Maréchal, Pierre
Overview
Works:  19 works in 29 publications in 2 languages and 144 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Thesis advisor, Other, Opponent 
Publication Timeline
.
Most widely held works by
Pierre Maréchal
Optimization, variational analysis and applications : IFSOVAA2020, Varanasi, India, February 24 by
Shashi Kant Mishra(
)
2 editions published in 2021 in Undetermined and English and held by 97 WorldCat member libraries worldwide
This book includes selected papers presented at the IndoFrench Seminar on Optimization, Variational Analysis and Applications (IFSOVAA2020), held at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, from 24 February 2020. The book discusses current optimization problems and their solutions by using the powerful tool of variational analysis. Topics covered in this volume include set optimization, multiobjective optimization, mathematical programs with complementary, equilibrium, vanishing and switching constraints, copositive optimization, intervalvalued optimization, sequential quadratic programming, boundconstrained optimization, variational inequalities, and more. Several applications in different branches of applied mathematics, engineering, economics, finance, and medical sciences have been included. Each chapter not only provides a detailed survey of the topic but also builds systematic theories and suitable algorithms to deduce the most recent findings in literature. This volume appeals to graduate students as well as researchers and practitioners in pure and applied mathematics and related fields that make use of variational analysis in solving optimization problems
2 editions published in 2021 in Undetermined and English and held by 97 WorldCat member libraries worldwide
This book includes selected papers presented at the IndoFrench Seminar on Optimization, Variational Analysis and Applications (IFSOVAA2020), held at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, from 24 February 2020. The book discusses current optimization problems and their solutions by using the powerful tool of variational analysis. Topics covered in this volume include set optimization, multiobjective optimization, mathematical programs with complementary, equilibrium, vanishing and switching constraints, copositive optimization, intervalvalued optimization, sequential quadratic programming, boundconstrained optimization, variational inequalities, and more. Several applications in different branches of applied mathematics, engineering, economics, finance, and medical sciences have been included. Each chapter not only provides a detailed survey of the topic but also builds systematic theories and suitable algorithms to deduce the most recent findings in literature. This volume appeals to graduate students as well as researchers and practitioners in pure and applied mathematics and related fields that make use of variational analysis in solving optimization problems
Optimization, Variational Analysis and Applications : IFSOVAA2020, Varanasi, India, February 24(
)
1 edition published in 2021 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2021 in English and held by 17 WorldCat member libraries worldwide
Mathématiques appliquées L3 : cours complet avec 500 tests et exercices corrigés by
Rémi Abgrall(
)
in French and held by 4 WorldCat member libraries worldwide
in French and held by 4 WorldCat member libraries worldwide
A Note on the Morozov Principle via Lagrange Duality by Xavier Bonnefond(
)
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2018 in English and held by 2 WorldCat member libraries worldwide
Méthode de MonteCarlo et nonlinéarités : de la physique du transfert radiatif à la cinétique des gaz by
Guillaume Terrée(
Book
)
2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide
In transport physics, especially in radiative transfer physics, the MonteCarlo method has been originally developed as the simulation of the history of numerous particles, from which are deduced mean observables. This numerical method owes its success to several qualities : a natural management of manydimensional phase space, a null systematic error away from the mathematical and physical model, the confidence intervals given with the results, an ability to take into account simultaneously numerous physical phenomenons, the simultaneous sensitivities calculating possibility, and an easy parallelization. In gas kinetics, particles collide each other, not with an external fixed medium ; it is said that their transport is nonlinear. These mutual collisions put out of action the aforesaid approach of the MonteCarlo method ; because in order to simulate the independent trajectories of multiple particles and thus estimate their distribution, this distribution must beforehand be exactly known...This thesis follows on from those of Jérémy DAUCHET (2012) and of Mathieu GALTIER (2014), dedicated to radiative transfer physics. Between other works, these authors have shown how the MonteCarlo method can bear nonlinearities, while keeping its customary formalism and specificities. The then overcome nonlinearities were respectively a chemistry/irradiance coupling law, and the dependence of the irradiance toward the absorption coefficient. We try in this manuscript to overcome the nonlinearity of the transport. In this aim, our main tools are a reverse following of particles, based on integral formulations of the transport equations, formulations largely inspired from the socalled null collisions algorithms. We show, on several academic examples, that we have indeed extended the Monte Carlo method to the resolution of the Boltzmann equation. These examples are also occasions to test the limits of what we have built. The most noteworthy results are certainly the absence of any mesh in the numerical method, and its capacity to calculate correctly the highspeed particles quantities (always rare compared to the total, in gas kinetics). Beyond the given examples, this manuscript is wanted as a formalism attempt and an exploration of the developed method basics. The focus is made on the reasoning leading to the method, rather than on particular implementations which have been realized. In the eyes of the author, the method is still largely reworkable. In particular, the maximal times on which the evolution of particles is computable, which constitute the main weakness of the developed numerical method, can surely be increased
2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide
In transport physics, especially in radiative transfer physics, the MonteCarlo method has been originally developed as the simulation of the history of numerous particles, from which are deduced mean observables. This numerical method owes its success to several qualities : a natural management of manydimensional phase space, a null systematic error away from the mathematical and physical model, the confidence intervals given with the results, an ability to take into account simultaneously numerous physical phenomenons, the simultaneous sensitivities calculating possibility, and an easy parallelization. In gas kinetics, particles collide each other, not with an external fixed medium ; it is said that their transport is nonlinear. These mutual collisions put out of action the aforesaid approach of the MonteCarlo method ; because in order to simulate the independent trajectories of multiple particles and thus estimate their distribution, this distribution must beforehand be exactly known...This thesis follows on from those of Jérémy DAUCHET (2012) and of Mathieu GALTIER (2014), dedicated to radiative transfer physics. Between other works, these authors have shown how the MonteCarlo method can bear nonlinearities, while keeping its customary formalism and specificities. The then overcome nonlinearities were respectively a chemistry/irradiance coupling law, and the dependence of the irradiance toward the absorption coefficient. We try in this manuscript to overcome the nonlinearity of the transport. In this aim, our main tools are a reverse following of particles, based on integral formulations of the transport equations, formulations largely inspired from the socalled null collisions algorithms. We show, on several academic examples, that we have indeed extended the Monte Carlo method to the resolution of the Boltzmann equation. These examples are also occasions to test the limits of what we have built. The most noteworthy results are certainly the absence of any mesh in the numerical method, and its capacity to calculate correctly the highspeed particles quantities (always rare compared to the total, in gas kinetics). Beyond the given examples, this manuscript is wanted as a formalism attempt and an exploration of the developed method basics. The focus is made on the reasoning leading to the method, rather than on particular implementations which have been realized. In the eyes of the author, the method is still largely reworkable. In particular, the maximal times on which the evolution of particles is computable, which constitute the main weakness of the developed numerical method, can surely be increased
