A proper time-frequency transform technique suppresses the blurring and smearing effect of the time-varying Doppler shift on the target image. The conventional target imaging method uses the Fourier transform for extracting the Doppler shift from the received radar pulse. Since the Doppler shift is timevarying for rotating targets, the constructed images will be degraded. In this thesis, the Doppler shift information required for the Range-Doppler image of the target is extracted by using high resolution time-frequency transform techniques. The Wigner-Ville Distribution and the Adaptive Gabor Representation with the Coarse-to-Fine and the Matching Pursuit Search Algorithms are examined techniques for the target imaging system. The modified Matching Pursuit Algorithm, the Matching Pursuit with Reduced Dictionary is proposed which decreases the signal processing time required by the Adaptive Gabor Representation. The Hybrid Matching Pursuit Search Algorithm is also introduced in this thesis work and the Coarse-to-Fine Algorithm and the Matching Pursuit Algorithm are combined for obtaining better representation quality of a signal in the time-frequency domain. The stated techniques are applied on to the sample signals and compared with each other. The application of these techniques in the target imaging system is also performed for the simulated aircrafts.

Neurological diseases in newborns are usually first revealed by seizures, which are characterised by a synchronous discharge of a large number of neurons. Failure to control seizures may lead to brain damage or even death. The importance of this problem prompted many researchers to look for accurate automatic methods for seizure detection. Nonstationarity and multicomponent behaviour of newborn EEG signals made this task very challenging. The significant overlap in the characteristic of background and seizure activities in newborn EEG signals added to the difficulty of seizure detection. This research uses time-frequency based methods for automatic seizure detection. Since time-frequency signal analysis methods use joint representation in both time and frequency domains, they proved to be very suitable for analysis and processing of nonstationary and multicomponent signals such as newborn EEG. Before using any seizure detector, the EEG data is pre-processed in order to reduce the noise effects using a time-frequency based technique. The proposed method is based on the singular value decomposition (SVD) technique applied to the matrix representing the time-frequency distribution (TFD) of the EEG signal. It has been shown that by appropriately filtering the singular vectors associated with the TFD, one can effectively enhance the desired information embedded in the signal. Neonatal EEG seizures can have signatures in both low frequency (lower than 10 Hz) and high frequency (higher than 70 Hz) areas. The seizure detection techniques proposed in the literature concentrated on using either low frequency or high frequency signatures but not both simultaneously. These methods tend to miss the seizures that reveal themselves only in one of the two frequency areas. In this research, we propose a detection method that uses seizure features in both low and high frequency areas. To detect EEG seizures using the low frequency signatures, an SVD-based technique is employed. The technique uses the estimated distribution function of the singular vectors associated with the time-frequency distribution of EEG epochs to discriminate between seizure and nonseizure patterns. The high frequency signatures of seizures are mostly the result of spike events in the EEG signals. To detect these spike events, the signal is mapped into the TF domain. The high instantaneous energy of spikes is reflected as a localised energy in the high frequency area of the TF domain. Consequently, a spike can be seen as a ridge in this area of the TF domain. It has been shown that during seizure activity there is regularity in the distribution of the interspike intervals. This feature has been used as the basis for discriminating between seizure and nonseizure patterns. The performance results obtained by applying the proposed methods on EEG signals extracted from a number of newborns show the superiority of these methods over the existing ones.

