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Talks and Presentations

2011

Splines of Complex Order, Fractional Operators, and Dirichlet Averages

PD Dr. Peter Massopust, Colloquiums Talk, Jacobs-University Bremen, October 24, 2011

Uncertainty relations in higher dimensions and vector valued functions

Stefan Held, GAMM Jahrestagung 2011 Graz, Austria, April 18 - 21, 2011.

Separation of Edges in X-Ray Images by Microlocal Analysis,

Martin Storath, GAMM Jahrestagung 2011 Graz, Austria, April 18 - 21, 2011.

Trennung von Kanten in Röntgenbildern

Martin Storath, 21. Rhein-Ruhr-Workshop, Pfeil Königswinter, February, 2011.

Interpolation with fundamental splines of fractional order

Dr. Peter Massopust, Invited presentation at the 9th International Conference on Sampling Theory and Applications (SampTA 2011), Nangyang Technical University in Singapore, May 2011

A sampling theorem for splines of fractional order

Dr. Peter Massopust, Invited presentation at the 82nd meeting of GAMM (Gesellschaft für Angewandte Mathematik und Mechanik) in Graz, Austria, April 2011

Oberwolfach Workshop on Operator Algebras and Representation Theory: Frames, Wavelets and Fractals

Dr. Peter Massopust, Invited research participation, Oberwolfach, March 2011

Complex spline approaches and phase information in signals and images

Prof. Dr. Brigitte Forster-Heinlein, Invited Lectures (6h) at the 16th European Intensive Course on Complex Analysis, its Generalizations and Applications, Universidade de Aveiro, Portugal, March 2011

Komplexe Spline-Ansätze und Phaseninformation in Signal- und Bilddaten

Prof. Dr. Brigitte Forster-Heinlein, Invited presentation, Universität Würzburg, March 2011

2010

Mathematical Methods in Biological Image Analysis

Prof. Dr. Brigitte Forster-Heinlein, Invited presentation, Lunch talk at the Soft Condensed Matter Group, Ludwig Maximilians Universität München, December 2010

Variations on Complex Splines

Prof. Dr. Brigitte Forster-Heinlein, Invited presentation, Second Bavaria-Québec Mathematical Meeting, Universität Würzburg, November 2010

B-Splines and Dirichlet Averages --- A complex perspective

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Göttingen, November 2010

Poster Presentation: A new framework for sparse regularization in limited angle x-ray tomography

Jürgen Frikel, IEEE International Symposium on Biomedical Imaging Pfeil, Rotterdam, The Netherlands, April 2010

We propose a new framework for limited angle tomographic reconstruction. Our approach is based on the observation that for a given acquisition geometry only a few (visible) structures of the object can be reconstructed reliably using a limited angle data set. By formulating this problem in the curvelet domain, we can characterize those curvelet coefficients which correspond to visible structures in the image domain. The integration of this information into the formulation of the reconstruction problem leads to a considerable dimensionality reduction and yields a speedup of the corresponding reconstruction algorithms.

Biomedical Image Analysis with Complex Wavelets

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Würzburg, April 2010

Eine Modifikation der Curvelet-Transformation basierend auf der Riesz-Transformation

Martin Storath, 20. Rhein-Ruhr-Workshop, Pfeil Borken, February 2010

Die kontinuierliche Curvelet-Transformation (CCT) ist eine stark richtungsselektive Multiskalen-Transformation. Sie eignet sich besonders um die Position und die Orientierung von Kurvensingularitäten in Bildern zu bestimmen. In diesem Vortrag betrachten wir die CCT aus dem Blickwinkel der Signalverarbeitung und identifizieren so die Curvelets, die Basiselemente der CCT, als analytische Signale im Sinne der partiellen Hilbert-Transformation. Diese Eigenschaft erlaubt es insbesondere, die Curvelet-Koeffizienten in Amplitude und Phase zu zerlegen. Das Konzept des auf der partiellen Hilbert-Transformation basierenden analytischen Signals hat jedoch Nachteile. Deswegen ersetzen wir dieses durch das geeignetere Konzept des monogenen Signals, welches auf der Riesz-Transformation basiert. Auf diese Weise erhalten wir neue Basiselemente, die monogenen Curvelets, mit deren Hilfe wir die monogene Curvelet-Transformation (MCT) definieren. Die MCT hat die interessante Eigenschaft, dass sie auf den groben Skalen gleich der monogenen Wavelet-Transformation ist und sich auf den feinen Skalen wie die übliche CCT verhält.

