2007, Polzehl, J., Tabelow, K.

Digital imaging has become omnipresent in the past years with a bulk of applications ranging from medical imaging to photography. When pushing the limits of resolution and sensitivity noise has ever been a major issue. However, commonly used non-adaptive filters can do noise reduction at the cost of a reduced effective spatial resolution only. Here we present a new package adimpro for R, which implements the propagationseparation approach by (Polzehl arid Spokoiriy 2006) for smoothing digital images. This method naturally adapts to different structures of different size in the image and thus avoids oversmoothing edges and fine structures. We extend the method for imaging data with spatial correlation. Furthermore we show how the estimation of the dependence between variance and mean value can be included. We illustrate the use of the package through some examples.

2008, Radziunas, Mindaugas, Tronciu, Vasile Z., Bandelow, Uwe, Lichtner, Mark, Spreemann, Martin, Wenzel, Hans

Theoretical and experimental investigations have been carried out to study the spectral and spatial behavior of monolithically integrated distributed-feedback tapered master-oscillators power-amplifiers emitting around 973 nm. Introduction of self and cross heating effects and the analysis of longitudinal optical modes allows us to explain experimental results. The results show a good qualitative agreement between measured and calculated characteristics.

2006, Fleischmann, Klaus, Wachtel, Vitali

In this paper we study the large deviation behavior of sums of i.i.d. random variables Xi defined on a supercritical Galton-Watson process Z. We assume the finiteness of the moments EX2 1 and EZ1 log Z1 . The underlying interplay of the partial sums of the Xi and the lower deviation probabilities of Z is clarified. Here we heavily use lower deviation probability results on Z we recently published in [FW06].

2006, Rjasanow, Sergej, Wagner, Wolfgang

The paper is concerned with the numerical treatment of the uniformly heated inelastic Boltzmann equation by the direct simulation Monte Carlo (DSMC) method. This technique is presently the most widely used numerical method in kinetic theory. We consider three modifications of the DSMC method and study them with respect to their efficiency and convergence properties. Convergence is investigated both with respect to the number of particles and to the time step. The main issue of interest is the time step discretization error due to various splitting strategies. A scheme based on the Strang-splitting strategy is shown to be of second order with respect to time step, while there is only first order for the commonly used Euler-splitting scheme. On the other hand, a no-splitting scheme based on appropriate Markov jump processes does not produce any time step error. It is established in numerical examples that the no-splitting scheme is about two orders of magnitude more efficient than the Euler-splitting scheme. The Strang-splitting scheme reaches almost the same level of efficiency compared to the no-splitting scheme, since the deterministic time step error vanishes sufficiently fast.

2008, Divine, D.V., Polzehl, J., Godtliebsen, F.

The paper presents an approach to estimate parameters of a local stationary AR(1) time series model by maximization of a local likelihood function. The method is based on a propagation-separation procedure that leads to data dependent weights defining the local model. Using free propagation of weights under homogeneity, the method is capable of separating the time series into intervals of approximate local stationarity. Parameters in different regions will be significantly different. Therefore the method also serves as a test for a stationary AR(1) model. The performance of the method is illustrated by applications to both synthetic data and real time-series of reconstructed NAO and ENSO indices and GRIP stable isotopes.

2006, Lefter, Cǎtǎlin

We prove the local exponential stabilizability for the MHD system, with internally distributed feedback controllers. These controllers take values in a finite dimensional space which is the unstable manifold of the elliptic part of the linearized operator. The stabilization of the linear system is derived using a unique continuation property for systems of parabolic and elliptic equations, as well as the equivalence between controllability and feedback stabilizability in the case of finite dimensional systems. The feedback that stabilizes the linearized system is also stabilizing the nonlinear system in the domain of a fractional power of the elliptic operator.

2008, Gloger, Oliver, Ehrhardt, Matthias, Dietrich, Thore, Hellwich, Olaf, Graf, Kristof, Nagel, Eike

In this work we propose an adapted level set segmentation technique for the recognition of atherosclerotic plaque tissue on magnetic resonance images. The images are 2dimensional crosssectional images and show different profiles from ex-vivo human vessels with high variability in vessel shape. We used a curvature based anisotropic diffusion technique to denoise the magnetic resonance images. The segmentation technique is subdivided into three level set steps. Hence, the result of every phase serves as constructive knowledge for the next level set step. By analyzing and combining carefully all available channel information during the first and second step we are capable to delineate exactly the vessel walls by using and adapting two well-known level set segmentation techniques. The third step controls an enclosing level set which separates the plaque patterns from healthy media tissue. In this step we introduce a local weighting concept to consider intensity information for conspicuous plaque patterns. Furthermore, we propose the introduction of a maximal shrinking distance for the third level set in the vessel wall and compare the results of the local weighting algorithm with and without the concept of the maximal shrinking distance. The incorporation of locally weighted intensity information into the level set method allows the algorithm to automatically distinguish plaque from healthy media tissue. The knowledge of the maximal shrinking distance can improve the segmentation results and enables to delineate tissue areas where plaque is most likely.

2006, Hüttl, Bernd

Inherent Q-switching as a source of intra-cavity pulse energy modulations, i.e. unwanted amplitude noise, is still a challenging task in order to fabricate monolithic mode-locked semiconductor lasers in view of different commercial applications. In this paper, the results of experimental investigations on the influence of the quantum well number on the occurrence and suppression of Q-switching in 40 GHz mode-locked multiple quantum well buried heterostructure lasers are presented. Improved mode-locked lasers emit short optical pulses (<=1.6 ps) with very low amplitude noise (1-2%) and timing jitter (50-100 fs).

2008, Reyes, Juan Carlos de los, Meyer, Christian, Vexler, Boris

An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerened with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the $L^infty$-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the $L^infty$-finite-element-error can be verified for different numerical settings. The theoretical results are confirmed by numerical examples.

2007, Gajewski, Herbert, Griepentrog, J.A., Mielke, A., Beuthan, J., Zabarylo, U., Minet, O.

Optical imaging in biomedicine is governed by the light absorption and scattering interaction on microscopic and macroscopic constituents in the medium. Therefore, light scattering characteristics of human tissue correlates with the stage of some diseases. In the near infrared range the scattering event with the coefficient approximately two orders of magnitude greater than absorption plays a dominant role. The potential of an experimental laser diode based setup for the transillumination of rheumatoid finger joints and the pattern of the stray light detection are demonstrated. For evaluating the scattering light images a new non-local image segmentation method is presented. Regarding a noisy picture as a multicomponent mixture of gray scaled particles, this method minimizes a non-convex free energy functional under the constraint of mass conservation of the components. Contrary to constructing equilibrium distributions as steady states of an adequate evolution equation, a direct descent method for the free energy is used to separate the components of the image.