institute of biomathematics and biometry

Analysis of One- and Multi-Dimensional Signals

for example time series, multi-dimensional data sets like images or series or stacks of images. In this part of our research, we focus on the extraction of morphological and spatial rather than quantitative features. Emphasis is on parsimonious and sparse data representations, based on variational approaches with complexity penalized likelihood functions. Real time algorithms for the solution of the respective optimization problems are a main part of this kind of research.

Another topic are discontinuities in digital images. Focus is on the design and on the theoretical study of geometry-based non-linear approximation methods for the representation of edges and lines in images. The main approaches are partition-regression (quadtree structures, wedgelets) and Delaunay triangulations.

There is also a body of work on probability theory and statistics in their own right.

some signals analysis publications

Mathematical Systems Biology

in particular probabilistic modelling of autoregulative intra- and intercellular mechanisms, as well as consistency in the limit of large numbers of molecules in certain compartments, while other types of molecules are rare. Typical examples are cellular clocks, appearing for instance in somitogenesis in the context of members of the Hes-family. Part of the research is done in the framework of (part of Helmholtz Alliance on Systems Biology) on the analysis of non-coding mRNA.

some systemsbiology publications

Other examples are biofilms. These are organized bacterial colonies. Their development is modelled by deterministic systems of reaction-diffusion equations. One approach leads to a model for high resistance of biofilms to antibiotics. Another one are complex hydrogeological systems, relevant in the field of groundwater protection.

Analysis of (Bio-) Medical Image Data

in the context of magnetic resonance imaging (MRI) and microscopy, developed over more then 10 years. Special topics are brain mapping, diffusion tensor imaging, functional MRI, as well as the morphological characterization of brain structures in order to discriminate healthy and morbid tissue. Main goal is to support diagnosis and therapy of diseases in the context of aging, like multiple sclerosis or the ubiquitous Alzheimer disease.

some publications

There is also a body of work about dose reduction in X-ray mamma screening. Additionally the quantitative representation and analysis of entities in data from fluorescence microscopy and confocal laser scanning microscopy (CLSM) mainly in histopathology and microbiology (oncology, microbial growth, biofilm, rhizosphere) are dealt with extensively.

some methodical publications

Biostatistics

We are concerned with the investigation and exploration of data, as well as descriptive and inferential data analysis, including aspects of data mining and respecitive algorithms like random forests.

some biostatistical publications

ImStatLab

is a consulting and service unit intended to serve as an interface between external scientists and the diverse IBB groups. It provides assistance for the solution of practical problems, in particular in statistics or image analysis, but also in other fields of mathematics.

ImStatLab Hotline: e-mail
Tel.: +49 89 3187 4080