Electrocardiography (ECG) has been established as one of the most useful diagnostic tools in medicine and is critical in the management of various heart conditions. Automated or semi-automated ECG analysis algorithms are expected to play an important role in the utilization of the ECG data. The correct identification of the QRS complexes is a fundamental step in every ECG analysis method. A major problem that is often encountered in automatic QRS detection is the presence of artifacts in the ECG data, which cause considerable alterations to the signal. Some common filters can smooth the effect of the artifacts, however they cannot eliminate them due to their spectral frequency overlap with the signal components. In this thesis, the objective was to develop a method, based on Time-Frequency Analysis that would be able to automatically detect and remove artifacts in order to increase the reliability of automatic QRS detection. The ECG data used for this purpose was taken from the Physionet library and more specifically from the MIMIC II database. The data in this database was acquired from ICU patients and it contains various types of rhythms as well as artifacts. First, a Graphical User Interface (GUI) was developed in order to manually annotate ECG data and was used for creating the ground truth for testing the methods developed. The Time-Frequency Analysis method used for the analysis of the ECG data, was based on a time-varying Autoregressive (AR) model whose solutions were obtained using Burg’s method. Several factors that affect the effectiveness of the method were investigated in order to optimize the algorithm experimentally. The algorithm implemented performs three main functions: “Artifact Hypothesis Testing,” “Artifact Detection and Removal,” and “QRS Complex Detection.” The first step, “Artifact Hypothesis Testing,” examines whether the signal contains any artifact or not. This is performed with a correct classification rate of 95.56%. The second step was the “Artifact Detection and Removal,” which could detect and remove the artifact area with an accuracy of 95.60% based on each signal sample identified as artifact or not. The final step, the “QRS Complex Detection,” correctly identified 92% of QRS complexes (322 out of 335 annotated QRS complexes). Finally, the proposed method was compared with one of the most commonly used methods in ECG analysis, the Wavelet Transform Analysis (WTA). The two methods were tested on exactly the same dataset. The WTA resulted in an overall score of 65.3% mainly due to the large number of false positive detections in the regions of artifact. / Το ηλεκτροκαρδιογράφημα (ΗΚΓ) έχει καθιερωθεί ως ένα από τα πιο χρήσιμα εργαλεία διάγνωσης στην ιατρική και είναι πολύ σημαντικό στη διαχείριση καρδιαγγειακών παθήσεων. Αυτοματοποιημένοι ή ημι-αυτοματοποιημένοι αλγόριθμοι ανάλυσης του ΗΚΓ αναμένεται να έχουν σημαντικό ρόλο στη χρήση των δεδομένων του ΗΚΓ. Η σωστή αναγνώριση των συμπλεγμάτων QRS είναι βασικό βήμα σε κάθε μέθοδο ανάλυσης του ΗΚΓ. Ένα σημαντικό πρόβλημα που συχνά προκύπτει σε αυτόματη ανίχνευση QRS είναι η παρουσία των τεχνητών σφαλμάτων (artifacts) στα δεδομένα ΗΚΓ, τα οποία προκαλούν σημαντικές αλλαγές στο σήμα. Κάποια κοινά φίλτρα μπορούν να εξομαλύνουν τις επιπτώσεις των τεχνητών σφαλμάτων, ωστόσο δεν μπορούν να τα εξαλείψουν λόγω της μεγάλης επικάλυψης του φάσματος συχνοτήτων τους με αυτού των στοιχείων του σήματος. Στην παρούσα εργασία στόχος ήταν η ανάπτυξη μιας μεθόδου, βασισμένης στην Ανάλυση Χρόνου-Συχνότητας, που θα είναι σε θέση να εντοπίσει αυτόματα και να αφαιρεί τα τεχνητά σφάλματα, ώστε να έχουμε μια πιο αξιόπιστη μέθοδο αυτόματης ανίχνευσης των QRS. Τα δεδομένα ΗΚΓ που χρησιμοποιήθηκαν για το σκοπό αυτό λήφθηκαν από τη βιβλιοθήκη Physionet και πιο συγκεκριμένα από τη βάση δεδομένων MIMIC II. Τα δεδομένα σε αυτή τη βάση δεδομένων προέρχονται από ασθενείς της Μονάδας Εντατικής Θεραπείας, και ως εκ τούτου, περιέχουν διάφορα είδη ρυθμών αλλά και τεχνητών σφαλμάτων. Αρχικά, ένα Γραφικό Περιβάλλον Χρήστη (GUI), σχεδιάστηκε για τη χειροκίνητη σηματοδότηση των διάφορων περιοχών ΗΚΓ σημάτων και χρησιμοποιήθηκε για τη δημιουργία των αληθών αποτελεσμάτων για δοκιμή της