Monogenic Wavelet Frames

Stefan Held, 20. Rhein-Ruhr-Workshop, Borken, Februar 2010

Biomedical Image Analysis with Complex Wavelets

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Koblenz-Landau, Jan. 2010

Biomedical Image Analysis with Complex Wavelets

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Passau, Jan. 2010

2009

Biomedical Image Analysis with Complex Wavelets

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Greifswald, November 2009

Wavelet Denoising on the Interval with an Application to Nondestructive Testing

Dr. Peter Massopust, Invited Lecture, Denmark Technical University, Lyngby, Denmark, October 2009.

Multivariate Complex B-Splines, Dirichlet Averages, and Approximation

Dr. Peter Massopust, International Conference on Wavelets and Applications, Euler International Mathematical Institute, St. Petersburg, Russia, June 2009.

Multivariate Complex B-Splines, Dirichlet Averages, and Difference Operators

Dr. Peter Massopust, International Conference on Sampling Theory and Applications (SampTA 2009), Marseille, France, May 2009.

Poster Presentation: Double Dirichlet Averages and Complex B-Splines

Dr. Peter Massopust, International Conference on Sampling Theory and Applications (SampTA 2009), Marseille, France, May 2009.

Biomedical Image Analysis with Complex Wavelets

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Lübeck, March 2009

Research Mini-Workshop on Coxeter Groups and Wavelet Sets

Dr. Peter Massopust, Texas A & M University, Texas, March/April 2009.

Complex B-Splines: Thema and Applications

Dr. Peter Massopust, Center for Approximation Theory Seminar, Texas A & M University, College Station, Texas, U.S.A., March 2009.

Complex B-Splines: Thema and Applications

Dr. Peter Massopust, Computational Analysis Seminar, Vanderbilt University, Nashville, Tennessee, U.S.A., March 2009.

Wavelets and Image Fusion

Prof. Dr. Brigitte Forster-Heinlein, Invited lecture, Regionale Lehrerfortbildung "Moderne Technologie in der Mathematik und den Naturwissenschaften", Landshut, Feb. 2009

Complex B-Splines, Dirichlet Averages and Difference Operators

Prof. Dr. Brigitte Forster-Heinlein, Invited talk, Department of Mathematics, Universität Osnabrück, Feb. 2009

2008

Complex Wavelets for Extended Depth of Field: Image Fusion for Multichannel Microscopy Images

Prof. Dr. Brigitte Forster, Invited talk, Department Informations- und Elektrotechnik, Hamburg University of Applied Sciences, Germany, Dec. 2008

Variations on Complex B-Splines

Prof. Dr. Brigitte Forster, Invited talk, Fakult\"at f\"ur Mathematik, Universit\"at Bielefeld, Nov. 2008

Variations on Complex B-Splines

Prof. Dr. Brigitte Forster, Invited talk, Colloquium, Department of Mathematics, Vanderbilt University, USA, Nov. 2008

Translation invariant spaces from rotation covariant functions

Prof. Dr. Brigitte Forster, Seminar talk, Department of Mathematics, Vanderbilt University, USA, Nov. 2008

Poster Presentation: Complex B-Splines and Dirichlet Means

Dr. Peter Massopust, Workshop on Mathematics in Biosciences, Helmholtz Zentrum München, Germany, July 2008.

Translationsinvariante Räume aus rotationskovarianten Funktionen

Prof. Dr. Brigitte Forster, Mecklenburger Workshop, Approximationsmethoden und schnelle Algorithmen, Hasenwinkel, Juni 6-8, 2008.

Kontinuierliche Wavelets auf die Sphäre und ihre Diskretisierung

Dr. Azita Mayeli, Technische Universität München, Juni 4, 2008.

Methods of Signal Denosing

Dr. Peter Massopust, NeuWave Imaging Workshop, Technische Universität München, April 2008.

Complex Splines and Dirichlet Means

Prof. Dr. Brigitte Forster, Jubilee for Michael Unser's birthday. EPF Lausanne, Switzerland, April 2008

The fractal dimension of fractal functions generated by a class of bilinear mappings

Dr. Peter Massopust, Seminar, Australian National University, February 27, 2008.

