Viability of Numerical Full-Wave Techniques in Telecommunication Channel Modelling

In telecommunication channel modelling the wavelength is small compared to the physical features of interest, therefore deterministic ray tracing techniques provide solutions that are more efficient, faster and still within time constraints than current numerical full-wave techniques. Solving fundamental Maxwell's equations is at the core of computational electrodynamics and best suited for modelling electrical field interactions with physical objects where characteristic dimensions of a computing domain is on the order of a few wavelengths in size. However, extreme communication speeds, wireless access points closer to the user and smaller pico and femto cells will require increased accuracy in predicting and planning wireless signals, testing the accuracy limits of the ray tracing methods. The increased computing capabilities and the demand for better characterization of communication channels that span smaller geographical areas make numerical full-wave techniques attractive alternative even for larger problems. The paper surveys ways of overcoming excessive time requirements of numerical full-wave techniques while providing acceptable channel modelling accuracy for the smallest radio cells and possibly wider. We identify several research paths that could lead to improved channel modelling, including numerical algorithm adaptations for large-scale problems, alternative finite-difference approaches, such as meshless methods, and dedicated parallel hardware, possibly as a realization of a dataflow machine

Radial Basis Functions: Biomedical Applications and Parallelization

Radial basis function (RBF) is a real-valued function whose values depend only on the distances between an interpolation point and a set of user-specified points called centers. RBF interpolation is one of the primary methods to reconstruct functions from multi-dimensional scattered data. Its abilities to generalize arbitrary space dimensions and to provide spectral accuracy have made it particularly popular in different application areas, including but not limited to: finding numerical solutions of partial differential equations (PDEs), image processing, computer vision and graphics, deep learning and neural networks, etc. The present thesis discusses three applications of RBF interpolation in biomedical engineering areas: (1) Calcium dynamics modeling, in which we numerically solve a set of PDEs by using meshless numerical methods and RBF-based interpolation techniques; (2) Image restoration and transformation, where an image is restored from its triangular mesh representation or transformed under translation, rotation, and scaling, etc. from its original form; (3) Porous structure design, in which the RBF interpolation used to reconstruct a 3D volume containing porous structures from a set of regularly or randomly placed points inside a user-provided surface shape. All these three applications have been investigated and their effectiveness has been supported with numerous experimental results. In particular, we innovatively utilize anisotropic distance metrics to define the distance in RBF interpolation and apply them to the aforementioned second and third applications, which show significant improvement in preserving image features or capturing connected porous structures over the isotropic distance-based RBF method. Beside the algorithm designs and their applications in biomedical areas, we also explore several common parallelization techniques (including OpenMP and CUDA-based GPU programming) to accelerate the performance of the present algorithms. In particular, we analyze how parallel programming can help RBF interpolation to speed up the meshless PDE solver as well as image processing. While RBF has been widely used in various science and engineering fields, the current thesis is expected to trigger some more interest from computational scientists or students into this fast-growing area and specifically apply these techniques to biomedical problems such as the ones investigated in the present work

Iterative Solvers for Physics-based Simulations and Displays

La génération d’images et de simulations réalistes requiert des modèles complexes pour capturer tous les détails d’un phénomène physique. Les équations mathématiques qui composent ces modèles sont compliquées et ne peuvent pas être résolues analytiquement. Des procédures numériques doivent donc être employées pour obtenir des solutions approximatives à ces modèles. Ces procédures sont souvent des algorithmes itératifs, qui calculent une suite convergente vers la solution désirée à partir d’un essai initial. Ces méthodes sont une façon pratique et efficace de calculer des solutions à des systèmes complexes, et sont au coeur de la plupart des méthodes de simulation modernes. Dans cette thèse par article, nous présentons trois projets où les algorithmes itératifs jouent un rôle majeur dans une méthode de simulation ou de rendu. Premièrement, nous présentons une méthode pour améliorer la qualité visuelle de simulations fluides. En créant une surface de haute résolution autour d’une simulation existante, stabilisée par une méthode itérative, nous ajoutons des détails additionels à la simulation. Deuxièmement, nous décrivons une méthode de simulation fluide basée sur la réduction de modèle. En construisant une nouvelle base de champ de vecteurs pour représenter la vélocité d’un fluide, nous obtenons une méthode spécifiquement adaptée pour améliorer les composantes itératives de la simulation. Finalement, nous présentons un algorithme pour générer des images de haute qualité sur des écrans multicouches dans un contexte de réalité virtuelle. Présenter des images sur plusieurs couches demande des calculs additionels à coût élevé, mais nous formulons le problème de décomposition des images afin de le résoudre efficacement avec une méthode itérative simple.Realistic computer-generated images and simulations require complex models to properly capture the many subtle behaviors of each physical phenomenon. The mathematical equations underlying these models are complicated, and cannot be solved analytically. Numerical procedures must thus be used to obtain approximate solutions. These procedures are often iterative algorithms, where an initial guess is progressively improved to converge to a desired solution. Iterative methods are a convenient and efficient way to compute solutions to complex systems, and are at the core of most modern simulation methods. In this thesis by publication, we present three papers where iterative algorithms play a major role in a simulation or rendering method. First, we propose a method to improve the visual quality of fluid simulations. By creating a high-resolution surface representation around an input fluid simulation, stabilized with iterative methods, we introduce additional details atop of the simulation. Second, we describe a method to compute fluid simulations using model reduction. We design a novel vector field basis to represent fluid velocity, creating a method specifically tailored to improve all iterative components of the simulation. Finally, we present an algorithm to compute high-quality images for multifocal displays in a virtual reality context. Displaying images on multiple display layers incurs significant additional costs, but we formulate the image decomposition problem so as to allow an efficient solution using a simple iterative algorithm

