IC Colloquium - Compressed Sensing meets Imaging Science
Event details
| Date | 18.11.2013 |
| Hour | 16:15 › 17:30 |
| Speaker | Gitta Kutyniok - TU Berlin |
| Location | |
| Category | Conferences - Seminars |
Abstract:
In imaging science, a customarily employed model is the cartoon model, which assumes that images are governed by edges, i.e., by anisotropic features. Shearlet theory might by now be considered the most versatile and successful methodology to efficiently represent such features, in particular, because it allows a unified treatment of the continuum and digital realm. One common problem is the extraction of such features from a mixture of anisotropic and isotropic phenomena, for example, the superposition of spines (pointlike objects) and dendrites (curvelike objects) of a neuron. A seemingly unrelated problem is inpainting, i.e., the recovery of missing parts of the image. These problems however share the similarity that both are ill-posed inverse problems.
Compressed sensing is a novel research area introduced in 2006, which surprisingly predicts that high-dimensional signals, which allow a sparse representation by a suitable basis or, more generally, a frame, can be recovered by efficient algorithms from what was previously considered highly incomplete linear measurements.
Utilizing the methodology of Compressed Sensing in combination with shearlet theory, we will show that both the geometric separation problem as well as the inpainting problem can be highly accurately solved numerically, but even theoretically. Asymptotically perfect separation and inpainting can indeed be proved as we will also discuss.
This is in collaboration with David Donoho, Emily King, Wang-Q Lim, and Xiaosheng Zhuang.
Biography:
Gitta Kutyniok completed her Diploma in Mathematics and Computer Science in 1996 at the Universität 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 Universität Osnabrück, 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 Universität Paderborn and the Justus-Liebig Universität Giessen for Excellence in Research, as well as the Weierstrass Prize for Outstanding Teaching. She also delivered the
Noether-Lecture at this year's annual meeting of the Mathematical Societies from Germany and Austria.
She is an Associate Editor as well as Corresponding Editor for several journals in the area of applied mathematics and electrical engineering. 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".
In imaging science, a customarily employed model is the cartoon model, which assumes that images are governed by edges, i.e., by anisotropic features. Shearlet theory might by now be considered the most versatile and successful methodology to efficiently represent such features, in particular, because it allows a unified treatment of the continuum and digital realm. One common problem is the extraction of such features from a mixture of anisotropic and isotropic phenomena, for example, the superposition of spines (pointlike objects) and dendrites (curvelike objects) of a neuron. A seemingly unrelated problem is inpainting, i.e., the recovery of missing parts of the image. These problems however share the similarity that both are ill-posed inverse problems.
Compressed sensing is a novel research area introduced in 2006, which surprisingly predicts that high-dimensional signals, which allow a sparse representation by a suitable basis or, more generally, a frame, can be recovered by efficient algorithms from what was previously considered highly incomplete linear measurements.
Utilizing the methodology of Compressed Sensing in combination with shearlet theory, we will show that both the geometric separation problem as well as the inpainting problem can be highly accurately solved numerically, but even theoretically. Asymptotically perfect separation and inpainting can indeed be proved as we will also discuss.
This is in collaboration with David Donoho, Emily King, Wang-Q Lim, and Xiaosheng Zhuang.
Biography:
Gitta Kutyniok completed her Diploma in Mathematics and Computer Science in 1996 at the Universität 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 Universität Osnabrück, 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 Universität Paderborn and the Justus-Liebig Universität Giessen for Excellence in Research, as well as the Weierstrass Prize for Outstanding Teaching. She also delivered the
Noether-Lecture at this year's annual meeting of the Mathematical Societies from Germany and Austria.
She is an Associate Editor as well as Corresponding Editor for several journals in the area of applied mathematics and electrical engineering. 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".
Links
Practical information
- General public
- Free
- This event is internal
Contact
- Host : Michael Gastpar