Contributions à la tomographie thermoacoustique : modélisation et inversion by Xavier Bonnefond(
Book
)
2 editions published in 2010 in French and held by 2 WorldCat member libraries worldwide
ThermoAcoustic Tomography (TAT) is a medical imaging technique using the pressure wave generated by a body illuminated by an electromagnetic pulse. Since the acoustic signal is recorded around the body, the resulting inverse problem can be formulated as follows : from the knowledge of a solution of the wave equation on some hypersurface, reconstruct its initial condition. Despite several inversion formulas, so far no efficient procedure, taking partial data and damping into account, is known. As well as a state of the art, this work is dedicated to the introduction of a variational approach for the TAT problem. We studied the regularization by mollification, which consists in replacing the original object by a limited resolution version of it, and treating the data so that they fit this new objective. Moreover, we used a noise level estimation provided by the GolubKahan bidiagonalization process to allow an accurate regularization parameter selection. In the second part of this work, we investigate the usual TAT model and put forward some damped wave equation with a finite wave front speed. This improvement yields to the use of the Back and Forth Nudging (BFN) method, which was first implemented for data assimilation purposes, to invert the TAT problem. This technique provides a sequence of approximations of the solution by iterating forward and backward implementations of a wave equation including a newtonian recall to the data. This method, which is proved to be convergent in an ideal framework, leads to convincing results in both partial data and attenuated wave cases
2 editions published in 2010 in French and held by 2 WorldCat member libraries worldwide
ThermoAcoustic Tomography (TAT) is a medical imaging technique using the pressure wave generated by a body illuminated by an electromagnetic pulse. Since the acoustic signal is recorded around the body, the resulting inverse problem can be formulated as follows : from the knowledge of a solution of the wave equation on some hypersurface, reconstruct its initial condition. Despite several inversion formulas, so far no efficient procedure, taking partial data and damping into account, is known. As well as a state of the art, this work is dedicated to the introduction of a variational approach for the TAT problem. We studied the regularization by mollification, which consists in replacing the original object by a limited resolution version of it, and treating the data so that they fit this new objective. Moreover, we used a noise level estimation provided by the GolubKahan bidiagonalization process to allow an accurate regularization parameter selection. In the second part of this work, we investigate the usual TAT model and put forward some damped wave equation with a finite wave front speed. This improvement yields to the use of the Back and Forth Nudging (BFN) method, which was first implemented for data assimilation purposes, to invert the TAT problem. This technique provides a sequence of approximations of the solution by iterating forward and backward implementations of a wave equation including a newtonian recall to the data. This method, which is proved to be convergent in an ideal framework, leads to convincing results in both partial data and attenuated wave cases
On the variational approach to mollification in the theory of illposed problems and applications by
Walter Cédric Simo Tao Lee(
Book
)
2 editions published in 2020 in French and held by 2 WorldCat member libraries worldwide
Les problèmes inverses constituent un domaine en pleine expansion en mathématiques appliquées qui a suscité une grande attention au cours des dernières décennies en raison de son omniprésence dans plusieurs domaines des sciences et technologies. Le plus souvent, les problèmes inverses donnent lieu à des équations mathématiques instables. Autrement dit, les solutions ne dépendent pas continument des données. En effet, de très petites perturbations sur les données peuvent causer des erreurs arbitrairement grandes sur les solutions. Étant donné que le bruit est généralement inévitable, inverser l'équation malposée échoue à résoudre le problème. Il est alors nécessaire d'appliquer une méthode de régularisation afin de récupérer des approximations stables des solutions. À cet égard, plusieurs techniques de régularisation ont été développées dans la littérature. Globalement, ces méthodes de régularisation peuvent être divisées en deux classes : Une classe de méthodes qui tentent de reconstruire les solutions inconnues initiales et une classe de méthodes qui tentent de reconstruire des versions lisses des solutions inconnues. L'objectif de cette thèse est de contribuer à la promotion de la deuxième classe de méthode de régularisation à travers l'étude et l'application de la formulation variationnelle de la mollification. Dans ce manuscrit, nous montrons que l'approche variationnelle de la mollification peut être étendue à la régularisation de problèmes malposés impliquant des opérateurs non compacts. À cet égard, nous étudions et appliquons avec succès la méthode à la régression instrumentale nonparamétrique. Une contribution supplémentaire de cette thèse est la conception et l'étude d'une nouvelle méthode de régularisation adaptée aux problèmes linéaires exponentiellement malposés. Une comparaison numérique de cette nouvelle méthode aux méthodes classiques de régularisation telles que Tikhonov, la spectral cutoff, la régularisation asymptotique et la méthode des gradients conjugués est effectuée sur trois problèmes test tirés de la littérature. L'aspect pratique de la sélection du paramètre de régularisation avec un niveau de bruit inconnu est également considéré. Outre l'étude et l'application des méthodes de régularisation, cette thèse traite également de l'application d'une règle de sélection de paramètres de régularisation très populaire connue sous le nom du principe de Morozov. En utilisant la dualité de Lagrange, nous fournissons un algorithme simple et rapide pour le calcul du paramètre de régularisation correspondant à cette règle pour les méthodes de régularisation du type Tikhonov. L'intérêt de cette étude est qu'elle met en avant une méthode de régularisation mal connue qui pourtant a un grand potentiel et est capable de fournir des solutions approchées comparativement meilleures que certaines techniques de régularisation classiques bien connues. Un autre apport de cette thèse est la conception d'une nouvelle méthode de régularisation qui, selon nous, est prometteuse dans la régularisation de problèmes exponentiellement malposés, en particulier pour les problèmes inverses de conduction thermique
2 editions published in 2020 in French and held by 2 WorldCat member libraries worldwide
