324 citations · 1.4k across the 135 of their papers we have counts for
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Analysis of simultaneous inpainting and geometric separation based on sparse decomposition
Van Tiep Do, Ron Levie, Gitta Kutyniok
Natural images are often the superposition of various parts of different geometric characteristics. For instance, an image might be a mixture of cartoon and texture structures. In…
Approximation spaces of deep neural networks
Rémi Gribonval, Gitta Kutyniok, Morten Nielsen +1
We study the expressivity of deep neural networks. Measuring a network's complexity by its number of connections or by its number of neurons, we consider the class of functions for…
Error bounds for approximations with deep ReLU neural networks in norms
Ingo Gühring, Gitta Kutyniok, Philipp Petersen
We analyze approximation rates of deep ReLU neural networks for Sobolev-regular functions with respect to weaker Sobolev norms. First, we construct, based on a calculus of ReLU net…
Compressed Sensing for Analog Signals
Bernard G. Bodmann, Axel Flinth, Gitta Kutyniok
In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in…
Anisotropic Multiscale Systems on Bounded Domains
Philipp Grohs, Gitta Kutyniok, Jackie Ma +2
We provide a construction of multiscale systems on a bounded domain coined boundary shearlet systems, which satisfy several properties advantageous for appl…
The Effect of Perturbations of Operator-Valued Frame Sequences and Fusion Frames on Their Duals
Gitta Kutyniok, Victoria Paternostro, Friedrich Philipp
Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences…
Dualizable Shearlet Frames and Sparse Approximation
Gitta Kutyniok, Wang-Q Lim
Shearlet systems have been introduced as directional representation systems, which provide optimally sparse approximations of a certain model class of functions governed by anisotr…
Classification of Edges Using Compactly Supported Shearlets
Gitta Kutyniok, Philipp Petersen
We analyze the detection and classification of singularities of functions , where and . It will be shown how the set can be…
-Molecules
Philipp Grohs, Sandra Keiper, Gitta Kutyniok +1
Within the area of applied harmonic analysis, various multiscale systems such as wavelets, ridgelets, curvelets, and shearlets have been introduced and successfully applied. The ke…
Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames
Gitta Kutyniok, Volker Mehrmann, Philipp Petersen
Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most pro…
Measures of scalability
Xuemei Chen, Gitta Kutyniok, Kasso A. Okoudjou +2
Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximat…
Asymptotic Analysis of Inpainting via Universal Shearlet Systems
Martin Genzel, Gitta Kutyniok
Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a car…
Cartoon Approximation with -Curvelets
Philipp Grohs, Sandra Keiper, Gitta Kutyniok +1
It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise -functions, separated by a singularity curve.…
Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements
Ben Adcock, Anders C. Hansen, Gitta Kutyniok +1
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-s…
Gabor Shearlets
Bernhard G. Bodmann, Gitta Kutyniok, Xiaosheng Zhuang
In this paper, we introduce Gabor shearlets, a variant of shearlet systems, which are based on a different group representation than previous shearlet constructions: they combine e…
Parabolic Molecules
Philipp Grohs, Gitta Kutyniok
Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significantly increased attention due to t…
Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis
Emily J. King, Gitta Kutyniok, Xiaosheng Zhuang
Recently, compressed sensing techniques in combination with both wavelet and directional representation systems have been very effectively applied to the problem of image inpaintin…
Clustered Sparsity and Separation of Cartoon and Texture
Gitta Kutyniok
Natural images are typically a composition of cartoon and texture structures. A medical image might, for instance, show a mixture of gray matter and the skull cap. One common task…
Geometric Separation by Single-Pass Alternating Thresholding
Gitta Kutyniok
Modern data is customarily of multimodal nature, and analysis tasks typically require separation into the single components. Although a highly ill-posed problem, the morphological…
Sparsity and spectral properties of dual frames
Felix Krahmer, Gitta Kutyniok, Jakob Lemvig
We study sparsity and spectral properties of dual frames of a given finite frame. We show that any finite frame has a dual with no more than non-vanishing entries, where …
Optimally sparse approximations of 3D functions by compactly supported shearlet frames
Gitta Kutyniok, Jakob Lemvig, Wang-Q Lim
We study efficient and reliable methods of capturing and sparsely representing anisotropic structures in 3D data. As a model class for multidimensional data with anisotropic featur…
Shearlets and Optimally Sparse Approximations
Gitta Kutyniok, Jakob Lemvig, Wang-Q Lim
Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for…
Sparsity Equivalence of Anisotropic Decompositions
Gitta Kutyniok
Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that t…
Compactly Supported Shearlets
Gitta Kutyniok, Jakob Lemvig, Wang-Q Lim
Shearlet theory has become a central tool in analyzing and representing 2D data with anisotropic features. Shearlet systems are systems of functions generated by one single generat…