Projects

Nowadays face and pattern detection is used in several areas as for example in Videosystems for museums, security applications and quality control of materials. With this project we intend to develop and to improve classification algorithms of high numerical efficiency for use in object indentification in images and object following in image sequences. Classifiers need to separate high dimensional vectors of attributes. Algorithms need to be robust and well structured. Support Vector Machines satisfy those demands and give an adequate base for further acceleration. Single approaches are sparse approximation of SVMs, cascadation of classifications, an efficient presentation of support vectors and effectively implemented operations. The goal of this project is the improvement of the existing algorithms in view to computational time, numerical efficiency, effect of restrictions and complexity with the goal of a flexible program library for further use in scientific and commercial applications.

The atmospheric boundary layer, which vertical extension is described by the mixing layer height (MLH), plays an important role for the exchange of heat, momentum and moisture between the surface and the free atmosphere. The MLH is one of the key parameters for the transportat and dispersion of air pollutants and an important input value for dispersion models. Therefore, a lot of efforts have been undertaken during the last decades to use ground-based remote sensing systems, like sodar, sodar/RASS, wind profiler radar or ceilometer for a continuous observation of the MLH.

This project aims at a thorough theory of compressed sensing for ill-posed inverse problems. Compressed sensing is a promising new field which tries to tackle the problem of high-dimensional data by combining the measuring and the compression step into one single process of "compressive sampling". It is the goal to get a proper formulation of this theory in infinite dimensional spaces and to treat ill-posed operators - both linear and nonlinear. Further we intend applications to the areas of medical imaging, geo-data analysis and color image restauration.

The goal of this project is to develop a mathematical algorithm that allows on the basis of cloud radar data a monitoring of: Depths of the cloud, sometimes in several cloud layers; Cloud coverage (per cloud layer); Overlap-factor of cloud layers; Characteristic droplet size; Mass density of liquid water/ice water; Optical depth; Mass density of drizzle, rainwater, snow; In-cloud dynamics, particularly vertical air motion. This project is in collaboration with G. Peters (Metek GmbH in Elmshorn) and U. Görsdorf (DWD-German Weather Agency).

The goal of this project is to determine basic earthquake parameters on the basis of a specific physical model (Okada approach or Green function approach) that relies on GPS data input. The associated inverse problem is ill-posed and adequate inversion techniques have to be developed. The project is in collaboration with the A. Babeyko (Geoforschungszentrum Potsdam).

Within this project we aim to develop wavelet-based accelerated support vector machines. The acceleration can be seen as a solution of an inverse problem. In particular, we have to treat nonlinear problems with sparsity constraints that lead to cascade structured very fast and efficient classification machines. These machines are used in the context of online face detection and 3d face modelling. In a case study for the LKA-Berlin, we have shown the relevance for the computation of 3d phantom images on the basis of one single phantom skecth. This project is in collaboration with the Prof. Vetter (University of Basel).

With Radar-Windprofiler devices one can analyze the dynamics of the atmosphere. In this project we want to make use of the relation between the measured clear air time series and the clear air refractive index field in the associated sampling volume. This relation is given by an special integral equation (relating the cross covariance function with the clear air refractive index field).
The main focus this project is the development of numerical methods that reconstruct the cross covariance function. The integral equation suggests a frame based inversion of the measured data. A direct frame reconstruction is obtained when the analyzing atoms fit with the device sampling functions. This project is in collaboration with the Prof. A. Muschinski (University of Amherst).

In this project we aim to develop numerically thrifty schemes for solving operator equations in its variational form with mixed constraints (e.g. sparsity and smoothness) that appear in the field of image decomposition, restoration, and classification. Sometimes it seems that wavelet bases are well suited, sometimes frames, and sometimes it is required to go completely beyond a ''basis''-like representation.
First experiments have shown that these techniques seem to be very well suited for texture analysis, classification problems etc. Here in this project we shall be concerned with seabed data/image restoration, i.e. a separation of the seabed pattern and the pattern caused by the ship movements made while measuring the echo of ultra sound waves transmitted down to the ocean ground. This particular application is done in collaboration with Ocean Margin Institute Bremen.