Les problèmes inverses constituent un domaine en pleine expansion en mathématiques appliquées qui a suscité une grande attention au cours des dernières décennies en raison de son omniprésence dans plusieurs domaines des sciences et technologies. Le plus souvent, les problèmes inverses donnent lieu à des équations mathématiques instables. Autrement dit, les solutions ne dépendent pas continument des données. En effet, de très petites perturbations sur les données peuvent causer des erreurs arbitrairement grandes sur les solutions. Étant donné que le bruit est généralement inévitable, inverser l'équation malposée échoue à résoudre le problème. Il est alors nécessaire d'appliquer une méthode de régularisation afin de récupérer des approximations stables des solutions. À cet égard, plusieurs techniques de régularisation ont été développées dans la littérature. Globalement, ces méthodes de régularisation peuvent être divisées en deux classes : Une classe de méthodes qui tentent de reconstruire les solutions inconnues initiales et une classe de méthodes qui tentent de reconstruire des versions lisses des solutions inconnues. L'objectif de cette thèse est de contribuer à la promotion de la deuxième classe de méthode de régularisation à travers l'étude et l'application de la formulation variationnelle de la mollification. Dans ce manuscrit, nous montrons que l'approche variationnelle de la mollification peut être étendue à la régularisation de problèmes malposés impliquant des opérateurs non compacts. À cet égard, nous étudions et appliquons avec succès la méthode à la régression instrumentale nonparamétrique. Une contribution supplémentaire de cette thèse est la conception et l'étude d'une nouvelle méthode de régularisation adaptée aux problèmes linéaires exponentiellement malposés. Une comparaison numérique de cette nouvelle méthode aux méthodes classiques de régularisation telles que Tikhonov, la spectral cutoff, la régularisation asymptotique et la méthode des gradients conjugués est effectuée sur trois problèmes test tirés de la littérature. L'aspect pratique de la sélection du paramètre de régularisation avec un niveau de bruit inconnu est également considéré. Outre l'étude et l'application des méthodes de régularisation, cette thèse traite également de l'application d'une règle de sélection de paramètres de régularisation très populaire connue sous le nom du principe de Morozov. En utilisant la dualité de Lagrange, nous fournissons un algorithme simple et rapide pour le calcul du paramètre de régularisation correspondant à cette règle pour les méthodes de régularisation du type Tikhonov. L'intérêt de cette étude est qu'elle met en avant une méthode de régularisation mal connue qui pourtant a un grand potentiel et est capable de fournir des solutions approchées comparativement meilleures que certaines techniques de régularisation classiques bien connues. Un autre apport de cette thèse est la conception d'une nouvelle méthode de régularisation qui, selon nous, est prometteuse dans la régularisation de problèmes exponentiellement malposés, en particulier pour les problèmes inverses de conduction thermique
Optimisation des routes de départ et d'arrivée aux approches des grands aéroports by
Jérémie Chevalier(
Book
)
2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide
The bottleneck of today's airspace is the Terminal Maneuvering Areas (TMA), where aircraft leave their routes to descend to an airport or take off and reach the enroute sector. To avoid congestion in these areas, an efficient design of departure and arrival routes is necessary. In this work, a solution for designing departure and arrival routes is proposed, which takes into account the runway configuration, the surroundings of the airport and operational constraints such as limited slopes or turn angles. The routes consist of two parts: a horizontal path in a graph constructed by sampling the TMA around the runway, to which is associated a cone of altitudes. The set of all routes is optimized by the Simulated Annealing metaheuristic. In the process and at each iteration, each route is computed by defining adequately the cost of the arcs in the graph and then searching a path on it. The costs are chosen so as to avoid zigzag behaviors as much as possible. Several tests were performed, one on an artificial problem designed specifically to test this approach and the three others on instances taken from the literature. The obtained results are satisfying with regard to the current state of air operations management and constraints
2 editions published in 2020 in English and held by 2 WorldCat member libraries worldwide
The bottleneck of today's airspace is the Terminal Maneuvering Areas (TMA), where aircraft leave their routes to descend to an airport or take off and reach the enroute sector. To avoid congestion in these areas, an efficient design of departure and arrival routes is necessary. In this work, a solution for designing departure and arrival routes is proposed, which takes into account the runway configuration, the surroundings of the airport and operational constraints such as limited slopes or turn angles. The routes consist of two parts: a horizontal path in a graph constructed by sampling the TMA around the runway, to which is associated a cone of altitudes. The set of all routes is optimized by the Simulated Annealing metaheuristic. In the process and at each iteration, each route is computed by defining adequately the cost of the arcs in the graph and then searching a path on it. The costs are chosen so as to avoid zigzag behaviors as much as possible. Several tests were performed, one on an artificial problem designed specifically to test this approach and the three others on instances taken from the literature. The obtained results are satisfying with regard to the current state of air operations management and constraints
Implémentations d'optimisationsimulation pour l'harmonisation des opérations dans les grands aéroports by
Paolo Maria Scala(
Book
)
2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide
L'augmentation constante du trafic aérien, spécialement en Europe, exerce une pression sur les aéroports, qui en conséquence sont souvent congestionnés. La zone aérienne entourant les aéroports, l'aire de manœuvre terminale (TMA), est particulièrement encombrée, puisqu'elle accueille tout le trafic aéroportuaire. Outre la zone aérienne, le partie sol fait aussi face à des problèmes d'encombrement, ainsi l'inefficacité des opérations en zone aérienne est transférée au sol. Cet encombrement des zones aériennes et terrestres des aéroports a pour conséquence de générer des retards, qui sont ensuite reportés sur les autres aéroports du réseau. Le problème d'encombrement affecte également la charge de travail des contrôleurs aériens qui doivent gérer ce large trafic. Cette thèse porte sur l'optimisation des opérations intégrées aux aéroports, en considérant l'aéroport d'un point de vue holistique et en incluant les activités aériennes et terrestres. Contrairement aux autres études dans ce domaine, cette thèse apporte sa contribution en appuyant les décisions des contrôleurs aériens en terme de séquencement des avions et en atténuant l'encombrement de la partie sol des aéroports. Les activités terrestres et aériennes peuvent être abordées avec deux différents niveaux d'abstractions, macroscopique, ou microscopique, en raison de différent délais de prise de décision. Dans cette thèse, les activités sont modélisées au niveau macroscopique. Le problème est formulé comme un modèle d'optimisation en identifiant une fonction objective qui prend en compte le nombre de conflits dans l'espace aérien et la surcharge au sol des aéroports; contraintes données par la régulation sur le minimum de séparation entre des avions consécutifs dans la zone aérienne et sur la piste de décollage; variables de décision liées au temps d'entrée de l'avion et à la vitesse d'entrée dans l'espace arien, au choix de la piste d'atterrissage et de la piste au départ et à l'heure de pushback. Le modèle d'optimisation est résolu en implémentant une approche par fenêtre glissante et par une version adaptée de la métaheuristique de recuit simulé. Des incertitudes sont ajoutées dans les activités en développant un modèle de simulation et en incluant des variables stochastiques représentant des sources d'incertitudes comme une variation de l'heure d'entrée dans l'espace aérien de l'aéroport, une variation de l'heure moyenne de temps du roulage ou encore une variation dans l'heure de pushback des avions