μεθόδου. H Ανάλυση Χρόνου-Συχνότητας έγινε με τη χρήση ενός χρονικά μεταβαλλόμενου Αυτοπαλινδρομικού (AR) μοντέλου οι λύσεις του οποίου βρέθηκαν με τη μέθοδο Burg. Ακολούθησε η διερεύνηση διαφόρων παραγόντων που επηρεάζουν την αποτελεσματικότητα της μεθόδου, προκειμένου να βελτιστοποιηθεί πειραματικά η μέθοδος. Ο αλγόριθμος που υλοποιήθηκε εκτελεί τρεις βασικές λειτουργίες: “Artifact Hypothesis Testing,” “Artifact Detection and Removal” και “QRS Complex Detection.” Κατ’ αρχήν, το βήμα "Artifact Hypothesis Testing" εξετάζει αν το σήμα περιέχει τεχνητό σφάλμα ή όχι, με το ποσοστό σωστής ταξινόμησης να ανέρχεται στο 95.56%. Το δεύτερο βήμα, η ανίχνευση και αφαίρεση της περιοχής του τεχνητού σφάλματος, έγινε με ακρίβεια 95.60% με βάση το πόσα σημεία του σήματος αναγνωρίστηκαν ως τεχνητό σφάλμα ή όχι. Τέλος, το συνολικό ποσοστό ορθής ανίχνευσης των συμπλεγμάτων QRS ήταν 92% (322 από τα 335 QRS που επισημάνθηκαν χειροκίνητα). Τέλος, έγινε μια σύγκριση μεταξύ της προτεινόμενης μεθόδου και μιας μεθόδου ανάλυσης ΗΚΓ που χρησιμοποιείται πολύ συχνά, της ανάλυσης με Μετασχηματισμό Wavelet (WTA). Οι δύο μέθοδοι δοκιμάστηκαν στα ίδια ακριβώς δεδομένα. Η ορθή ανίχνευση των συμπλεγμάτων QRS με τη μέθοδο WTA ήταν 65.3% κυρίως λόγω του μεγάλου αριθμού ψευδώς θετικών αποτελεσμάτων στις περιοχές των τεχνητών σφαλμάτων.

La surveillance automatique consiste à vérifier le bon fonctionnement d'un système tout au long de sa durée d'utilisation et ce, sans intervention humaine. Elle permet de mettre en place une stratégie de maintenance prévisionnelle qui présente un intérêt économique majeur, en particulier dans le cas de systèmes isolés comme les éoliennes construites en pleine mer. La surveillance automatique se base sur l'acquisition plus ou moins régulière de signaux pendant le fonctionnement du système surveillé. L'analyse de ces signaux doit permettre d'établir un diagnostic et de prendre une décision sur le déclenchement des opérations de maintenance. Dans cette thèse, nous proposons une méthode d'analyse générique permettant de s'adapter à n'importe quel système surveillé. La méthode se déroule en plusieurs étapes. Premièrement, chaque signal est analysé individuellement pour en extraire son contenu spectral, c'est-à-dire identifier les pics spectraux, les séries harmoniques et les bandes de modulation présents dans sa densité spectrale. Ensuite, ce contenu spectral est suivi au cours du temps pour former des trajectoires sur l'ensemble de la séquence de signaux acquis. Ces trajectoires permettent de générer des tendances qui sont le reflet de la santé du système. Enfin, les tendances sont analysées pour identifier un changement au cœur du système qui serait synonyme d'usure ou de défaut naissant. Cette méthodologie est validée sur de nombreux signaux réels provenant de la surveillance de différents systèmes mécaniques. / The automatic monitoring consists in verifying without any human intervention that a system is operating well. The monitoring allows to use a predictive maintenance strategy, which is economically interesting, especially in the case of isolated systems like off-shore wind turbines. The automatic monitoring is based on signals acquired more or less regularly while the monitored system is operating. The analysis of these signals should be sufficient to diagnose the system and to decide whether or not the maintenance operations should be done. In this thesis, we propose a generic analysis method able to adapt itself to any monitored system. This method is composed by several steps. First, each signal is analyzed individually in order to extract its spectral content, that is to identify the spectral peaks, the harmonic series and the modulation sidebands presents in the signal spectrum. Then, the spectral content is tracked through time to construct spectral trajectories in the sequence of acquired signal. These trajectories are used to generate trends which indicate the state of the system health. Finally, the trends are analyzed to identify a change in the system response which would indicate some wear or a fault in is early stage. This analysis method is validated on real world signals acquired on different mechanical systems.

