Decomposition of stochastic properties within images using non-parametric methods

This paper discusses the application of three different nonparametric methods for decomposing images into regions which exhibit special stochastic properties, together with the constituent components of the stochastic. These are: (1) order statistics in connection with steps in the empirical estimated distribution functions; (2) detection of stochastic information within an image by hypothesis testing; and (3) rank order statistics to decompose the different types of stochastic within an image. The decomposition is used to isolate different image regions and to estimate the processes which are the constituent stochastic components. In order to achieve this, decisions based upon membership relations are employed and adapted thresholds used. The thresholds are obtained by the ordering of terms calculated by stochastic estimation methods together with one of the aforementioned technique

Ionization and bound-state relativistic quantum dynamics in laser-driven multiply charged ions

Die Wechselwirkung von ultra-starken Laserfeldern mit mehrfach geladenen wasserstoffartigen Ionen lässt sich zum einen in die Ionisationsdynamik und zum anderen in die gebundene Dynamik unterteilen. Beide Bereiche werden numerisch mittels der Diracgleichung in zwei Dimensionen und der klassisch relativistischen Monte-Carlo Simulation untersucht. Zum Besseren Verständnis der zugrunde liegenden höchst nichtlinearen physikalischen Prozesse wird die Entwicklung von wohldefinierten ultra-starken Laserfeldern weiter vorangetrieben, die bestens geeignet sind um z.B. Magnetfeldeffekte des Laserfeldes zu studieren, welche eine zusätzliche Bewegung des Elektrons in die Laserpropagationsrichtung bewirken. Eine neue Methode zur sensitiven Bestimmung dieser ultra-starker Laserintensitäten vom optischen Frequenzbereich über den UV zum XUV Bereich wird in dieser Arbeit vorgestellt und angewendet. Im Bereich der gebundenen Dynamik ist die Bestimmung der Mehrphotonenübergangsmatrixelemente zwischen verschieden Zuständen mittels Rabi Oszillationen untersucht worden

Peak intensity measurement of relativistic lasers via nonlinear Thomson scattering

The measurement of peak laser intensities exceeding 10^{20} \text{W/cm^2} is in general a very challenging task. We suggest a simple method to accurately measure such high intensities up to about 10^{23} \text{W/cm^2}, by colliding a beam of ultrarelativistic electrons with the laser pulse. The method exploits the high directionality of the radiation emitted by ultrarelativistic electrons via nonlinear Thomson scattering. Initial electron energies well within the reach of laser wake-field accelerators are required, allowing in principle for an all-optical setup. Accuracies of the order of 10% are theoretically envisaged.Comment: 4 pages, 2 figure

Interference effects in above-threshold ionization from diatomic molecules: determining the internuclear separation

We calculate angle-resolved above-threshold ionization spectra for diatomic molecules in linearly polarized laser fields, employing the strong-field approximation. The interference structure resulting from the individual contributions of the different scattering scenarios is discussed in detail, with respect to the dependence on the internuclear distance and molecular orientation. We show that, in general, the contributions from the processes in which the electron is freed at one center and rescatters off the other obscure the interference maxima and minima obtained from single-center processes. However, around the boundary of the energy regions for which rescattering has a classical counterpart, such processes play a negligible role and very clear interference patterns are observed. In such energy regions, one is able to infer the internuclear distance from the energy difference between adjacent interference minima.Comment: 10 pages, 8 figures; discussions slightly modified and an additional figure inserted for clarit

Image Processing for Detection of Fuzzy Structures in Medical Images

The study of fuzzy structures in medical images is important for operation and radiotherapy planning. To study this, the fuzzy objects will be additionally described by their stochastic properties using the martingale theory in combination with fuzzy measures and fuzzy functions. The detected signal contains implicit stochastic information which is separated to get precise data about the region of interest. The applied methods and algorithms are used for the detection of tumors and nerve branches in MR, CT and PET images