WAVELET REGULARIZATION OF A FOURIER-GALERKIN METHOD FOR SOLVING THE 2D INCOMPRESSIBLE EULER EQUATIONS

International audienceWe employ a Fourier-Galerkin method to solve the 2D incompressible Euler equations, and study several ways to regularize the solution by wavelet filtering at each timestep. Real-valued orthogonal wavelets and complex-valued wavelets are considered, combined with either linear or non-linear filtering. The results are compared with those obtained via classical viscous and hyperviscous regularization methods. Wavelet regularization using complex-valued wavelets performs as well in terms of L2 convergence rate to the reference solution. The compression rate for homogeneous 2D turbulence is around 3 for this method, suggesting that memory and CPU time could be reduced in an adaptive wavelet computation. Our results also suggest L2 convergence to the reference solution without any regularization, in contrast to what is obtained for the 1D Burgers equation

Untersuchung von Verarbeitungsalgorithmen zur automatischen Auswertung neuronaler Signale aus Multielektroden-Arrays

Mit Hilfe von Multielektroden-Arrays (MEAs) können viele Zellen gleichzeitig kontaktiert und deren elektrische Aktivität abgeleitet werden. Für die weitere Analyse müssen die abgeleiteten Signale in ihre Einzelbestandteile zerlegt werden. Dieser Vorgang wird als Spike Sorting bezeichnet. In der vorliegenden Arbeit werden Ansätze für ein vollständig automatisiertes Spike Sorting vorgestellt und untersucht. Dabei werden Verfahren aufgezeigt, die mit Hilfe von adaptiven Verfahren die abgeleiteten Zellsignale optimal filtern und automatisch in deren Einzelkomponenten zerlegen

Parallel Wavelet Transform for Large Scale Image Processing

In this paper we discuss several issues relevant to the parallel implementation of a 2-D Discrete Wavelet Transform (DWT) on general purpose multiprocessors. Our interest in this transform is motivated by its usage in an image fusion application which has to manage large image sizes, making parallel computing highly advisable. We have also paid much attention to memory hierarchy exploitation, since it has a tremendous impact on performance due to the lack of spatial locality when the DWT processes image columns