, which enable the study of brain (dys)function. While the EEG is measured with a limited set of scalp electrodes which record rapid electrical changes resulting from neural activity, fMRI offers a superior spatial resolution at the expense of only picking up slow fluctuations of oxygen concentration that takes place near active brain cells. Hence, combining these very complementary modalities is an appealing, but complicated task due to their heterogeneous nature. In this thesis, we devise advanced signal processing techniques which integrate the multimodal data stemming from ...

This thesis focuses on the design of various automatic signal processing algorithms to extract information from physiological signals of preterm infants. Overall, the aim was to improve the neurodevelopmental outcome of the neonate. More specifically, three main research objectives were carried out. The first objective was to describe the maturation of neonates during their stay in the neonatal intensive care unit. The second objective was to assess the stress and pain in premature infants and their impact on the development of neonates. The third objective was to predict developmental disabilities, such as autism. The first part of this thesis presents an extensive overview of various developmental models to describe the maturation of premature infants. Three main strategies were proposed. The first strategy proposed an investigation of EEG connectivity networks. A variety of functional and effective connectivity methods were combined with ...

Localization, separation and tracking of acoustic sources are ancient challenges that lots of animals and human beings are doing intuitively and sometimes with an impressive accuracy. Artificial methods have been developed for various applications and conditions. The majority of those methods are centralized, meaning that all signals are processed together to produce the estimation results. The concept of distributed sensor networks is becoming more realistic as technology advances in the fields of nano-technology, micro electro-mechanic systems (MEMS) and communication. A distributed sensor network comprises scattered nodes which are autonomous, self-powered modules consisting of sensors, actuators and communication capabilities. A variety of layout and connectivity graphs are usually used. Distributed sensor networks have a broad range of applications, which can be categorized in ecology, military, environment monitoring, medical, security and surveillance. In this dissertation we develop algorithms for distributed sensor networks ...

Various real-life data such as time series and multi-sensor recordings can be represented by vectors and matrices, which are one-way and two-way arrays of numerical values, respectively. Valuable information can be extracted from these measured data matrices by means of matrix factorizations in a broad range of applications within signal processing, data mining, and machine learning. While matrix-based methods are powerful and well-known tools for various applications, they are limited to single-mode variations, making them ill-suited to tackle multi-way data without loss of information. Higher-order tensors are a natural extension of vectors (first order) and matrices (second order), enabling us to represent multi-way arrays of numerical values, which have become ubiquitous in signal processing and data mining applications. By leveraging the powerful utitilies offered by tensor decompositions such as compression and uniqueness properties, we can extract more information from multi-way ...

Today’s society is characterized by an abundance of data that is generated at an unprecedented velocity. However, much of this data is immediately thrown away by compression or information extraction. In a compressed sensing (CS) setting the inherent sparsity in many datasets is exploited by avoiding the acquisition of superfluous data in the first place. We combine this technique with tensors, or multiway arrays of numerical values, which are higher-order generalizations of vectors and matrices. As the number of entries scales exponentially in the order, tensor problems are often large-scale. We show that the combination of simple, low-rank tensor decompositions with CS effectively alleviates or even breaks the so-called curse of dimensionality. After discussing the larger data fusion optimization framework for coupled and constrained tensor decompositions, we investigate three categories of CS type algorithms to deal with large-scale problems. First, ...

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 ...

Single-pixel imaging is a recent paradigm that allows the acquisition of images at reasonably low cost by exploiting hardware compression of the data. The architecture of a single-pixel camera consists of only two elements: a spatial light modulator, and a single-point detector. The key idea is to measure the projection at the detector (i.e., the inner product) of the scene under view -the image- with some patterns. The post-processing of a sequence of measurements obtained with different patterns permits the restoring of the desired image. Single-pixel imaging has several advantages, which are of interest for different applications, and especially in the biomedical field. In particular, a time-resolved single-pixel imaging system benefits fluorescence lifetime sensing. Such a set-up can be coupled to a spectrometer, to supplement the lifetime with spectral information. However, the main limitation of single-pixel imaging is the speed ...

In many fields, such as linear algebra, computational geometry, combinatorial optimization, analytical chemistry and geoscience, nonnegativity of the solution is required, which is either due to the fact that the data is physically nonnegative, or that the mathematical modeling of the problem requires nonnegativity. Image and audio processing are two examples for which the data are physically nonnegative. Probability and graph theory are examples for which the mathematical modeling requires nonnegativity. This thesis is about the nonnegative factorization of matrices and tensors: namely nonnegative matrix factorization (NMF) and nonnegative tensor factorization (NTF). NMF problems arise in a wide range of scenarios such as the aforementioned fields, and NTF problems arise as a generalization of NMF. As the title suggests, the contributions of this thesis are centered on NMF and NTF over three aspects: modeling, algorithms and applications. On the modeling ...

The growing interest in neuroimaging technologies generates a massive amount of biomedical data that exhibit high dimensionality. Tensor-based analysis of brain imaging data has by now been recognized as an effective approach exploiting its inherent multi-way nature. In particular, the advantages of tensorial over matrix-based methods have previously been demonstrated in the context of functional magnetic resonance imaging (fMRI) source localization; the identification of the regions of the brain which are activated at specific time instances. However, such methods can also become ineffective in realistic challenging scenarios, involving, e.g., strong noise and/or significant overlap among the activated regions. Moreover, they commonly rely on the assumption of an underlying multilinear model generating the data. In the first part of this thesis, we aimed at investigating the possible gains from exploiting the 3-dimensional nature of the brain images, through a higher-order tensorization ...

Earth observation and land-cover analysis became a reality in the last 2-3 decades thanks to NASA airborne and spacecrafts such as Landsat. Inclusion of Hyperspectral Imaging (HSI) technology in some of these platforms has made possible acquiring large data sets, with high potential in analytical tasks but at the cost of advanced signal processing. In this thesis, effective/efficient feature extraction methods are proposed. Initially, contributions are introduced for efficient computation of the covariance matrix widely used in data reduction methods such as Principal Component Analysis (PCA). By taking advantage of the cube structure in HSI, onsite and real-time covariance computation is achieved, reducing memory requirements as well. Furthermore, following the PCA algorithm, a novel method called Folded-PCA (Fd-PCA) is proposed for efficiency while extracting both global and local features within the spectral pixels, achieved by folding the spectral samples from ...