Verlustbehaftete Bildkompression - Techniken und Bildqualität

Prof. Dr. Brigitte Forster, Invited talk, Konsensuskonferenz "Kompression Digitaler Bilddaten in der Radiologie", Nürnberg, Feburary 23, 2008.

Spherical Wavelets and their applications in CMB

Dr. Azita Mayeli, invited talk, University of Waterloo, Canada, Feburary 15, 2008.

Variationen zum Thema komplexe Splines

Prof. Dr. Brigitte Forster, 18. Rhein-Ruhr-Workshop, Gemen, Feburary 8-9, 2008.

Abstract: Komplexe B-Splines sind eine Erweiterung der klassischen Schoenberg- Splines auf komplexwertige Ordnungen. Wir untersuchen verschiedene Aspekte aus den zahlreichen Eigenschaften der B-Splines für die komplexe Erweiterung; darunter Glattheit, Multiskalen-Eigenschaften, sowie Verbindungen zu verallgemeinerten Differenzenoperatoren und der Hermite-Genocchi- Formel. Als Dichtefunktionen erlauben die komplexen B-Splines interessante Beziehungen zur Stochastik.

2007

Multivariable Komplexe B-Splines

Dr. Peter Massopust, Oberseminar Technische Universität München, November 29, 2007.

Complex Splines and Wavelets

Prof. Dr. Brigitte Forster, Invited lecture, Denmark Technical University, October 30, 2007.

Abstract: We consider two differnt approaches to complex splines and the corresponding wavelets. Applications in denoising, image fusion, feature detection in biomedical images and others show the performance of complex wavelet methods.

Biomedizinische Bildanalyse mit komplexen Wavelets

Prof. Dr. Brigitte Forster, Workshop "The Best of Graduiertenkolleg" , Center for Mathematics, TUM, September 21, 2007.

Besov Spaces and Frames on Stratified Lie Groups

Dr. Azita Mayeli, Summer School " New Trends and Direction in Harmonic Analysis, Apporximation Theory, and Image Analysis", Inzell, Germany, September 17 – 21, 2007.

Complete interpolating sequences, the discrete Muckenhoupt condition, and conformal mapping

Dr. Gunter Semmler, Summer School "New Trends and Direction in Harmonic Analysis, Apporximation Theory, and Image Analysis", Inzell, Germany, September 17 – 21, 2007.

Poster presentation: Monogenic Wavelets

Stefan Held, Summer School " New Trends and Direction in Harmonic Analysis, Apporximation Theory, and Image Analysis", Inzell, Germany, September 17 – 21, 2007.

Poster Presentation: Nearly Tight Wavelet Frames for Stratified Lie Groups

Dr. Azita Mayeli, Trends in Harmonic Analysis Strobl, Salzburg, Austria, June 18-22, 2007.

Invitation to Miniworkshop: Geometric Measure Theoretic Approaches to Potentials on Fractals and Manifolds

Dr. Peter Massopust, Oberwolfach Research Institute, Oberwolfach, Germany, April 2007.

An Introduction to the Schwartz Frames on Stratified Groups

Dr. Azita Mayeli, invited talk, Fourth Seminar in Linear Algebra and its Applications and Wavelet Workshop, Rafsanjan, Iran, March 6-9, 2007.

Analysing multi-dimensional signals: beyond separable methods on the Cartesian lattice

Dr. Laurent Condat, Technische Universität München, Garching, February 13, 2007.

Wavelets and Approximation Theory

Dr. Azita Mayeli, 47. Workshop Approximationstheorie Universität Erlangen – Nürnberg, Feburary 02, 2007.

Komplexe B-Splines treffen auf Dirichlet-Poisson Prozesse

Dr. Peter Massopust, 47. Workshop Approximationstheorie Universität Erlangen – Nürnberg, Feburary 02, 2007.

Boundary interpolation problems for finite Blaschke products

Dr. Gunter Semmler, AMS Annual Meeting, New Orleans, U.S.A, Janaury 5-8, 2007.

Boundary interpolation problems for finite Blaschke products

Dr. Gunter Semmler, University of Knoxville, Tennessee, January, 2007.

2006

Invited participation and presentation in Workshop Operator methods in fractal analysis, wavelets, and dynamical systems

Dr. Peter Massopust, Banff, Canada, December 2-7, 2006.

