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Compressed Sensing and Medical Applications

Organizers:
A. Schindele, A. Borzi, and H. Kostler (Institut fur Mathematik, Univer- sitat Wurzburg, Germany)

Abstract:
In many applications in medicine and engineering the examination of images like organs in the human body play an important role. The acquisition of these images may be quite expensive. In order to accelerate this aqcuisition process one can measure a small part of the whole data set and reconstruct the exact signal afterwards. The reconstruction of undersampled data is radically improved by the compressed sensing theory that investigates the necessary assumptions where exact reconstruction of the undersampled signal is obtained. The reconstruction involves nonsmooth l1-minimization, which requires sophisticated numerical optimization algorithms. From the application point of view the l1-minimization is highly used in magnetic resonance imaging (MRI), where the scanning duration can be reduced significantly. MRI is one of the most important diagnosis tool in medicine. In this mini-symposium, we discuss recent developments of the compressed sensing theory and the numerical solutions by using l1-minimization algorithms as well as their application MRI.