2 editions published in 2019 in French and held by 2 WorldCat member libraries worldwide
L'augmentation constante du trafic aérien, spécialement en Europe, exerce une pression sur les aéroports, qui en conséquence sont souvent congestionnés. La zone aérienne entourant les aéroports, l'aire de manœuvre terminale (TMA), est particulièrement encombrée, puisqu'elle accueille tout le trafic aéroportuaire. Outre la zone aérienne, le partie sol fait aussi face à des problèmes d'encombrement, ainsi l'inefficacité des opérations en zone aérienne est transférée au sol. Cet encombrement des zones aériennes et terrestres des aéroports a pour conséquence de générer des retards, qui sont ensuite reportés sur les autres aéroports du réseau. Le problème d'encombrement affecte également la charge de travail des contrôleurs aériens qui doivent gérer ce large trafic. Cette thèse porte sur l'optimisation des opérations intégrées aux aéroports, en considérant l'aéroport d'un point de vue holistique et en incluant les activités aériennes et terrestres. Contrairement aux autres études dans ce domaine, cette thèse apporte sa contribution en appuyant les décisions des contrôleurs aériens en terme de séquencement des avions et en atténuant l'encombrement de la partie sol des aéroports. Les activités terrestres et aériennes peuvent être abordées avec deux différents niveaux d'abstractions, macroscopique, ou microscopique, en raison de différent délais de prise de décision. Dans cette thèse, les activités sont modélisées au niveau macroscopique. Le problème est formulé comme un modèle d'optimisation en identifiant une fonction objective qui prend en compte le nombre de conflits dans l'espace aérien et la surcharge au sol des aéroports; contraintes données par la régulation sur le minimum de séparation entre des avions consécutifs dans la zone aérienne et sur la piste de décollage; variables de décision liées au temps d'entrée de l'avion et à la vitesse d'entrée dans l'espace arien, au choix de la piste d'atterrissage et de la piste au départ et à l'heure de pushback. Le modèle d'optimisation est résolu en implémentant une approche par fenêtre glissante et par une version adaptée de la métaheuristique de recuit simulé. Des incertitudes sont ajoutées dans les activités en développant un modèle de simulation et en incluant des variables stochastiques représentant des sources d'incertitudes comme une variation de l'heure d'entrée dans l'espace aérien de l'aéroport, une variation de l'heure moyenne de temps du roulage ou encore une variation dans l'heure de pushback des avions
Optimisation du réseau de routes en zone terminale by
Man Liang(
Book
)
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Congestion in Terminal Manoeuvring Area (TMA) at hub airports is the main problem in Chinese air transportation system. Facing extremely dense operations in complex TMA, we can consider reducing traffic complexity by solving all potential conflicts in advance with a feasible trajectory control for controllers, or automating a large proportion of routine operations, such as sequencing, merging and spacing. As parallel runways are a common structure of Chinese hub airports, in this thesis, we propose a novel system to integrated sequencing and merging aircraft to parallel runways. Our methodology integrates a Area Navigation (RNAV)based 3D MultiLevel and MultiPoint Merge System (MLMPMS), a hybrid heuristic optimization algorithm and a simulation module to find good, systematic, operationallyacceptable solutions. First, a Receding Horizon Control (RHC) technique is applied to divide 24hour traffic optimization problem into several sub problems. Then, in each subproblem, a tailored Simulated Annealing (SA) algorithm and a trajectory generation module worn together to find a nearoptimal solution. Our primary objective is to rapidly generate conflictfree and economical trajectories with easy, flexible and feasible control methods. Based on an initial solution, we continuously explore possible good solutions with less delay and shorter landing interval on runway. Taking Beijing Capital International Airport (BCIA) as a case to study, numerical results show that our optimization system performs well. First, it has very stable deconflict performance to handle continuously dense traffic flows. Compared with Hill Climbing (HC), the tailored SA algorithm can always guarantee a conflictfree solution not only for the mixed or segregated parallel approach (arrivals only) pattern, but also for the independent parallel operation (integrated departures and arrivals) pattern. Second, with its unique MultiLevel Point Merge (MLPM) route network, it can provide a good trajectory control solution to efficiently and economically handle different kinds of arrival flows. It can realize a shorter flying time and a nearContinuous Descent Approach (CDA) descent for arrival aircraft, compared with baseline. It also realizes an easier resequencing of aircraft with more relaxed position shifting as well, compared with conventional sequencing method. Theoretically, the Maximum Position Shifting (MPS) can be up to 6 positions, overcoming the hard constraint of 3 position shifts (MPS <= 3). Third, it is efficient for the segregated parallel approach patterns. Compared with hard constrained position shifting, which is often used in current Arrival Manager (AMAN) system and controller's manualcontrol First Come First Served (FCFS) method, it can reduce the average delay, average additional transit time in super dense arrival situations. The average time flown level per flight is less than 12% of total transit time in TMA. Fourth, in independent parallel patterns, it can provide a range of useful information concerning the associated objective value, the average flying time, crossing trajectories in hot spots between arrivals and departures, the efficiency of using different designed sequencing legs in MLPM route network
2 editions published in 2018 in English and held by 2 WorldCat member libraries worldwide
Congestion in Terminal Manoeuvring Area (TMA) at hub airports is the main problem in Chinese air transportation system. Facing extremely dense operations in complex TMA, we can consider reducing traffic complexity by solving all potential conflicts in advance with a feasible trajectory control for controllers, or automating a large proportion of routine operations, such as sequencing, merging and spacing. As parallel runways are a common structure of Chinese hub airports, in this thesis, we propose a novel system to integrated sequencing and merging aircraft to parallel runways. Our methodology integrates a Area Navigation (RNAV)based 3D MultiLevel and MultiPoint Merge System (MLMPMS), a hybrid heuristic optimization algorithm and a simulation module to find good, systematic, operationallyacceptable solutions. First, a Receding Horizon Control (RHC) technique is applied to divide 24hour traffic optimization problem into several sub problems. Then, in each subproblem, a tailored Simulated Annealing (SA) algorithm and a trajectory generation module worn together to find a nearoptimal solution. Our primary objective is to rapidly generate conflictfree and economical trajectories with easy, flexible and feasible control methods. Based on an initial solution, we continuously explore possible good solutions with less delay and shorter landing interval on runway. Taking Beijing Capital International Airport (BCIA) as a case to study, numerical results show that our optimization system performs well. First, it has very stable deconflict performance to handle continuously dense traffic flows. Compared with Hill Climbing (HC), the tailored SA algorithm can always guarantee a conflictfree solution not only for the mixed or segregated parallel approach (arrivals only) pattern, but also for the independent parallel operation (integrated departures and arrivals) pattern. Second, with its unique MultiLevel Point Merge (MLPM) route network, it can provide a good trajectory control solution