Stent-induced arterial deformation

Prof. Dr. Brigitte Forster, Joint Work with Iris Grabmair, Karin Knör, Stefan Pfeifer, Thomas Schratzenstaller, Erich Wintermantel, poster, invited presentation, Leopoldina-Meeting, Ergebnisse des Leopoldina Förderprogramms V, Halle an der Saale, November 17-18, 2006.

Fraktale Funktionen und Wavelet-Sets

Dr. Peter Massopust, Technische Universität München, Oberseminar, November 07, 2006.

Fraktale Funktionen und ihre Eigenschaften

Dr. Peter Massopust, GSF-IBB, Neuherberg Munich, October 18, 2006.

Constructing and Implementing Wavelets on the Torus

Dr. Azita Mayeli, HASSIP 06, Multiscale Methods, Sparse Decompositions and Parsimonious Statistics, GSF-IBB, Neuherberg Munich, September 11-14, 2006.

Schwartz wavelets on compact manifolds and some implementation

Dr. Azita Mayeli, Technische Universität München, Garching, September 06, 2006.

Abstract: In this talk we will first have a look at the definition of wavelets and their abstract constructions on general compact manifolds. Then we will demonstrate some concrete examples of wavelets on some well known manifolds such as a circle, a sphere and a torus. We will conclude the talk with an implementation on a torus by the "Mexican hat" wavelet.

Discrete and Continuous Mexican Hat wavelet on the Heisenberg group

Dr. Azita Mayeli, International Congress of Mathematicans MADRID 2006, Madrid, Spain, August 23-30, 2006.

Discrete and Continuous Mexican Hat wavelet on the Heisenberg group

Dr. Azita Mayeli, Poster presentation, Wavelets and Applications Semester, EPFL, Lausanne, Switzerland, July 10-14, 2006.

Wavelets for Image Fusion in Bright-Field Microscopy

Prof. Dr. Brigitte Forster, Kolloquium der Nachwuchsgruppenleiter der GSF, Physiologisches Institut der LMU München, July 2006.

Complex B- and Polyharmonic Splines

Prof. Dr. Brigitte Forster, Invited talk, Kolloquium des Mathematischen Instituts der Universität Gießen, Germany, July 15, 2006.

Abstract: We give approaches to complexify classical splines, while keeping the nice properties such as smoothness and decay of their real-valued fellows. Our motivation comes from piecewise polynomials as e.g. Schoenberg's cardinal B-Splines or Duchon's polyharmonic splines, which have proved to be adequate tools for many analysis problems. They also showed to fit perfectly into the concept of multiresolution bases and wavelets. However, it is unnecessary to restrict spline bases to real valued functions. Moreover, it is known that phase information is important for may applications in signal and image processing. This gives rise to consider more general forms of splines. (Joint work with D. Van De Ville, T. Blu, M. Unser, EPFL Lausanne, Switzerland)

Complex wavelets and an application to image fusion

Prof. Dr. Brigitte Forster, invited talk, MeVis/CeVis Oberseminar, Bremen, July 3, 2006.

Abstract: Multiresolution analyses have proven to be an adequate tool for signal analysis. But for some applications, e.g. in speech processing and digital holography, complex-valued scaling functions and wavelets are more favourable than real ones, since they allow to deduce the crucial phase information. Our approach to complex multiresolution analyses consists in the extension of the classical resp. fractional B-splines to complex B-splines. We perform this by choosing a complex exponent, i.e., a complex order z of the B-spline, and show that this does not influence the basic properties such as smothness and decay, recurrence relations and others. Moreover, the resulting complex B-splines satisfy a two-scale relation and generate a multiresolution analysis of L^2(R). We show that the complex B-splines converge to Gabor functions as Re z increases and Im z is fixed. Thus they are approximately optimally time-frequency localized. As an example for the application of complex wavelets we give a method for image fusion in bright field microscopy. This is joint work with Michael Unser and the Biomedical Imaging Group, EPF Lausanne.

Translation Invariant Spaces from Rotation Covariant Splines

Prof. Dr. Brigitte Forster, Harmonic Analysis and Applications, June 1-2, 2006, IBB/GSF and TU Munich.

