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


Imaging Science Meets Compressed Sensing

Modern imaging data are often composed of several geometrically
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

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.

Speaker Bio:
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

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".