to efficiently and economically handle different kinds of arrival flows. It can realize a shorter flying time and a nearContinuous Descent Approach (CDA) descent for arrival aircraft, compared with baseline. It also realizes an easier resequencing of aircraft with more relaxed position shifting as well, compared with conventional sequencing method. Theoretically, the Maximum Position Shifting (MPS) can be up to 6 positions, overcoming the hard constraint of 3 position shifts (MPS <= 3). Third, it is efficient for the segregated parallel approach patterns. Compared with hard constrained position shifting, which is often used in current Arrival Manager (AMAN) system and controller's manualcontrol First Come First Served (FCFS) method, it can reduce the average delay, average additional transit time in super dense arrival situations. The average time flown level per flight is less than 12% of total transit time in TMA. Fourth, in independent parallel patterns, it can provide a range of useful information concerning the associated objective value, the average flying time, crossing trajectories in hot spots between arrivals and departures, the efficiency of using different designed sequencing legs in MLPM route network
Modelling fatigue spectra of aircraft structure under gust loads by
Thomas Reytier(
Book
)
2 editions published in 2012 in English and held by 2 WorldCat member libraries worldwide
This thesis is dedicated to the fatigue and damage tolerance analysis of the aircraft structures under gust loads. The fatigue and damage tolerance analysis is a significant issue in the aircraft structure design. It aims at defining the inspection program of the aircraft structure in order to ensure its safety through its entire life. The first part reviews the stateoftheart in the various involved topics for the global process for fatigue analysis of aircraft structure under gust loads: the atmospheric turbulence modelling, the load and stress computation by a finite element analysis, the generation of the fatigue spectrum and at the end, the fatigue and damage tolerance analysis. The second part presents the whole process currently implemented at Airbus. The main strengths and weaknesses are pointed out and this enables the identification of several improvement axes. From the continuous turbulence model based on the Von Karman Power Spectral Density(PSD), the computed stresses are included according to statistics established from inflight measurements in the fatigue spectrum in order to build a stress cycle sequence. The input data for the fatigue and damage tolerance analysis are obtained from the definition of the various fatigue mission profiles, the unitary stress values, the dynamic response of the structure and the turbulence statistics. In the third part,a new methodology is presented in order to obtaine efficiently and accurately the temporal stress sequences due to the atmospheric turbulence. This method relies on new results enabling the generation of correlated time signals from the PSD functions. First, the PSD of the various stress components are directly obtained from the Von Karman PSD via a finite element analysis. Then, the correlated temporal stress sequences are generated and distributed in the fatigue spectrum according to the turbulence intensity statistical law. This new process enables the improvement of the stress computation and the fatigue spectrum generation. It replaces the turbulence statistics by stress exceedance statistics which are defined by an analytical formula in a reasonably conservative way. In addition, the lead time to build the input data for the fatigue and damage tolerance analysis is significantly reduced. Results from the fatigue and damage tolerance analysis are presented in order to highlight the quality of the improved processes both in terms of accuracy and lead time
2 editions published in 2012 in English and held by 2 WorldCat member libraries worldwide
This thesis is dedicated to the fatigue and damage tolerance analysis of the aircraft structures under gust loads. The fatigue and damage tolerance analysis is a significant issue in the aircraft structure design. It aims at defining the inspection program of the aircraft structure in order to ensure its safety through its entire life. The first part reviews the stateoftheart in the various involved topics for the global process for fatigue analysis of aircraft structure under gust loads: the atmospheric turbulence modelling, the load and stress computation by a finite element analysis, the generation of the fatigue spectrum and at the end, the fatigue and damage tolerance analysis. The second part presents the whole process currently implemented at Airbus. The main strengths and weaknesses are pointed out and this enables the identification of several improvement axes. From the continuous turbulence model based on the Von Karman Power Spectral Density(PSD), the computed stresses are included according to statistics established from inflight measurements in the fatigue spectrum in order to build a stress cycle sequence. The input data for the fatigue and damage tolerance analysis are obtained from the definition of the various fatigue mission profiles, the unitary stress values, the dynamic response of the structure and the turbulence statistics. In the third part,a new methodology is presented in order to obtaine efficiently and accurately the temporal stress sequences due to the atmospheric turbulence. This method relies on new results enabling the generation of correlated time signals from the PSD functions. First, the PSD of the various stress components are directly obtained from the Von Karman PSD via a finite element analysis. Then, the correlated temporal stress sequences are generated and distributed in the fatigue spectrum according to the turbulence intensity statistical law. This new process enables the improvement of the stress computation and the fatigue spectrum generation. It replaces the turbulence statistics by stress exceedance statistics which are defined by an analytical formula in a reasonably conservative way. In addition, the lead time to build the input data for the fatigue and damage tolerance analysis is significantly reduced. Results from the fatigue and damage tolerance analysis are presented in order to highlight the quality of the improved processes both in terms of accuracy and lead time
Classification en espaces fonctionnels utilisant la norme BV avec applications aux images ophtalmologiques et à la complexité
du trafic aérien by
Bang Giang Nguyen(
Book
)
2 editions published between 2014 and 2015 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we deal with two different problems using Total Variation concept. The first problem concerns the classification of vasculitis in multiple sclerosis fundus angiography, aiming to help ophthalmologists to diagnose such autoimmune diseases. It also aims at determining potential angiography details in intermediate uveitis in order to help diagnosing multiple sclerosis. The second problem aims at developing new airspace congestion metric, which is an important index that is used for improving Air Traffic Management (ATM) capacity. In the first part of this thesis, we provide preliminary knowledge required to solve the abovementioned problems. First, we present an overview of the Total Variation and express how it is used in our methods. Then, we present a tutorial on Support Vector Machines (SVMs) which is a learning algorithm used for classification and regression. In the second part of this thesis, we first provide a review of methods for segmentation and measurement of blood vessel in retinal image that is an important step in our method. Then, we present our proposed method for classification of retinal images. First, we detect the diseased region in the pathological images based on the computation of BV norm at each point along the centerline of the blood vessels. Then, to classify the images, we introduce a feature extraction strategy to generate a set of feature vectors that represents the input image set for the SVMs. After that, a standard SVM classifier is applied in order to classify the images. Finally, in the third part of this thesis, we address two applications of TV in the ATM domain. In the first application, based on the ideas developed in the second part, we introduce a methodology to extract the main air traffic flows in the airspace. Moreover, we develop a new airspace complexity indicator which can be used to organize air traffic at macroscopic level. This indicator is then compared to the regular density metric which is computed just by counting the number of aircraft in the airspace sector. The second application is based on a dynamical system model of air traffic. We propose a method for developing a new traffic complexity metric by computing the local vectorial total variation norm of the relative deviation vector field. Its aim is to reduce complexity. Three different traffic situations are investigated to evaluate the fitness of the proposed method
