She received a research award from the Universität Paderborn in 2003, the Research Prize of Gießen and a Heisenberg-Fellowship in 2006, the von Kaven Prize by the DFG in 2007, and an Einstein Chair in 2008. She gave the Noether Lecture at the ÖMG-DMV Congress in 2013 and the Hans Schneider ILAS Lecture at IWOTA in 2016, became a member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2017, and was selected as SIAM Fellow in 2019. She is currently spokesperson for the Research Training Group on "Differential Equation- and Data-driven Models in Life Sciences and Fluid Dynamics" and of the main priority program "Compressed Sensing in Information Processing", both of the German Research Foundation. She is also Scientific and Executive Director of the international graduate school BIMoS at TU Berlin and Chair of the SIAM Activity Group on Imaging Sciences as well as of the MATH+ Activity Group on Mathematics of Data Science. Her main research interests are in the areas of applied and computational harmonic analysis, approximation theory, compressed sensing, deep learning, frame theory, imaging sciences, inverse problems, machine learning, numerical analysis of partial differential equations, and applications to life sciences and telecommunication.
Gitta Kutyniok's research work covers, in particular, the areas of applied and computational harmonic analysis, approximation theory, compressed sensing, deep learning, frame theory, imaging sciences, inverse problems, machine learning, numerical analysis of partial differential equations, and applications to life sciences and telecommunication. She is primarily interested to develop mathematical methodologies and associated theories to solve application motivated problems.
The most significant of Gitta Kutyniok's contributions is perhaps the introduction of the directional multiscale system of shearlets (see also www.ShearLab.org), which is by now exploited by various research groups worldwide. Since many important problem classes are governed by anisotropic structures such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images, and the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. By now, shearlets are the first anisotropic system which not only provides optimal sparse approximation rates for appropriate model classes, but also allows for faithful and highly efficient implementations.
In the area of inverse problems, Gitta Kutyniok pursued foremost the direction of sparse regularization, in which the regularizer is designed using an orthonormal basis or, more generally, a frame, which provides sparse approximations of the respective model class. Using results from harmonic analysis and microlocal analysis, Gitta Kutyniok provided a comprehensive analysis of this approach for several problems in imaging sciences by using shearlets, revealing the underlying reasons for its success.
Lately, she entered the area of machine learning. One of her main goals is to develop a theoretical foundation for deep learning, also for its application within mathematics. In this direction, some of her most well-known contributions are the analysis and construction of memory-optimal deep neural networks by using classical approximation theory as well as a theoretical analysis of deep neural networks and parametric partial differential equations. Another focus of hers is on optimal combinations of model- and data-based approaches, where she, for instance, developed a state-of-the-art algorithm for the limited-angle computed tomography problem using a combination of deep neural networks and sparse regularization by shearlets.