Cette thèse s'articule autour de deux axes de recherche. Le premier axe aborde les aspects méthodologiques liés au traitement temps-fréquence des signaux issus d'un radar FMCW (à onde continue modulée en fréquence) dans le contexte de la mesure des déplacements fins. Le second axe est dédié à la conception et à la validation d'une chaîne de traitement des images RSO (radar à synthèse d'ouverture) satellitaire. Lorsqu'un maillage 3D de la structure envisagée est disponible, les traitements proposés sont validés par l'intercomparaison avec les techniques conventionnelles d'auscultation des grands ouvrages d'art.D'une part, nous étudions la correction de la non-linéarité d'un radar FMCW en bande X, à courte portée, conçu pour la mesure des déplacements millimétriques. La caractéristique de commande non linéaire de l'oscillateur à large bande, entraine une perte de résolution à la réception. Afin de pallier cet inconvénient, nous avons développé deux méthodes basées sur le ré-échantillonnage temporel (time warping) dans le cas des signaux à large bande non-stationnaires. La première approche estime la loi de fréquence instantanée non linéaire à l'aide de la fonction d'ambiguïté d'ordre supérieur, tandis que la deuxième approche exploite la mesure de concentration spectrale du signal de battement dans un algorithme d'autofocus radial.D'autre part, nous proposons un cadre méthodologique général pour la détection et le pistage des centres de diffusion dans les images RSO pour la surveillance des grands ouvrages d'art. La méthode est basée sur la ré-focalisation de chaque image radar sur le maillage 3D de l'infrastructure étudiée afin d'identifier les diffuseurs pertinents par tomographie 4D (distance – azimut – élévation – vitesse de déformation). L'algorithme de ré-focalisation est parfaitement compatible avec les images RSO acquises dans les différents modes (« stripmap », « spotlight » et « sliding spotlight ») : dé-focalisation en azimut suivie par rétroprojection modifiée (conditionnée par la structure temps-fréquence du signal) sur l'ensemble donné des points. Dans la pile d'images ré-focalisées, les centres de diffusion sont détectés par tomographie 4D : test de conformité à l'hypothèse d'élévation zéro dans le plan élévation – vitesse de déformation. La vitesse moyenne correspond au maximum à l'élévation zéro, tandis que la série temporelle des déplacements est obtenue par double différence de phase des amplitudes complexes pour chaque diffuseur pertinent.Nous présentons également les campagnes in situ effectuées au barrage de Puylaurent (et glissement de Chastel) : les relevés GPS, topographiques et LIDAR sol employées au calcul des maillages 3D. La comparaison entre les déplacements mesurés in situ et les résultats obtenus par l'exploitation conjointe de la télédétection RSO satellitaires et les maillages 3D valident la chaîne de traitement proposée. / The thesis is composed of two research axis. The first one consists in proposing time-frequency signal processing tools for frequency modulated continuous wave (FMCW) radars used for displacements measurements, while the second one consists in designing a spaceborne synthetic aperture radar (SAR) signal processing methodology for infrastructure monitoring when an external point cloud of the envisaged structure is available. In the first part of the thesis, we propose our solutions to the nonlinearity problem of an X-band FMCW radar designed for millimetric displacement measurements of short-range targets. The nonlinear tuning curve of the voltage controlled oscillator from the transceiver can cause a dramatic resolution degradation for wideband sweeps. To mitigate this shortcoming, we have developed two time warping-based methods adapted to wideband nonlinearities: one estimates the nonlinear terms using the high order ambiguity function, while the other is an autofocus approach which exploits the spectral concentration of the beat signal. Onwards, as the core of the thesis, we propose a novel method for scattering centers detection and tracking in spaceborne SAR images adapted to infrastructure monitoring applications. The method is based on