Although fine granularity scalability (FGS) video coding based on matching pursuits and bit-plane coding have been proven to have better coding efficiency than discrete-cosine-transform-based FGS at low bit rates, it might not be the most efficient method in terms of rate-distortion optimization (RDO). We propose a rate-distortion optimization FGS video coding by dividing a frame into blocks to generate block-based embedded bit-streams and reorganize the bit-streams into several quality layers according to the rate-distortion slopes. The comparison between FGS matching pursuit video coding and RDO-FGS matching pursuit video coding is shown in the experimental results.

Research in robotics has recently broadened its traditional focus on industrial applications to include natural, human-like systems. The human musculoskeletal system has over 600 muscles and 200 joint degrees-of-freedom that provide extraordinary flexibility in tailoring its overall configuration and dynamics to the demands of different tasks. The importance of understanding human movement has spurred efforts to build systems with similar capabilities and has led to the construction of actuators, such as pneumatic artificial muscles, that have properties similar to those of human muscles. However, muscles are far more complex than these robotic actuators and will require new control perspectives. Specifying how to encode high degree-of-freedom muscle functions in order to recreate such movements in anthropomorphic robotic systems is an imposing challenge. This dissertation attempts to advance our understanding by modeling the workings of human muscles in a way that explains how the low temporal bandwidth control of the human brain could direct the high temporal bandwidth requirements of the human movement system. We extend the motor primitives model, a popular strategy for human motor control, by coding a fixed library of movements such that their temporal codes are pre-computed and can be looked up and combined on demand. In this dissertation we develop primitives that lead to various smooth, natural human movements and obtain a sparse-code representation for muscle fiber length changes by applying Matching Pursuit on a parameterized representation of such movements. We employ accurate three-dimensional musculoskeletal models to simulate the lower body muscle fiber length changes for multiple repeatable movements captured from human subjects. We recreate the length changes and show that the signal can be economically encoded in terms of discrete movement elements. Each movement can thus be visualized as a sequence of coefficients for temporally displaced motor primitives. The primary research contribution of describing movements as a compact code develops a clear hierarchy between the spinal cord and higher brain areas. The code has several other advantages. First, it provides an overview of how the elaborate computations in abstract motor control could be ‘parcellated’ into the brain’s primary subsystems. Second, its parametric description could be used in the extension of learned movements to similar movements with different goals. Thirdly, the sensitivity of the parameters can allow the differentiation of very subtle variations in movement. This research lays the groundwork for understanding and developing further human motor control strategies and provides a mathematical framework for experimental research. / text

