Prof. Gitta Kutyniok, Institut für Mathematik, Technische Universität Berlin

Imaging Science Meets Compressed Sensing

distinct constituents. For instance, neurobiological images could

consist of a superposition of spines (pointlike objects) and

dendrites (curvelike objects) of a neuron. A neurobiologist might

then seek to extract both components to analyze their structure

separately for the study of Alzheimer specific characteristics.

However, this task seems impossible, since there are two unknowns

for every datum.

Compressed sensing is a novel research area, which was introduced in

2006, and since then has already become a key concept in various

areas of applied mathematics, computer science, and electrical

engineering. It surprisingly predicts that high-dimensional signals,

which allow a sparse representation by a suitable basis or, more

generally, a frame, can be recovered from what was previously

considered highly incomplete linear measurements, by using efficient

algorithms.

Utilizing the methodology of compressed sensing, this geometric

separation problem can indeed be efficiently solved numerically by

iterative thresholding using wavelets to capture the pointlike

structures and shearlets to capture the curvelike structures. We

then analyze this methodology theoretically by considering a

distributional model situation and prove asymptotically perfect

separation. Surprisingly, it turns out that the thresholding index

sets even converge to the wavefront sets of the point- and

curvilinear singularities in phase space and that those wavefront

sets are perfectly separated by the thresholding procedure.

Gitta Kutyniok completed her Diploma in Mathematics and Computer

Science in 1996 at the Universitat Paderborn in Germany. She

received her Ph.D. degree in the area of time-frequency analysis

from the same university in 2000. She completed her Habilitation in

Mathematics in 2006 and received her venia legendi. In 2007, she was

awarded a Heisenberg Fellowship by the DFG-German Research

Foundation.

From 2001 to 2008 she held visiting appointments at several US

institutions, including Princeton University, Stanford University,

Yale University, Georgia Institute of Technology, and Washington

University in St. Louis.

After returning to Germany in October 2008, she became a full

professor of mathematics at the Universitat Osnabrueck, and headed

the Applied Analysis Group. Since October 2011, she has an Einstein

Chair at the Technical University of Berlin and is head of the

Applied Functional Analysis Group (AFG).

Her research and teaching have been recognized by various awards,

including the von Kaven Prize by the German Research Foundation,

awards by the University Paderborn and the Justus-Liebig University

Giessen for Excellence in Research, as well as the Weierstrass Prize

for Outstanding Teaching. She is an Associate Editor and also

Corresponding Editor for several journals in the area of applied

mathematics. She is also a board member of the Berlin Mathematical

School, a member of the council of the MATHEON "Mathematics for key

technologies" in Berlin, and the chair of the GAMM activity group on

"Mathematical Signal- and Image Processing".