refocusing each SAR image on a provided 3D point cloud of the envisaged infrastructure and identifying the reliable scatterers to be monitored by means of four dimensional (4D) tomography. The refocusing algorithm is compatible with stripmap, spotlight and sliding spotlight SAR images and consists of an azimuth defocusing followed by a modified back-projection algorithm on the given set of points which exploits the time-frequency structure of the defocused azimuth signal. The scattering centers of the refocused image are detected in the 4D tomography framework by testing if the main response is at zero elevation in the local elevation-velocity spectral distribution. The mean displacement velocity is estimated from the peak response on the zero elevation axis, while the displacements time series for detected single scatterers is computed as double phase difference of complex amplitudes.Finally, we present the measurement campaigns carried out on the Puylaurent water-dam and the Chastel landslide using GPS measurements, topographic surveys and laser scans to generate the point clouds of the two structures. The comparison between in-situ data and the results obtained by combining TerraSAR-X data with the generated point clouds validate the developed SAR signal processing chain. / Teza cuprinde două axe principale de cercetare. Prima axă abordează aspecte metodologice de prelucraretimp-frecvenţă a semnalelor furnizate de radare cu emisie continuă şi modulaţie de frecvenţă (FMCW)în contextul măsurării deplasărilor milimetrice. În cadrul celei de-a doua axe, este proiectată şi validatăo metodă de prelucrare a imaginilor satelitare SAR (radar cu apertură sintetică) ce este destinatămonitorizării infrastructurii critice şi care se bazează pe existenţa unui model 3D al structurii respective.În prima parte a tezei, sunt investigate soluţii de corecţie a neliniarităţii unui radar FMCW în bandaX destinat măsurării deplasărilor milimetrice. Caracteristica de comandă neliniară a oscilatorului debandă largă determină o degradare a rezoluţiei în distanţă. Pentru a rezolva acest inconvenient, au fostelaborate două metode de corecţie a neliniarităţii, adaptate pentru semnale de bandă largă, ce se bazeazăpe conceptul de reeşantionare neuniformă sau deformare a axei temporare. Prima abordare estimeazăparametrii neliniarităţii utilizând funcţii de ambiguitate de ordin superior, iar cea de-a doua exploateazăo măsură de concentraţie spectrală a semnalului de bătăi într-un algoritm de autofocalizare în distanţă.În a doua parte a lucrării, este propusă o metodologie generală de detecţie şi monitorizare a centrilorde împrăştiere în imagini SAR în scopul monitorizării elementelor de infrastructură critică. Metoda sebazează pe refocalizarea fiecărei imagini radar pe un model 3D al structurii investigate în scopul identificăriicentrilor de împrăştiere pertinenţi (ţinte fiabile ce pot fi monitorizate în timp) cu ajutorul tomografiei SAR4D (distanţă-azimut-elevaţie-viteză de deplasare). Algoritmul de refocalizare este compatibil cu imaginiSAR achiziţionate în moduri diferite (« stripmap », « spotlight » şi « sliding spotlight ») şi constă într-odefocalizare în azimut urmată de o retroproiecţie modificată (condiţionată de structura timp-frecvenţă asemnalului) pe modelul 3D al structurii. Ţintele sunt identificate în stiva de imagini refocalizate cu ajutorultomografiei 4D prin efectuarea unui test de conformitate cu ipoteza că centrii de împrăştiere pertinenţivor avea elevaţie zero în planul local elevaţie-viteză. Viteza medie de deformare corespunde maximuluide pe axa de elevaţie nulă, iar seria temporară a deplasărilor se obţine printr-o dublă diferenţă de fază aamplitudinilor complexe corespunzătoare ţintelor identificate.În final sunt prezentate campaniile de măsurători pe teren efectuate la un baraj şi o alunecare de terendin regiunea Puylaurent (Franţa) destinate obţinerii modelului 3D al celor două elemente de infrastructurăprin măsurători GPS, topografice şi LIDAR. Comparaţia între deformările măsurate pe teren şi rezultateleobţinute prin combinarea imaginilor SAR cu modelele 3D au permis validarea metodologiei propuse.