2 editions published between 2014 and 2015 in English and held by 2 WorldCat member libraries worldwide
In this thesis, we deal with two different problems using Total Variation concept. The first problem concerns the classification of vasculitis in multiple sclerosis fundus angiography, aiming to help ophthalmologists to diagnose such autoimmune diseases. It also aims at determining potential angiography details in intermediate uveitis in order to help diagnosing multiple sclerosis. The second problem aims at developing new airspace congestion metric, which is an important index that is used for improving Air Traffic Management (ATM) capacity. In the first part of this thesis, we provide preliminary knowledge required to solve the abovementioned problems. First, we present an overview of the Total Variation and express how it is used in our methods. Then, we present a tutorial on Support Vector Machines (SVMs) which is a learning algorithm used for classification and regression. In the second part of this thesis, we first provide a review of methods for segmentation and measurement of blood vessel in retinal image that is an important step in our method. Then, we present our proposed method for classification of retinal images. First, we detect the diseased region in the pathological images based on the computation of BV norm at each point along the centerline of the blood vessels. Then, to classify the images, we introduce a feature extraction strategy to generate a set of feature vectors that represents the input image set for the SVMs. After that, a standard SVM classifier is applied in order to classify the images. Finally, in the third part of this thesis, we address two applications of TV in the ATM domain. In the first application, based on the ideas developed in the second part, we introduce a methodology to extract the main air traffic flows in the airspace. Moreover, we develop a new airspace complexity indicator which can be used to organize air traffic at macroscopic level. This indicator is then compared to the regular density metric which is computed just by counting the number of aircraft in the airspace sector. The second application is based on a dynamical system model of air traffic. We propose a method for developing a new traffic complexity metric by computing the local vectorial total variation norm of the relative deviation vector field. Its aim is to reduce complexity. Three different traffic situations are investigated to evaluate the fitness of the proposed method
Progrès en tomographie par synthèse de Fourier by
Abdelhadi El Asmai(
Book
)
2 editions published in 2011 in French and held by 2 WorldCat member libraries worldwide
Tomographic image reconstruction is used to visualize 3D distribution of a radiopharmaceutical inside a patient's body from a series of 2D images taken under various incidences. In these last years significant progress were obtained by taking into account more realistic model of image acquisition system, which includes in particular the impulse response of the camera and other factors of image degradation. However, from a mathematical viewpoint the problem is an illposed inverse problem. In this thesis we considered a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to the Fourier synthesis. It refines previous contributions, in which the preprocessing of the data was performed according to the Fourier slice theorem. Since real models must account for the geometrical system response and possibly Compton scattering and attenuation, The Fourier slice theorem does not apply, yielding redefinition of the preprocessing. In general, the latter is not explicit, and must be performed numerically. The most natural choice of preprocessing involves the computation of unstable solutions. A proximal strategy is proposed for this step, which allows for accurate computations and preserves global stability of the reconstruction process
2 editions published in 2011 in French and held by 2 WorldCat member libraries worldwide
Tomographic image reconstruction is used to visualize 3D distribution of a radiopharmaceutical inside a patient's body from a series of 2D images taken under various incidences. In these last years significant progress were obtained by taking into account more realistic model of image acquisition system, which includes in particular the impulse response of the camera and other factors of image degradation. However, from a mathematical viewpoint the problem is an illposed inverse problem. In this thesis we considered a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to the Fourier synthesis. It refines previous contributions, in which the preprocessing of the data was performed according to the Fourier slice theorem. Since real models must account for the geometrical system response and possibly Compton scattering and attenuation, The Fourier slice theorem does not apply, yielding redefinition of the preprocessing. In general, the latter is not explicit, and must be performed numerically. The most natural choice of preprocessing involves the computation of unstable solutions. A proximal strategy is proposed for this step, which allows for accurate computations and preserves global stability of the reconstruction process
Contributions à la tomographie thermoacoustique modélisation et inversion by Xavier Bonnefond(
)
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
ThermoAcoustic Tomography (TAT) is a medical imaging technique using the pressure wave generated by a body illuminated by an electromagnetic pulse. Since the acoustic signal is recorded around the body, the resulting inverse problem can be formulated as follows : from the knowledge of a solution of the wave equation on some hypersurface, reconstruct its initial condition. Despite several inversion formulas, so far no efficient procedure, taking partial data and damping into account, is known. As well as a state of the art, this work is dedicated to the introduction of a variational approach for the TAT problem. We studied the regularization by mollification, which consists in replacing the original object by a limited resolution version of it, and treating the data so that they fit this new objective. Moreover, we used a noise level estimation provided by the GolubKahan bidiagonalization process to allow an accurate regularization parameter selection. In the second part of this work, we investigate the usual TAT model and put forward some damped wave equation with a finite wave front speed. This improvement yields to the use of the Back and Forth Nudging (BFN) method, which was first implemented for data assimilation purposes, to invert the TAT problem. This technique provides a sequence of approximations of the solution by iterating forward and backward implementations of a wave equation including a newtonian recall to the data. This method, which is proved to be convergent in an ideal framework, leads to convincing results in both partial data and attenuated wave cases
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