Physics-Based Probabilistic Motion Compensation of Elastically Deformable Objects

A predictive tracking approach and a novel method for visual motion compensation are introduced, which accurately reconstruct and compensate the deformation of the elastic object, even in the case of complete measurement information loss. The core of the methods involves a probabilistic physical model of the object, from which all other mathematical models are systematically derived. Due to flexible adaptation of the models, the balance between their complexity and their accuracy is achieved

Myocardial Motion Analysis for Determination of Tei-Index of Human Heart

The Tei index, an important indicator of heart function, lacks a direct method to compute because it is difficult to directly evaluate the isovolumic contraction time (ICT) and isovolumic relaxation time (IRT) from which the Tei index can be obtained. In this paper, based on the proposed method of accurately measuring the cardiac cycle physical phase, a direct method of calculating the Tei index is presented. The experiments based on real heart medical images show the effectiveness of this method. Moreover, a new method of calculating left ventricular wall motion amplitude is proposed and the experiments show its satisfactory performance

Efficient global illumination calculation for inverse lighting problems

La luz es un elemento clave en la manera en que percibimos y experimentamos nuestro entorno. Como tal, es un objeto mas a modelar en el proceso de diseño, de forma similar a como ocurre con las formas y los materiales. Las intenciones de iluminacion (LI) son los objetivos y restricciones que el diseñador pretende alcanzar en el proceso del diseño de iluminaci´on: ¿qué superficies se deben iluminar con luz natural y cuales con luz artificial?, ¿qué zonas deben estar en sombra?, ¿cuales son las intensidades maximas y mínimas permitidas? Satisfacer las LI consiste en encontrar la ubicacion, forma e intensidad adecuada de las fuentes luminosas. Este tipo de problemas se define como un problema inverso de iluminacion (ILP) que se resuelve con tecnicas de optimizacion. En el contexto anterior, el objetivo de esta tesis consiste en proponer metodos eficientes para resolver ILP. Este objetivo es motivado por la brecha percibida entre los problemas habituales de diseño de iluminacion y las herramientas computacionales existentes para su resolucion. Las herramientas desarrolladas por la industria se especializan en evaluar configuraciones de iluminacion previamente diseñadas, y las desarrolladas por la academia resuelven problemas relativamente sencillos a costos elevados. Las propuestas cubren distintos aspectos del proceso de optimizacion, que van desde la formulacion del problema a su resolucion. Estan desarrolladas para el caso en que las superficies poseen reflexion e iluminacion difusas y se basan en el calculo de una aproximacion de rango bajo de la matriz de radiosidad. Algunos resultados obtenidos son: el calculo acelerado de la radiosidad de la escena en una unidad de procesamiento gr´afico (GPU); el uso de la heuristica \201Cvariable neighborhood search\201D (VNS) para la resolucion de ILP; el planteo de una estructura multinivel para tratar ILP de forma escalonada; y el uso de tecnicas para optimizar la configuracion de filtros de luz. Otros resultados obtenidos se basan en la formulacion de las LI en funcion de la media y desviacion estandar de las radiosidades halladas. Se propone un metodo para generar LI que contengan esos parametros estadisticos, y otro metodo para acelerar su evaluacion. Con estos resultados se logran tiempos de respuesta interactivos. Por último, las tecnicas anteriores adolecen de una etapa de pre-cómputo relativamente costosa, por tanto se propone acelerar el calculo de la inversa de la matriz de radiosidad a partir de una muestra de factores de forma. Los métodos aquí presentados fueron publicados en seis articulos, tres de ellos en congresos internacionales y tres en revistas arbitradas.Light is a key element that influences the way we perceive and experience our environment. As such, light is an object to be modeled in the design process, as happens with the forms and materials. The lighting intentions (LI) are the objectives and constraints that designers want to achieve in the process of lighting design: which surfaces should be illuminated with natural and which with artificial light?, which surfaces should be in shadow?, which are the maximum and minimum intensities allowed? The fulfillment of the LI consists in finding the location, shape and intensity appropriate for the light sources. This problem is defined as an inverse lighting problem (ILP), solved by optimization techniques. In the above context, the aim of this thesis is the proposal of efficient methods to solve ILP. This objective is motivated by the perceived gap between the usual problems of lighting design, and the computational tools developed for its resolution. The tools developed by the industry specialize in evaluating previously designed lighting configurations, and those developed by the academia solve relatively simple problems at a high computational cost. The proposals cover several aspects of the optimization process, ranging from the formulation of the problem to its resolution. They are developed for the case in which the surfaces have Lambertian reflection and illumination, and are based on the calculation of a low rank approximation to the radiosity matrix. Some results are: rapid calculation of radiosity of the scene in a graphics processing unit (GPU), the use of heuristics “variable neighborhood search” (VNS) for solving ILP, the proposition of a multilevel structure to solve ILP in a stepwise approach, and the use of these techniques to optimize the configuration of light filters. Other results are based on the formulation of LI that use the mean and standard deviation of the radiosity values found. A method is proposed for generating LI containing these parameters, and another method is developed to speed up their evaluations. With these results we achieve interactive response times. Finally, the above techniques suffer from a costly pre-computing stage and therefore, a method is proposed to accelerate the calculation of the radiosity inverse matrix based on a sample of the form factors. The methods presented here were published in six articles, three of them at international conferences and three in peer reviewed journals