abstract: This work examines two main areas in model-based time-varying signal processing with emphasis in speech processing applications. The first area concentrates on improving speech intelligibility and on increasing the proposed methodologies application for clinical practice in speech-language pathology. The second area concentrates on signal expansions matched to physical-based models but without requiring independent basis functions; the significance of this work is demonstrated with speech vowels. A fully automated Vowel Space Area (VSA) computation method is proposed that can be applied to any type of speech. It is shown that the VSA provides an efficient and reliable measure and is correlated to speech intelligibility. A clinical tool that incorporates the automated VSA was proposed for evaluation and treatment to be used by speech language pathologists. Two exploratory studies are performed using two databases by analyzing mean formant trajectories in healthy speech for a wide range of speakers, dialects, and coarticulation contexts. It is shown that phonemes crowded in formant space can often have distinct trajectories, possibly due to accurate perception. A theory for analyzing time-varying signals models with amplitude modulation and frequency modulation is developed. Examples are provided that demonstrate other possible signal model decompositions with independent basis functions and corresponding physical interpretations. The Hilbert transform (HT) and the use of the analytic form of a signal are motivated, and a proof is provided to show that a signal can still preserve desirable mathematical properties without the use of the HT. A visualization of the Hilbert spectrum is proposed to aid in the interpretation. A signal demodulation is proposed and used to develop a modified Empirical Mode Decomposition (EMD) algorithm. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2016

[pt] Uma das principais etapas na exploração de petróleo é a definição de um modelo geológico que justifique a existência de uma acumulação de hidrocarbonetos. Ferramentas que possam aumentar o grau de precisão deste modelo são foco de constante estudo na indústria do petróleo. Neste contexto, recentemente, Partyka et al. apresentaram uma nova técnica que utiliza a decomposição espectral dos dados sísmicos para refinar o modelo geológico em termos de definição de espessura de camadas. Nesta pesquisa, essa técnica é estudada e testada, e é proposta a utilização da transformada S, desenvolvida por Stockwell et al., para localizar as componentes de freqüência no domínio do tempo. Os testes realizados com dados sintéticos apontam o uso da técnica de Partyka et al. para fins mais qualitativos, já que, quando os modelos dos testes são perturbados, as análises quantitativas ficam comprometidas. A transformada S mostrou bons resultados na localização das componentes de freqüência no domínio do tempo; no entanto, ela acarreta a suavização do espectro de amplitudes. Ao final deste trabalho é apresentado um exemplo da utilização da técnica em dados reais tridimensionais. / [en] One of the main steps in oil exploration is the definition of a geological model that can justify the existence of a hydrocarbon accumulation. Tools that can improve the precision of this geological model are a constant goal of the oil industry research. In this context, Partyka et al. have recently presented a new technique that uses spectral seismic data decomposition in order to improve the model's accuracy in terms of the thickness definition of geological layers. In the present research, this technique is studied and tested, and a use for the S transform is proposed to locate the frequency components in the time domain. The S transform was recently developed by Stockwell et al. The tests performed with synthetic data indicate that the technique developed by Partyka et al. provide a better qualitative response, because, when the models in the tests are disturbed, qualitative analyses are compromised. The S transform showed good results in locating the frequency components in the time domain, but it smoothes the amplitude spectrum. At the end of this work, an example of the use of this technique with real three-dimensional data is presented.