Η παρούσα εργασία πραγματεύεται την αποτελεσματικότητα του αλγορίθμου Matching Pursuit στον τομέα της επεξεργασίας σήματος. Περιγράφονται οι γενικότερες δυνατότητες του στην επεξεργασία βασικών βιοϊατρικών σημάτων και ειδικότερα εξετάζονται τα πλεονεκτήματά του στην επεξεργασία του ηλεκτροκαρδιογράφηματος, μιας και η εργασία αποτελεί μέρος του προγράμματος τηλεκαρδιολογίας e-Herofilus. Αρχικά λοιπόν γίνεται μία αναλυτική περιγραφή του τρόπου λήψης και καταγραφής του καρδιογραφικού σήματος. Στη συνέχεια γίνεται μία περιγραφή του αλγορίθμου Matching Pursuit και των αποτελεσμάτων που είχε η εφαρμογή του σε γνωστά βιοσήματα και κυρίως σε εγκεφαλογραφήματα και καρδιογραφήματα, από όπου προκύπτουν τα πλεονεκτήματα της συγκεκριμένης μεθόδου έναντι των άλλων μεθόδων που έχουν χρησιμοποιηθεί στο παρελθόν για τη μεταφορά και επεξεργασία σημάτων στο πεδίο χρόνου- συχνότητας. Τέλος ακολουθεί η υλοποιήση του αλγορίθμου του Matching Pursuit και η εφαρμογή του σε πραγματικά ηλεκτροκαρδιογραφήματα τόσο υγιή όσο και παθολογικά, που λήφθηκαν από τη βάση Physionet του MIT. Η ανάλυση των αποτελεσμάτων της εφαρμογής αυτής οδηγεί σε συμπεράσματα σχετικά με την αξία και την αποτελεσματικότητα του αλγορίθμου στους τομείς της αποθορυβοποίησης του καρδιογραφικού σήματος και του εντοπισμού της χρήσιμης πληροφορίας που αυτό μεταφέρει. Επίσης, μέσα από τη σύγκριση υγιών και παθολογικών καρδιογραφημάτων γίνεται μία προσπάθεια αναγνώρισης στοιχείων που εμφανίζονται στο πεδίο χρόνου-συχνότητας και συσχέτισής τους με τις εκάστοτε παθολογίες, γεγονός που μελλοντικά μπορεί να αποτελέσει το εφαλτήριο για την ανάπτυξη αλγορίθμου αυτόματης διάγνωσης καρδιογραφημάτων. / The following project, which is a part of telemedicine program e-Herofilus, examines the effectiveness of Matching Pursuit method. Its ability of processing in biomedical signals is described in a general format, as well as the advantages in processing of electrocardiogram (ECG) in more details. Firstly, there is an analytical description of collection and record of ECG. Afterwards, there is a description of Matching Pursuit algorithm and its results in biosignal processing. The algorithm is applied in electrocardiogram (ECG) and electroencephalogram (EEG). The results of those applications showed the advantages of Matching Pursuit method over the other methods were used in the past in the signal processing field in the time frequency plane. Finally, the implementation of Matching Pursuit algorithm in real ECGs is following. These ECGs are taken from healthy as well as from pathological specimens. The source of these specimens is Physionet Bank of MIT. In the conclusions of this project, it is underlined the value and the efficiency of Matching Pursuit method in denoising of ECG, and in detecting the useful signal information in time frequency plane. Additionally, comparing the results of processing healthy and pathological ECGs, could lead us in the future in the development of an automated diagnosis algorithm, which can be an innovation in both Engineering and Medicine Sciences.

Recent theoretical study shows that the sparsest solution to an underdetermined linear system is unique, provided the solution vector is sufficiently sparse, and the operator matrix has sufficiently incoherent column vectors. In addition, efficient algorithms have been discovered to find such solutions. This intriguing result opens a new door for many potential applications. In this thesis, we study the design of a class of greedy algorithms that are extremely efficient, e.g., Orthogonal Matching Pursuit (OMP). These greedy algorithms suffer from a stability issue that the greedy selection approach always make locally optimal decisions, thereby easily biasing and mistaking the solutions in particular under data noise. We propose a solution approach that in designing greedy algorithms, new constraints can be devised by leveraging application-specific insights and incorporated into the algorithms. Given that sparse recovery problems by definition are underdetermined, introducing additional constraints can significantly improve the stability of greedy algorithms, yet retain their efficiency. / Engineering and Applied Sciences

In any quantum dynamics method that approximates wave functions as a linearly combined basis set, non-orthogonality can be is a problem. It has been proven in previous studies that, by using the most standard form of Matching Pursuit in combination with a Gaussian wave packet ansatz, exact quantum-mechanical correspondence can be obtained for particle tunneling in one and two dimensions. This study is an attempt to prove that this approach can be generally applicable to systems of arbitrary dimension propagating with an an-harmonic potential, and that adaptive initial state sampling can be used to make the method even more computationally efficient.

Les membranes Nafion©, composant essentiel des piles à combustibles (PEMFC), ont des performances liées à leur hydratation. En collaboration avec le CEA, nous avons développé une méthode de mesure de la vitesse ultrasonore et du gonflement de ce type de membranes par insertion-substitution. Conséquence de la faible épaisseur des échantillons devant la longueur d'onde, un phénomène de recouvrement apparait entre les différents échos d'aller-retour dans le matériau. Un algorithme de Matching Pursuit a été adapté au cas des membranes afin de déconvoluer les échos et ainsi de permettre la mesure de la vitesse de propagation ultrasonore et de l'atténuation. Nos mesures nous ont également permis de déterminer l'épaisseur de ces membranes. Une étude sur la robustesse et le domaine de validité de notre méthode de traitement est présentée. Ce manuscrit recense également l'ensemble des résultats sur la caractérisation des membranes Nafion dans différents états d'équilibre hydrique, attestant de la possibilité de caractériser la reprise hydrique de ce polymère par méthode ultrasonore. / No summary available

