This one semester program will bring together researchers from mathematics, imaging technology, biology, and the life sciences to explore new ways to bridge these diverse disciplines, and to facilitate the use of mathematics for key problems in imaging, medicine, and the life sciences in general.
The hardware side of imaging has been undergoing a revolution in the past 15 years with the advent of faster, more accurate, and cheaper imaging modalities. This powerful new hardware has driven the need for corresponding new mathematical ideas that can be turned into practical algorithms and in turn implemented in software that may be used by the medical/biology community. A number of algorithms based on partial differential equations, curvature driven flows, geometry, and novel statistical techniques have already made their impact felt in image processing.
Mathematical models form the basis of biomedical computing in general and medical imaging in particular. Basing those models on data extracted from images continues to be a fundamental technique for achieving scientific progress in experimental, clinical biomedical, and behavioral research. Data and in particular imagery, acquired in a multiscale manner by a range of techniques, are central to understanding biological problems and their impacts on clinical and natural sciences. One can consider this type of data as geometrically arranged arrays of data samples measuring such diverse physical quantities as time-varying hemoglobin deoxygenation during neuronal metabolism or vector-valued measurements of water diffusion through and within tissue.
The broadening scope of imaging as a way to organize our observations of the biophysical world has led to a dramatic increase in our ability to apply novel processing techniques and to combine multiple channels of data into sophisticated and complex mathematical models including biological systems, physiological function and dysfunction. We note that many relevant data sets from biomedical imaging, genomics and proteomics have high-dimensionality, high heterogeneity due to different data modalities (across different spatial and temporal scales, but also across different biological layers) that need to be fused, low sample size and possibly low reproducibility of per-patient data. These challenging aspects demand concepts from compressive sensing, learning and information theory, and novel algebra-geometric/topological techniques that accordingly will constitute some of the key topics of this MBI program.
The workshops will bring together a diverse group of researchers from mathematics, imaging, signal processing and control, medicine, biology, and the statistics communities to exchange ideas, build collaborations, and provide new directions in mathematical and biological research. Concepts and techniques from bioinformatics, genomics/proteomics, and dynamics will be a part of these workshops as well.