ThermoAcoustic Tomography (TAT) is a medical imaging technique using the pressure wave generated by a body illuminated by an electromagnetic pulse. Since the acoustic signal is recorded around the body, the resulting inverse problem can be formulated as follows : from the knowledge of a solution of the wave equation on some hypersurface, reconstruct its initial condition. Despite several inversion formulas, so far no efficient procedure, taking partial data and damping into account, is known. As well as a state of the art, this work is dedicated to the introduction of a variational approach for the TAT problem. We studied the regularization by mollification, which consists in replacing the original object by a limited resolution version of it, and treating the data so that they fit this new objective. Moreover, we used a noise level estimation provided by the GolubKahan bidiagonalization process to allow an accurate regularization parameter selection. In the second part of this work, we investigate the usual TAT model and put forward some damped wave equation with a finite wave front speed. This improvement yields to the use of the Back and Forth Nudging (BFN) method, which was first implemented for data assimilation purposes, to invert the TAT problem. This technique provides a sequence of approximations of the solution by iterating forward and backward implementations of a wave equation including a newtonian recall to the data. This method, which is proved to be convergent in an ideal framework, leads to convincing results in both partial data and attenuated wave cases
Quelques contributions aux problèmes inverses de synthèse de Fourier by
Yaowaluk Saesor(
Book
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
Approche novatrice pour la conception et l'exploitation d'avions écologiques by Sylvain Prigent(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
L'objectif de ce travail de thèse est de poser, d'analyser et de résoudre le problème multidisciplinaire et multiobjectif de la conception d'avions plus écologiques et plus économiques. Dans ce but, les principaux drivers de l'optimisation des performances d'un avion seront: la géométrie de l'avion, son moteur ainsi que son profil de mission, autrement dit sa trajectoire. Les objectifs à minimiser considérés sont la consommation de carburant, l'impact climatique et le coût d'opération de l'avion. L'étude sera axée sur la stratégie de recherche de compromis entre ces objectifs, afin d'identifier les configurations d'avions optimales selon le critère sélectionné et de proposer une analyse de ces résultats. L'incertitude présente au niveau des modèles utilisés sera prise en compte par des méthodes rigoureusement sélectionnées. Une configuration d'avion hybride est proposée pour atteindre l'objectif de réduction d'impact climatique
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
L'objectif de ce travail de thèse est de poser, d'analyser et de résoudre le problème multidisciplinaire et multiobjectif de la conception d'avions plus écologiques et plus économiques. Dans ce but, les principaux drivers de l'optimisation des performances d'un avion seront: la géométrie de l'avion, son moteur ainsi que son profil de mission, autrement dit sa trajectoire. Les objectifs à minimiser considérés sont la consommation de carburant, l'impact climatique et le coût d'opération de l'avion. L'étude sera axée sur la stratégie de recherche de compromis entre ces objectifs, afin d'identifier les configurations d'avions optimales selon le critère sélectionné et de proposer une analyse de ces résultats. L'incertitude présente au niveau des modèles utilisés sera prise en compte par des méthodes rigoureusement sélectionnées. Une configuration d'avion hybride est proposée pour atteindre l'objectif de réduction d'impact climatique
Approches basées sur DCA pour la programmation mathématique avec des contraintes d'équilibre by
Thi Minh Tam Nguyen(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
In this dissertation, we investigate approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for mathematical programs with equilibrium constraints. Being a classical and challenging topic of nonconvex optimization, and because of its many important applications, mathematical programming with equilibrium constraints has attracted the attention of many researchers since many years. The dissertation consists of four main chapters. Chapter 2 studies a class of mathematical programs with linear complementarity constraints. By using four penalty functions, we reformulate the considered problem as standard DC programs, i.e. minimizing a DC function on a convex set. The appropriate DCA schemes are developed to solve these four DC programs. Two among them are reformulated again as general DC programs (i.e. minimizing a DC function under DC constraints) in order that the convex subproblems in DCA are easier to solve. After designing DCA for the considered problem, we show how to develop these DCA schemes for solving the quadratic problem with linear complementarity constraints and the asymmetric eigenvalue complementarity problem. Chapter 3 addresses a class of mathematical programs with variational inequality constraints. We use a penalty technique to recast the considered problem as a DC program. A variant of DCA and its accelerated version are proposed to solve this DC program. As an application, we tackle the secondbest toll pricing problem with fixed demands. Chapter 4 focuses on a class of bilevel optimization problems with binary upper level variables. By using an exact penalty function, we express the bilevel problem as a standard DC program for which an efficient DCA scheme is developed. We apply the proposed algorithm to solve a maximum flow network interdiction problem. In chapter 5, we are interested in the continuous equilibrium network design problem. It was formulated as a Mathematical Program with Complementarity Constraints (MPCC). We reformulate this MPCC problem as a general DC program and then propose a suitable DCA scheme for the resulting problem
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
In this dissertation, we investigate approaches based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for mathematical programs with equilibrium constraints. Being a classical and challenging topic of nonconvex optimization, and because of its many important applications, mathematical programming with equilibrium constraints has attracted the attention of many researchers since many years. The dissertation consists of four main chapters. Chapter 2 studies a class of mathematical programs with linear complementarity constraints. By using four penalty functions, we reformulate the considered problem as standard DC programs, i.e. minimizing a DC function on a convex set. The appropriate DCA schemes are developed to solve these four DC programs. Two among them are reformulated again as general DC programs (i.e. minimizing a DC function under DC constraints) in order that the convex subproblems in DCA are easier to solve. After designing DCA for the considered problem, we show how to develop these DCA schemes for solving the quadratic problem with linear complementarity constraints and the asymmetric eigenvalue complementarity problem. Chapter 3 addresses a class of mathematical programs with variational inequality constraints. We use a penalty technique to recast the considered problem as a DC program. A variant of DCA and its accelerated version are proposed to solve this DC program. As an application, we tackle the secondbest toll pricing problem with fixed demands. Chapter 4 focuses on a class of bilevel optimization problems with binary upper level variables. By using an exact penalty function, we express the bilevel problem as a standard DC program for which an efficient DCA scheme is developed. We apply the proposed algorithm to solve a maximum flow network interdiction problem. In chapter 5, we are interested in the continuous equilibrium network design problem. It was formulated as a Mathematical Program with Complementarity Constraints (MPCC). We reformulate this MPCC problem as a general DC program and then propose a suitable DCA scheme for the resulting problem
Modelling fatigue spectra of aircraft structure under gust loads by
Thomas Reytier(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