Ingeniero Civil Eléctrico / El sueño es un tema que ha tomado mucha fuerza en los últimos años sobre todo por su función neurofisiológica y reparadora. Dentro de los fenómenos fisiológicos más importantes del sueño se encuentra una actividad eléctrica registrada en el EEG (electroencefalograma) llamada Huso Sigma. Este patrón eléctrico se ha asociado por una parte a procesos involucrados en la consolidación de la memoria y por otra a desórdenes tales como retardo mental, hiperkinesia, desarrollo cognitivo, entre otros. Por lo tanto pesquisar y caracterizar este patrón es de suma importancia en el área de la medicina. El objetivo de esta tesis consiste en construir características morfológicas con el fin de caracterizar Husos Sigma y posteriormente detectarlos a través de un sistema de detección automático. Los Husos Sigmas corresponden a trenes de ondas distinguibles de la actividad de fondo del EEG, principalmente notorios en las derivaciones centrales, que comienzan con una baja amplitud, llegan a un máximo y luego decaen, teniendo duraciones típicas entre 0,5 a 2 [s]. El problema de detección consiste en lograr separar entre Husos Sigmas, correspondientes a trozos de señales marcadas por expertos que a su juicio consideran que son Husos Sigmas, de otras marcas hechas por un pre-detector y que no corresponden a Husos Sigmas. Para resolver el problema propuesto se propone un esquema: Descomposición Modal Empírica (EMD por Empirical Mode Decomposition en inglés) - detector de zonas - Matching Pursuit (MP). La EMD permite aislar la componente fusiforme que se busca caracterizar mediante MP en las zonas detectadas por el detector de zonas. El algoritmo MP se encuentra equipado con un diccionario de wavelets Morlet, cuya función es describir de manera sucinta cuando se trata de HS y de manera más compleja cuando se trata de no-HS. La creación del diccionario se hace en base a características extraídas del detector de zonas aplicado previamente. Luego de aplicar el método propuesto se extraen características basadas en el comportamiento morfológico de la componente seleccionada. Tras generar estas características se entrena una Máquina de Soporte Vectorial (SVM por Support Vector Machine en inglés) empleando un kernel Gaussiano. Los SVM se calibran para cada experimento realizado. El funcionamiento del sistema, considerando un largo mínimo del detector de zonas de 0,3 [s], es revisado en el punto de operación TVP=80% y FPR=30%. TVP significa tasa de verdaderos positivos y FPR tasa de falsos positivos. De este análisis se concluye que la aproximación morfológica es buena, sin embargo el método opera de manera similar en varios HS y no-HS. Realizando un análisis entre las características basado en información mutua se concluye que gran parte de la información se encuentra contenida en 3 características; sin embargo el desempeño de ocupar estas tres características en algunos puntos de operación se diferencia bastante con respecto al desempeño de un sistema que emplea todas las características creadas. Finalmente se sugieren nuevos pasos a seguir con el fin de mejorar el sistema propuesto.

<p>Conventional image compression algorithms use transform coding to achieve a compact representation of the image. Most transforms used in image compression algorithms map image data to a complete set of transform basis functions which can decorrelate image information and represent data in a more compact form. This technique has proven to be very efficient and is used in most state of the art compression algorithms. However, if an over-complete set of basis functions is available, the image information can be captured by fewer basis functions. This results in a more compact image representation and can potentially yield a better compression performance. In this thesis, we study the use of over-complete image representation as an alternative to transform coding techniques used in image compression. The matching pursuit (MP) algorithm is used to map the image to an over-complete dictionary. We develop new quantization and encoding algorithms for matching pursuit image coding and compare the proposed MP image encoder with state of the art image codecs that use transform coding techniques. Additionally, the iterative nature of the matching pursuit algorithm can be used to design progressive encoders. We also study progressive coding by matching pursuit and design new progressive MP encoders and show how they outperform existing solutions.</p> <p>We start by study of progressive coding by matching pursuit and design a progressive encoder for i.i.d. Gaussian sources. The choice of Gaussian sources is motivated by the fact that theoretical bounds on progressive coding of Gaussian sources are known and therefore can be used to determine the efficiency of matching pursuit in progressive coding. Our proposed MP progressive encoder outperforms all existing progressive encoders designed for Gaussian sources. However, redundancies in the MP algorithm prevents us from closing the gap that exists between progressive and non-progressive Gaussian source coding. Therefore, we design another progressive encoder based on lattice quantization and address some of the issues associated with our proposed MP encoder.</p> <p>In the second part of this thesis we study the application of matching pursuit m image compression. We start our study by developing a new adaptive quantization technique that can outperform existing quantization techniques designed for matching pursuit image coding. We continue our study by designing an optimal encoding algorithm for encoding MP coefficients and atom positions. The proposed encoding algorithm results in significant rate distortion improvement over existing encoding techniques. The use of our proposed encoding technique enables comparison of matching pursuit image coding with state of the art compression algorithms that use transform coding such as JPEG2000. Our proposed MP image encoder outperforms JPEG2000 at low bit rates and results in better visual quality at moderate bit rates. We show that the flexibility offered by the over-complete dictionary can result in superior performance compared to image compression using transform coding techniques.</p> / Thesis / Doctor of Philosophy (PhD)