A Smooth Continuous Wavelet on the Heisenberg Group

Dr. Azita Mayeli, PhD Defence, Technische Universität München, Garching, May 29, 2006.

Komplexe Wavelets und Anwendungen in der Hellfeld-Mikroskopie

Prof. Dr. Brigitte Forster, Get-Together, Zentralinstitut für Medizintechnik IMETUM, Technische Universtität München, Garching, May 10, 2006.

Approaches to complex splines

Prof. Dr. Brigitte Forster, Invited talk, Wavelets and Applications Semester EPFL, Lausanne, Switzerland, May 10, 2006.

Abstract: We give approaches to complexify classical splines, while keeping the nice properties such as smoothness and decay of their real-valued fellows. Extensions to more general corpses are also considered. Our motivation comes from piecewise polynomials as e.g. Schoenberg's cardinal B-Splines or Duchon's polyharmonic splines, which have proved to be adequate tools for many analysis problems. They also showed to fit perfectly into the concept of multiresolution bases and wavelets. However, from a mathematical point of view, it is unnecessary to restrict spline bases to real valued function. Moreover, it is known that phase information is important for may applications in signal and image processing. This gives rise to consider more general forms of splines.

Continuous wavelets and frames on the stratified Lie groups (e.g the Heisenberg group)

Dr. Azita Mayeli, joint HASSIP/DFG-SPP1114 Workshop: "Recent Progress in Wavelet Analysis and Frame Theory", Bremen, Germany, January 23 - 26, 2006.

Abstract: In collaboration with D.Geller, we construct compactly supported smooth continuous wavelets, with arbitrarily many vanishing moments, on any stratified Lie group G. We also show that if the wavelets satisfies a generalization of Daubechies' criteria, then they generate a wavelet frame for any sufficiently fine lattice of G.

2005

Continuous Mexican Hat Wavelet on the Heisenberg Group

Dr. Azita Mayeli, Institute of Biomathematics and Biometry IBB, GSF, December 16, 2005.

Abstract: We construct the "Mexican Hat" wavelet on the Heisenberg group, and we shall then look at the class of compactly supported smooth continuous wavelets, with arbitrarily many vanishing moments, on the Heisenberg Lie group. We also show that if the wavelets satisfy a generalization of "Daubechies' criteria", then they generate a wavelet frame for any sufficiently fine lattice of the Heisenberg group.

Solvability of Explicit Riemann-Hilbert Problems

Dr. Gunter Semmler, Conference on Analysis and related Topics, Lviv, Ukraine, November 17-20, 2005.

Solvability of Explicit Riemann-Hilbert Problems

Dr. Gunter Semmler, Oberseminar Mathematische Modellbildung, TU München, November, 2005.

Abstract: We consider the boundary value problem

v(t) = f (t, u(t)) (1)

for a function w = u + iv holomorphic in the unit disc D := {z in C : |z | < 1}, where the boundary condition (1) is required to hold (almost everywhere) on the unit circle t := ∂ D. These problems have been studied subsequently by von Wolfersdorf, Wegert, Efendiev, and the author for differentiable, Lipschitz- continuous, continuous and compactly supported, continuous and bounded right- hand sides f : T × R → R. The talk summarizes these results and presents generalizations to the case where f is continuous and at most linearly growing. It turns out that in this case solutions can be found in some appropriate Hardy space Hp , and that there occur additional solutions which have been missed in previous work due to the solution space. These wrapping solutions can be understood best if we transform the problem into a Riemann-Hilbert problem with closed restriction manifold. Since this manifold is not everywhere smooth, certain technical difficulties arise.

Wavelets for extended depth-of-field in light microscopy: Image fusion and 3D visualization

Dr. Brigitte Forster, ECMTB'05, Dresden, July 2005

Spline interpolated Dirichlet series and their order of approximation

Dr. Brigitte Forster, Computational Methods in Function Theory, Joensuu, Finnland, Apr. 2005

Complex B-splines

Dr. Brigitte Forster, Invited talk, Workshop Harmonic Analysis and Applications, Institut für Biomathematik und Biometrie, GSF, Neuherberg, Apr. 2005

Wavelets for Image Fusion in Bright Field Microscopy

Dr. Brigitte Forster (Invited talk) Mathematical Methods in Systems Biology, Ludwig Maximilians Universität, M\"unchen, Feb. 2005