Les superpositions d'ondes modulées en amplitude et en fréquence (modes AM--FM) sont couramment utilisées pour modéliser de nombreux signaux du monde réel : cela inclut des signaux audio (musique, parole), médicaux (ECG), ou diverses séries temporelles (températures, consommation électrique). L'objectif de ce travail est l'analyse et la compréhension fine de tels signaux, dits "multicomposantes" car ils contiennent plusieurs modes. Les méthodes mises en oeuvre vont permettre de les représenter efficacement, d'identifier les différents modes puis de les démoduler (c'est-à-dire déterminer leur amplitude et fréquence instantanée), et enfin de les reconstruire. On se place pour cela dans le cadre bien établi de l'analyse temps-fréquence (avec la transformée de Fourier à court terme) ou temps-échelle (transformée en ondelettes continue). On s'intéressera également à une méthode plus algorithmique et moins fondée mathématiquement, basée sur la notion de symétrie des enveloppes des modes : la décomposition modale empirique. La première contribution de la thèse propose une alternative au processus dit ``de tamisage'' dans la décomposition modale empirique, dont la convergence et la stabilité ne sont pas garanties. \`A la place, une étape d'optimisation sous contraintes ainsi qu'une meilleure détection des extrema locaux du mode haute fréquence garantissent l'existence mathématique du mode, tout en donnant de bons résultats empiriques. La deuxième contribution concerne l'analyse des signaux multicomposantes par la transformée de Fourier à court terme et à la transformée en ondelettes continues, en exploitant leur structure particulière ``en ridge'' dans le plan temps-fréquence. Plus précisément, nous proposons une nouvelle méthode de reconstruction des modes par intégration locale, adaptée à la modulation fréquentielle, avec des garanties théoriques. Cette technique donne lieu à une nouvelle méthode de débruitage des signaux multicomposantes. La troisième contribution concerne l'amélioration de la qualité de la représentation au moyen de la ``réallocation'' et du ``synchrosqueezing''. Nous prolongeons le synchrosqueezing à la transformée de Fourier à court terme, et en proposons deux extensions inversibles et adaptées à des modulations fréquentielles importantes, que nous comparons aux méthodes originelles. Une généralisation du synchrosqueezing à la dimension 2 est enfin proposée, qui utilise le cadre de la transformée en ondelettes monogène. / Many signals from the physical world can be modeled accurately as a superposition of amplitude- and frequency-modulated waves. This includes audio signals (speech, music), medical data (ECG) as well as temporal series (temperature or electric consumption). This thesis deals with the analysis of such signals, called multicomponent because they contain several modes. The techniques involved allow for the detection of the different modes, their demodulation (ie, determination of their instantaneous amplitude and frequency) and reconstruction. The thesis uses the well-known framework of time-frequency and time-scale analysis through the use of the short-time Fourier and the continuous wavelet transforms. We will also consider a more recent algorithmic method based on the symmetry of the enveloppes : the empirical mode decomposition. The first contribution proposes a new way to avoid the iterative ``Sifting Process'' in the empirical mode decomposition, whose convergence and stability are not guaranteed. Instead, one uses a constrained optimization step together with an enhanced detection of the local extrema of the high-frequency mode. The second contribution analyses multicomponent signals through the short-time Fourier transform and the continuous wavelet transform, taking advantage of the ``ridge'' structure of such signals in the time-frequency or time-scale planes. More precisely, we propose a new reconstruction method based on local integration, adapted to the local frequency modulation. Some theoretical guarantees for this reconstruction are provided, as well as an application to multicomponent signal denoising. The third contribution deals with the quality of the time-frequency representation, using the reassignment method and the synchrosqueezing transform: we propose two extensions of the synchrosqueezing, that enable mode reconstruction while remaining efficient for strongly modulated waves. A generalization of the synchrosqueezing in dimension 2 is also proposed, based on the so-called monogenic wavelet transform.

Cette thèse propose une nouvelle méthode pour modéliser les fonctions non linéaires de modulations d’amplitude et de fréquence de signaux multicomposantes non stationnaires de durée longue. La méthode repose sur une décomposition du signal en segments courts pour une modélisation locale sur les segments. Pour initialiser la modélisation, nous avons conçu une première étape qui peut être considérée comme un estimateur indépendant et non paramétrique des fonctions de modulations. L’originalité de l’approche réside dans la définition d’une matrice de convergence totale intégrant simultanément les valeurs d’amplitude et de fréquence et utilisé pour l’association d’un pic à une composante selon un critère d’acceptation stochastique. Suite à cette initialisation, la méthode estime les fonctions de modulations par l'enchaînement des étapes de segmentation, modélisation et fusion. Les fonctions de modulations estimées localement par maximum de vraisemblance sont connectées dans l'étape de fusion, qui supprime les discontinuités, et produit l’estimation globale sur la durée totale du signal. Les étapes sont conçues afin de pouvoir modéliser des signaux multicomposantes avec des morts et naissances, ce qui en fait une de ses originalités par rapport aux techniques existantes. Les résultats sur des signaux réels et simulés ont illustré les bonnes performances et l’adaptabilité de la méthode proposée. / In this thesis, a novel method is proposed for modeling the non-linear amplitude and frequency modulations of non-stationary multi-component signals of long duration. The method relies on the decomposition of the signal into short time segments to carry out local modelings on these segments. In order to initialize the modeling, a first step is designed which can be considered as an independent estimator of the modulations over the entire duration of the signal. The originality of this approach lies in the definition of the total divergence matrix integrating simultaneously the amplitude and frequency values, which are employed for the association of a peak to a component according to a stochastic acceptation criteria. Following the initialization, the proposed method estimates the modulations by the step sequence of segmentation, modeling and fusion. The locally obtained modulation functions estimated by maximum likelihood are finally connected in the fusion step which suppresses their discontinuity and yields the global estimation over the entire signal duration. All these steps are defined in order to be able to model multicomponent signals with births and deaths, making one of its original features compared to existing techniques. The results on real and simulated signals have shown the good performance and adaptability of the proposed method.