Constrained by practical and economical considerations, one often uses seismic data with missing traces. The use of such data results in image artifacts and poor spatial resolution. Sometimes due to practical limitations, measurements may be available on a perturbed grid, instead of on the designated grid. Due to algorithmic requirements, when such measurements are viewed as those on the designated grid, the recovery procedures may result in additional artifacts. This paper interpolates incomplete data onto regular grid via the Fourier domain, using a recently developed greedy algorithm. The basic objective is to study experimentally as to what could be the size of the perturbation in measurement coordinates that allows for the measurements on the perturbed grid to be considered as on the designated grid for faithful recovery. Our experimental work shows that for compressible signals, a uniformly distributed perturbation can be offset with slightly more number of measurements.

L'imagerie médicale ultrasonore est une modalité en perpétuelle évolution et notamment en post-traitement où il s'agit d'améliorer la résolution et le contraste des images. Ces améliorations devraient alors aider le médecin à mieux distinguer les tissus examinés améliorant ainsi le diagnostic médical. Il existe déjà une large palette de techniques "hardware" et "software". Dans ce travail nous nous sommes focalisés sur la mise en oeuvre de techniques dites de "déconvolution aveugle", ces techniques temporelles utilisant l'enveloppe du signal comme information de base. Elles sont capables de reconstruire des images parcimonieuses, c'est-à-dire des images de diffuseurs dépourvues de bruit spéculaire. Les principales étapes de ce type de méthodes consistent en i) l'estimation aveugle de la fonction d'étalement du point (PSF), ii) l'estimation des diffuseurs en supposant l'environnement exploré parcimonieux et iii) la reconstruction d'images par reconvolution avec une PSF "idéale". La méthode proposée a été comparée avec des techniques faisant référence dans le domaine de l'imagerie médicale en utilisant des signaux synthétiques, des séquences ultrasonores réelles (1D) et images ultrasonores (2D) ayant des statistiques différentes. La méthode, qui offre un temps d'exécution très réduit par rapport aux techniques concurrentes, est adaptée pour les images présentant une quantité réduite ou moyenne des diffuseurs. / The ultrasonic imaging knows a continuous advance in the aspect of increasing the resolution for helping physicians to better observe and distinguish the examined tissues. There is already a large range of techniques to get the best results. It can be found also hardware or signal processing techniques. This work was focused on the post-processing techniques of blind deconvolution in ultrasound imaging and it was implemented an algorithm that works in the time domain and uses the envelope signal as input information for it. It is a blind deconvolution technique that is able to reconstruct reflectors and eliminate the diffusive speckle noise. The main steps are: the estimation of the point spread function (PSF) in a blind way, the estimation of reflectors using the assumption of sparsity for the examined environment and the reconstruction of the image by reconvolving the sparse tissue with an ideal PSF. The proposed method was tested in comparison with some classical techniques in medical imaging reconstruction using synthetic signals, real ultrasound sequences (1D) and ultrasound images (2D) and also using two types of statistically different images. The method is suitable for images that represent tissue with a reduced amount or average scatters. Also, the technique offers a lower execution time than direct competitors.