Ultrasound Measurements

The University of Arkansas for Medical Sciences (C. Lowery) and the University of Tübingen (H. Preissl) have developed SQUID (Superconducting Quantum Interference Device) which is a device for prenatal diagnostics. With the help of this medical device one hopes to understand and to identify pregnancies at risk.
The mathematical task is to develop methods that extract information about uterine contraction activities (by means of classification models) and to reconstruct the location and activity of the fetal brain activity.

Silex Systemi Integrati (F. Gekat) manufactures radar devices that analyze the lower atmosphere. The overall goal is that weather radar systems should achieve an optimal sampling (in time and space) of the atmosphere. However, the sampling is limited by the range doppler dilemma (sampling range vs. doppler frequency).
The focus is the development of methods to overcome the range doppler dilemma. To this end, an optimization of the pulse transmission technique and an efficient scheme to solve the resulting large system of equations need to be developed.

The focus was the construction of optimal analyzing atoms (wavelets) that allow optimal representations of meteorological and medical data for further analysis. This project was done in collaboration with V. Lehmann (DWD-German Weather Agency) and H. Preissl (MEG Zentrum, University Tübingen).

Operator equations appear in several fields of science and technology; typically given as an inverse and ill-posed problem.

In collaboration with I. Daubechies (Princeton University), L. Vese (UCLA-IPAM) and, moreover, with R. Ramlau (RICAM, Linz) and C. DeMol (ULB Brussels) we develop iterative strategies for inverse problems where the solution is assumed to have a particular (possibly sparse) representation with respect to preassigned families of frames. Typically the minimization of the inverse problem in its variational form amounts to a (fixed point) iteration with a special shrinkage operation applied in each step.
In the linear theory, typical examples are image deblurring, inversion of the Radon transform, image decomposition and restoration. The technology can also be applied to audio data coding. In the nonlinear theory one can attack the full nonlinear SPECT problem.

Simultaneously computed deblurred version, cartoon and texture component

The most important question in inverse problems is to reconstruct a solution with the help of an observation. In this project we consider the field of image processing, in particular nonlinear diffusion equations. With the help special operator adapted wavelet systems, we develop a numerical scheme to solve this special nonlinear partial differential equation. This project is in collaboration with J. Soares, (Universidade Minho, Portugal).

Original and noisy image

A few steps of the iterative nonlinear smoothing

The main goal of the german-portugese cooperation was the analysis of wavelets in Banach spaces and its usage in solving partial differential equations. We have developed strategies for nonlinear elliptic problems. This project was done in collaboration with U. Kähler and P. Cerejeiras (Universidade de Aveiro, Portugal).

The IfG GmbH in Berlin-Adlershof has developed new 2Dim-CCD-Cameras that were used for testing the quality of two layered materials. The goal of this project was the development of an algorithm that reconstructs the material density automatically.

The goal of this long lasting and very fruitful collaboration with the DWD-German Weather Agency (V. Lehmann) is the analysis of wind profiler radar data. Typically, wind profiler data contain not only the clear air return but also contamination from objects passing the radar beam. In order to identify atmospheric informations, we focus on the modelling of clear air signals and clutter components such echoes from migrating birds, airplanes or surrounding objects such as wind turbines, digital video broadcast (DVBT) or trees.
On the basis of advanced time-frequency methods such as wavelet frame and Gabor frame theory we have developed stochastic signal filtering procedures that allow an efficient and serious eleminination of the signal clutter components.Our latest state of the art procedure performs in average much better than all other methods on the "radar market" and is therefore implemented in the DWD's radar data processing unit.

Scientific and Industrial Projects Funded by Industries and Publics Grants such as DFG, AIF, BMBF, DAAD, ... (the order of projects is almost chronological and not by its relevance)
Grant / Funding	Project Description

BMBF (2009-2013)	Real-time pattern classification and object following in images and image sequences Nowadays face and pattern detection is used in several areas as for example in Videosystems for museums, security applications and quality control of materials. With this project we intend to develop and to improve classification algorithms of high numerical efficiency for use in object indentification in images and object following in image sequences. Classifiers need to separate high dimensional vectors of attributes. Algorithms need to be robust and well structured. Support Vector Machines satisfy those demands and give an adequate base for further acceleration. Single approaches are sparse approximation of SVMs, cascadation of classifications, an efficient presentation of support vectors and effectively implemented operations. The goal of this project is the improvement of the existing algorithms in view to computational time, numerical efficiency, effect of restrictions and complexity with the goal of a flexible program library for further use in scientific and commercial applications.