This thesis is dedicated to the fatigue and damage tolerance analysis of the aircraft structures under gust loads. The fatigue and damage tolerance analysis is a significant issue in the aircraft structure design. It aims at defining the inspection program of the aircraft structure in order to ensure its safety through its entire life. The first part reviews the stateoftheart in the various involved topics for the global process for fatigue analysis of aircraft structure under gust loads: the atmospheric turbulence modelling, the load and stress computation by a finite element analysis, the generation of the fatigue spectrum and at the end, the fatigue and damage tolerance analysis. The second part presents the whole process currently implemented at Airbus. The main strengths and weaknesses are pointed out and this enables the identification of several improvement axes. From the continuous turbulence model based on the Von Karman Power Spectral Density(PSD), the computed stresses are included according to statistics established from inflight measurements in the fatigue spectrum in order to build a stress cycle sequence. The input data for the fatigue and damage tolerance analysis are obtained from the definition of the various fatigue mission profiles, the unitary stress values, the dynamic response of the structure and the turbulence statistics. In the third part,a new methodology is presented in order to obtaine efficiently and accurately the temporal stress sequences due to the atmospheric turbulence. This method relies on new results enabling the generation of correlated time signals from the PSD functions. First, the PSD of the various stress components are directly obtained from the Von Karman PSD via a finite element analysis. Then, the correlated temporal stress sequences are generated and distributed in the fatigue spectrum according to the turbulence intensity statistical law. This new process enables the improvement of the stress computation and the fatigue spectrum generation. It replaces the turbulence statistics by stress exceedance statistics which are defined by an analytical formula in a reasonably conservative way. In addition, the lead time to build the input data for the fatigue and damage tolerance analysis is significantly reduced. Results from the fatigue and damage tolerance analysis are presented in order to highlight the quality of the improved processes both in terms of accuracy and lead time
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
This thesis is dedicated to the fatigue and damage tolerance analysis of the aircraft structures under gust loads. The fatigue and damage tolerance analysis is a significant issue in the aircraft structure design. It aims at defining the inspection program of the aircraft structure in order to ensure its safety through its entire life. The first part reviews the stateoftheart in the various involved topics for the global process for fatigue analysis of aircraft structure under gust loads: the atmospheric turbulence modelling, the load and stress computation by a finite element analysis, the generation of the fatigue spectrum and at the end, the fatigue and damage tolerance analysis. The second part presents the whole process currently implemented at Airbus. The main strengths and weaknesses are pointed out and this enables the identification of several improvement axes. From the continuous turbulence model based on the Von Karman Power Spectral Density(PSD), the computed stresses are included according to statistics established from inflight measurements in the fatigue spectrum in order to build a stress cycle sequence. The input data for the fatigue and damage tolerance analysis are obtained from the definition of the various fatigue mission profiles, the unitary stress values, the dynamic response of the structure and the turbulence statistics. In the third part,a new methodology is presented in order to obtaine efficiently and accurately the temporal stress sequences due to the atmospheric turbulence. This method relies on new results enabling the generation of correlated time signals from the PSD functions. First, the PSD of the various stress components are directly obtained from the Von Karman PSD via a finite element analysis. Then, the correlated temporal stress sequences are generated and distributed in the fatigue spectrum according to the turbulence intensity statistical law. This new process enables the improvement of the stress computation and the fatigue spectrum generation. It replaces the turbulence statistics by stress exceedance statistics which are defined by an analytical formula in a reasonably conservative way. In addition, the lead time to build the input data for the fatigue and damage tolerance analysis is significantly reduced. Results from the fatigue and damage tolerance analysis are presented in order to highlight the quality of the improved processes both in terms of accuracy and lead time
Progrès en tomographie par synthèse de Fourier by
Abdelhadi El Asmai(
)
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
Tomographic image reconstruction is used to visualize 3D distribution of a radiopharmaceutical inside a patient's body from a series of 2D images taken under various incidences. In these last years significant progress were obtained by taking into account more realistic model of image acquisition system, which includes in particular the impulse response of the camera and other factors of image degradation. However, from a mathematical viewpoint the problem is an illposed inverse problem. In this thesis we considered a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to the Fourier synthesis. It refines previous contributions, in which the preprocessing of the data was performed according to the Fourier slice theorem. Since real models must account for the geometrical system response and possibly Compton scattering and attenuation, The Fourier slice theorem does not apply, yielding redefinition of the preprocessing. In general, the latter is not explicit, and must be performed numerically. The most natural choice of preprocessing involves the computation of unstable solutions. A proximal strategy is proposed for this step, which allows for accurate computations and preserves global stability of the reconstruction process
1 edition published in 2012 in French and held by 1 WorldCat member library worldwide
Tomographic image reconstruction is used to visualize 3D distribution of a radiopharmaceutical inside a patient's body from a series of 2D images taken under various incidences. In these last years significant progress were obtained by taking into account more realistic model of image acquisition system, which includes in particular the impulse response of the camera and other factors of image degradation. However, from a mathematical viewpoint the problem is an illposed inverse problem. In this thesis we considered a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to the Fourier synthesis. It refines previous contributions, in which the preprocessing of the data was performed according to the Fourier slice theorem. Since real models must account for the geometrical system response and possibly Compton scattering and attenuation, The Fourier slice theorem does not apply, yielding redefinition of the preprocessing. In general, the latter is not explicit, and must be performed numerically. The most natural choice of preprocessing involves the computation of unstable solutions. A proximal strategy is proposed for this step, which allows for accurate computations and preserves global stability of the reconstruction process
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Related Identities
 Laha, Vivek Editor
 Mishra, Shashi Kant 1967 Author Editor
 Université Toulouse 3 Paul Sabatier (1969....). Degree grantor
 Mishra, S. K. Editor
 Delahaye, Daniel (19......; enseignantchercheur) Thesis advisor
 École doctorale AéronautiqueAstronautique (Toulouse) Other
 École Nationale de l'Aviation Civile (Toulouse) Other
 Dedieu, JeanPierre (19..2012)
 Abgrall, Sophie
 Aussel, Didier
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