Dans le cadre de la surveillance maritime, les opérationnels ont de plus en plus recours à l'imagerie radar pour classifier à grande distance un objet marin. Le traitement ISAR (Inverse Synthetic Aperture Radar) répond à ce besoin. Il repose en particulier sur l'analyse des mouvements propres de l'objet marin. Une fois l'objet détecté, il s'agit d'afficher sur la console tactique la représentation de la fréquence Doppler en fonction de la distance, aussi appelée image range-Doppler. Le travail présenté dans ce mémoire s'inscrit dans une perspective d'évolution opérationnelle de la chaîne de traitement existante. Il vise à produire de manière automatique la « meilleure » image range-Doppler. Dans cette thèse, nos contributions s'appuient sur l'idée de reconsidérer la chaîne de traitement en tenant compte de l'a priori que l'objet marin est un objet rigide dont la géométrie structure l'évolution du signal radar. Ainsi, dans une première contribution, nous proposons une nouvelle méthode d'analyse temps-fréquence du signal radar afin d'obtenir une image instantanée où l'opérationnel peut distinguer « au mieux » les superstructures de l'objet marin. Cette dernière est fondée sur la fusion de plusieurs représentations temps-fréquence issues de la classe de Cohen en faisant l'hypothèse que les composantes temps-fréquence sont des trajectoires structurées 2D dans le plan temps-fréquence, contrairement aux termes d'interférences induits par la propriété de bilinéarité des membres de cette classe. Une étude comparative sur données synthétiques et ISAR est menée pour confirmer la pertinence de notre approche, notamment du point de vue de la résolution temps-fréquence et de la suppression des termes d'interférences.Dans une seconde contribution, nous établissons une nouvelle procédure pour qualifier chaque image range-Doppler, obtenue à l'issue de l'analyse temps-fréquence, avec des mesures d'irrégularité de formes que nous fusionnons à l'aide d'un opérateur d'agrégation. Des simulations sur données réelles sont réalisées. Les résultats concordent avec une analyse subjective menée par des opérationnels, ce qui confirme l'efficacité de notre méthode. / In maritime surveillance, radar imaging plays a key role to classify a maritime object. ISAR processing is one of the solutions, which takes advantage of the object rotational motion to provide a range-Doppler image.The work, presented in this report, is an evolution of the existing ISAR processing chain. Therefore, our contributions are based on the processing chain reconsideration by taking into account the fact that the maritime object is a rigid object, the geometry of which influences the radar signal evolution.In a first contribution, we propose a new time-frequency analysis method based on the aggregation of some time-frequency representations obtained with Cohen class members. It consists in differentiating the signal, assumed to be characterized by 2-D near-linear stable trajectories in the time-frequency plane, and the cross-terms, assumed to be geometrically unstructured. A comparative study is then carried out on ISAR synthetic data to confirm the efficiency of our approach.In a second contribution, we present a new procedure to characterize each range-Doppler image, obtained from a time-frequency analysis, by means of shape irregularity measures that are combined with a fuzzy logic operator. To validate our approach, simulations on real data are done. The results are compared to a subjective analysis carried out with practionners.