JenOptik (2009-2010)	Development of a wavelet-based algorithm for the detection of mixing layer heights on the basis of Ceilometer measurements The atmospheric boundary layer, which vertical extension is described by the mixing layer height (MLH), plays an important role for the exchange of heat, momentum and moisture between the surface and the free atmosphere. The MLH is one of the key parameters for the transportat and dispersion of air pollutants and an important input value for dispersion models. Therefore, a lot of efforts have been undertaken during the last decades to use ground-based remote sensing systems, like sodar, sodar/RASS, wind profiler radar or ceilometer for a continuous observation of the MLH. In collaboration with JenOptik and the German Weather Agency we aim to develop efficient algorithms for retrieving the MLH on the basis of Ceilometer measurements.

DFG-SPP 1324 (2008-2011)	Sparsity and compressed sensing in inverse problems This project aims at a thorough theory of compressed sensing for ill-posed inverse problems. Compressed sensing is a promising new field which tries to tackle the problem of high-dimensional data by combining the measuring and the compression step into one single process of "compressive sampling". It is the goal to get a proper formulation of this theory in infinite dimensional spaces and to treat ill-posed operators - both linear and nonlinear. Further we intend applications to the areas of medical imaging, geo-data analysis and color image restauration.

DFG/FWF (2007-2011)	Where sparse makes robust – nonlinear inverse problems in science and engineering There are many important applications, using the theory of inverse problems, which have a nonlinear structure. Usually, regularization is necessary because the problem is ill-posed due to noisy data. While the theory of regularization methods treating linear problems in a Hilbert space setting is well developed, there is still a considerable need to improve the methods for solving nonlinear problems. The aim of this project is the development of algorithms and regularization theory for nonlinear ill-posed problems with sparsity constraints. In particular, the goal is the development of iterative strategies for nonlinear inverse problems and to prove norm convergence and convergence rates. Furthermore we shall be concerned with the application of the developed methods to the analysis of cellular networks, rotor dynamics and SPECT. This project is in collaboration with R. Ramlau and S. Anzengruber (RICAM, Linz).

DFG (2007-2010)	Image modelling, inpainting, decomposition and restoration by redundant representations and variational calculus The goal of this project is the analysis of frames and their use in numerical applications in the field of inverse problems (color image inpainting, image restoration and decompostion). In image processing, when dealing with spaces of (special) bounded variation functions the problem is often that the associated PDE schemes that approximate the solution are numerically very intensive and time consuming. It would be desirable to bypass this drawback and to derive the solution of the image restoration problem in some numerically thrifty way. Therefore we replace the classical characterization of the function space of bounded variations by an easier to handle framework, which is in our situation a frame-based approach. This allows a simple reformulation of the image restoration problem by means of the associated frame coefficients leading to efficient algorithms. This project is in collaboration with R. Ramlau and M. Fornasier (RICAM, Linz).

AIF (2007-2009) DWD (2006)	A new approach for target classification of Ka-band radar data The goal of this project is to develop a mathematical algorithm that allows on the basis of cloud radar data a monitoring of: Depths of the cloud, sometimes in several cloud layers; Cloud coverage (per cloud layer); Overlap-factor of cloud layers; Characteristic droplet size; Mass density of liquid water/ice water; Optical depth; Mass density of drizzle, rainwater, snow; In-cloud dynamics, particularly vertical air motion. This project is in collaboration with G. Peters (Metek GmbH in Elmshorn) and U. Görsdorf (DWD-German Weather Agency).

partly DFG (since 2005)	Earthquake parameter estimation - Tsunami Early Warning System The goal of this project is to determine basic earthquake parameters on the basis of a specific physical model (Okada approach or Green function approach) that relies on GPS data input. The associated inverse problem is ill-posed and adequate inversion techniques have to be developed. The project is in collaboration with the A. Babeyko (Geoforschungszentrum Potsdam).

partly DFG (since 2005)	Machine learning, support vector machines and 3d face modelling Within this project we aim to develop wavelet-based accelerated support vector machines. The acceleration can be seen as a solution of an inverse problem. In particular, we have to treat nonlinear problems with sparsity constraints that lead to cascade structured very fast and efficient classification machines. These machines are used in the context of online face detection and 3d face modelling. In a case study for the LKA-Berlin, we have shown the relevance for the computation of 3d phantom images on the basis of one single phantom skecth. This project is in collaboration with the Prof. Vetter (University of Basel).

DFG (2005-2007)	Frame-based methods for the inversion of meteorological integral equations With Radar-Windprofiler devices one can analyze the dynamics of the atmosphere. In this project we want to make use of the relation between the measured clear air time series and the clear air refractive index field in the associated sampling volume. This relation is given by an special integral equation (relating the cross covariance function with the clear air refractive index field). The main focus this project is the development of numerical methods that reconstruct the cross covariance function. The integral equation suggests a frame based inversion of the measured data. A direct frame reconstruction is obtained when the analyzing atoms fit with the device sampling functions. This project is in collaboration with the Prof. A. Muschinski (University of Amherst).

DFG-SPP1114 (2005-07)	Wavelet- and frame-based treatments of variational problems with applications in geophysical data processing In this project we aim to develop numerically thrifty schemes for solving operator equations in its variational form with mixed constraints (e.g. sparsity and smoothness) that appear in the field of image decomposition, restoration, and classification. Sometimes it seems that wavelet bases are well suited, sometimes frames, and sometimes it is required to go completely beyond a ''basis''-like representation. First experiments have shown that these techniques seem to be very well suited for texture analysis, classification problems etc. Here in this project we shall be concerned with seabed data/image restoration, i.e. a separation of the seabed pattern and the pattern caused by the ship movements made while measuring the echo of ultra sound waves transmitted down to the ocean ground. This particular application is done in collaboration with Ocean Margin Institute Bremen. Ultrasound Measurements

UAMS (NIH) and partly DFG (since 2004)	Analysis of uterine contractions and reconstruction of fetal brain activities The University of Arkansas for Medical Sciences (C. Lowery) and the University of Tübingen (H. Preissl) have developed SQUID (Superconducting Quantum Interference Device) which is a device for prenatal diagnostics. With the help of this medical device one hopes to understand and to identify pregnancies at risk. The mathematical task is to develop methods that extract information about uterine contraction activities (by means of classification models) and to reconstruct the location and activity of the fetal brain activity.

Silex Systemi Integrati (since 2003)	Optimal sampling functions and the range doppler dilemma Silex Systemi Integrati (F. Gekat) manufactures radar devices that analyze the lower atmosphere. The overall goal is that weather radar systems should achieve an optimal sampling (in time and space) of the atmosphere. However, the sampling is limited by the range doppler dilemma (sampling range vs. doppler frequency). The focus is the development of methods to overcome the range doppler dilemma. To this end, an optimization of the pulse transmission technique and an efficient scheme to solve the resulting large system of equations need to be developed.

DFG-SPP1114 (2003-05)	Construction of Wavelets and Applications in Analyzing Meteorological and Medical Data The focus was the construction of optimal analyzing atoms (wavelets) that allow optimal representations of meteorological and medical data for further analysis. This project was done in collaboration with V. Lehmann (DWD-German Weather Agency) and H. Preissl (MEG Zentrum, University Tübingen).

DAAD and partly DFG, HASSIP (since 2002)	Iterative methods for linear (and nonlinear) operator equations with mixed sparsity and smoothness constraints Operator equations appear in several fields of science and technology; typically given as an inverse and ill-posed problem. In collaboration with I. Daubechies (Princeton University), L. Vese (UCLA-IPAM) and, moreover, with R. Ramlau (RICAM, Linz) and C. DeMol (ULB Brussels) we develop iterative strategies for inverse problems where the solution is assumed to have a particular (possibly sparse) representation with respect to preassigned families of frames. Typically the minimization of the inverse problem in its variational form amounts to a (fixed point) iteration with a special shrinkage operation applied in each step. In the linear theory, typical examples are image deblurring, inversion of the Radon transform, image decomposition and restoration. The technology can also be applied to audio data coding. In the nonlinear theory one can attack the full nonlinear SPECT problem. Simultaneously computed deblurred version, cartoon and texture component

partly DAAD (since 2002)	Wavelet-based regularisation methods for nonlinear diffusion equations The most important question in inverse problems is to reconstruct a solution with the help of an observation. In this project we consider the field of image processing, in particular nonlinear diffusion equations. With the help special operator adapted wavelet systems, we develop a numerical scheme to solve this special nonlinear partial differential equation. This project is in collaboration with J. Soares, (Universidade Minho, Portugal). Original and noisy image A few steps of the iterative nonlinear smoothing

EU Craft (2002-04)	Mepros - a new and innovative meteorological profiling system Within the EU Craft Program (Cooperative Research Action For Technology) of the European Union SM-enterprises are funded in order to develop with help of research institutes new and innovative technologies. MEPROS (Meteorological profiling system based on wavelet technology for radar and acoustic devices) was a project to provide an analysis tool (software unit) that will provide in the field of meteorology high quality measurements. Meteorological stations, airports (Frankfurt International Airport) or Off-Shore-Windparks will have a significant benefit by MEPROS by receiving more accurate weather data. To achieve such an impact, we have collaborated within an impressive team of engineers, researchers and manufacturers: SHE AG (Ludwigshafen, Germany), BIRAL (Bristol, UK), Scintec AG (Tübingen, Germany), Eurelettronica Icas Srl (Rom, Italy), Espace Eolien Developement (Lille, France), (Aveiro, Protugal), Universidade de AveiroFH Worms (Germany), ZETEM (Bremen, Germany). MEPROS Software Toolbox EU-MEPROS-Homepage

DAAD (2002-03)	Wavelets in Banach-Spaces and Solving PDE's The main goal of the german-portugese cooperation was the analysis of wavelets in Banach spaces and its usage in solving partial differential equations. We have developed strategies for nonlinear elliptic problems. This project was done in collaboration with U. Kähler and P. Cerejeiras (Universidade de Aveiro, Portugal).

partly EU HASSIP (since 2001)	Coorbit theory, Banach frames and nonlinear approximation As a participant within this project we have established a fruitful collaboration between several European research institutes. The focus is on (non-)harmonic analysis and its application in several fields of image and signal processing. Together with S. Dahlke (University of Marburg), G. Steidl (University of Mannheim) and M. Fornasier (RICAM, Linz) we consider the construction of smoothness spaces (coorbit spaces)and the construction of Banach frames (to represent functions in them) . All this yields new insights when going beyond Hilbert spaces on the Euclidian plane, e.g. we are able to consider Gabor frame expansions on the sphere (or more general manifolds) and related nonlinear approximations.

DFG-SPP1114 (2001-03)	Construction of Wavelets and Applications in Analyzing Meteorological Data The focus was an improvement of the modelling and the analysis of radar echoes. In collaboration with the DWD-German Weather Agency (V. Lehmann) and the GKSS-Research Center Geesthacht (M. Quante) we reconstruted specific structures (e.g. fall traces of ice cristals) based on cloud radar measurements. Reconstructed cloud data and extracted structures

IfG Berlin (1999-00)	Analysis of X-Ray radiography images for an automatic detection of material errors The IfG GmbH in Berlin-Adlershof has developed new 2Dim-CCD-Cameras that were used for testing the quality of two layered materials. The goal of this project was the development of an algorithm that reconstructs the material density automatically.

BMBF (1998) since 1998 DWD, DFG	Analysis of atmosperic spatial-temporal data; Reconstruction of vertical wind profiles The goal of this long lasting and very fruitful collaboration with the DWD-German Weather Agency (V. Lehmann) is the analysis of wind profiler radar data. Typically, wind profiler data contain not only the clear air return but also contamination from objects passing the radar beam. In order to identify atmospheric informations, we focus on the modelling of clear air signals and clutter components such echoes from migrating birds, airplanes or surrounding objects such as wind turbines, digital video broadcast (DVBT) or trees. On the basis of advanced time-frequency methods such as wavelet frame and Gabor frame theory we have developed stochastic signal filtering procedures that allow an efficient and serious eleminination of the signal clutter components.Our latest state of the art procedure performs in average much better than all other methods on the "radar market" and is therefore implemented in the DWD's radar data processing unit.

Image modelling, inpainting, decomposition and restoration by redundant representations and variational calculus

A new approach for target classification of Ka-band radar data

Analysis of uterine contractions and reconstruction of fetal brain activities

Iterative methods for linear (and nonlinear) operator equations with mixed sparsity and smoothness constraints

Wavelet-based regularisation methods for nonlinear diffusion equations

Wavelets in Banach-Spaces and Solving PDE's

Analysis of X-Ray radiography images for an automatic detection of material errors