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 Gitta Kutyniok

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Average citations per article2.72
Citation Count49
Publication count18
Publication years2007-2017
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Average downloads per article180.00
Downloads (cumulative)180
Downloads (12 Months)83
Downloads (6 Weeks)11
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18 results found Export Results: bibtexendnoteacmrefcsv

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1
November 2017 Journal of Mathematical Imaging and Vision: Volume 59 Issue 3, November 2017
Publisher: Kluwer Academic Publishers
Bibliometrics:
Citation Count: 0


2
October 2016
Bibliometrics:
Citation Count: 0

Since publication of the initial papers in 2006, compressed sensing has captured the imagination of the international signal processing community, and the mathematical foundations are nowadays quite well understood. Parallel to the progress in mathematics, the potential applications of compressed sensing have been explored by many international groups of, in ...

3 published by ACM
January 2016 ACM Transactions on Mathematical Software (TOMS): Volume 42 Issue 1, February 2016
Publisher: ACM
Bibliometrics:
Citation Count: 2
Downloads (6 Weeks): 11,   Downloads (12 Months): 83,   Downloads (Overall): 180

Full text available: PDFPDF
Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient in sparsely approximating and also in analyzing in the sense of, for instance, detecting their direction. Shearlets are a ...
Keywords: software package, Imaging sciences, shearlets, wavelets

4
August 2015 Image Communication: Volume 36 Issue C, August 2015
Publisher: Elsevier Science Inc.
Bibliometrics:
Citation Count: 0

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using FIR filtering, (b) promoting sparsity in a selected dictionary through hard thresholding to obtain an approximation, and (c) extracting high frequency ...
Keywords: Shearlets, Interpolation, Sparse representation

5
July 2015
Bibliometrics:
Citation Count: 0

Since publication of the initial papers in 2006, compressed sensing has captured the imagination of the international signal processing community, and the mathematical foundations are nowadays quite well understood. Parallel to the progress in mathematics, the potential applications of compressed sensing have been explored by many international groups of, in ...

6
July 2015 Journal of Mathematical Imaging and Vision: Volume 52 Issue 3, July 2015
Publisher: Kluwer Academic Publishers
Bibliometrics:
Citation Count: 0


7
June 2014 Computational Statistics: Volume 29 Issue 3-4, June 2014
Publisher: Kluwer Academic Publishers
Bibliometrics:
Citation Count: 1

Frame theory is closely intertwined with signal processing through a canon of methodologies for the analysis of signals using (redundant) linear measurements. The canonical dual frame associated with a frame provides a means for reconstruction by a least squares approach, but other dual frames yield alternative reconstruction procedures. The novel ...
Keywords: Dual frames, Frames, Redundancy, Tight frames, Signal processing

8
April 2014 Foundations of Computational Mathematics: Volume 14 Issue 2, April 2014
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significant attention due to the fact that they were shown to provide optimally sparse approximations of functions exhibiting singularities on lower dimensional embedded manifolds. The literature now contains various direct proofs of this ...
Keywords: 41AXX, 53B, Sparsity equivalence, 22E, Nonlinear approximation, Smoothness spaces, Shearlets, 41A25, Curvelets, Parabolic scaling

9
February 2014 Journal of Mathematical Imaging and Vision: Volume 48 Issue 2, February 2014
Publisher: Kluwer Academic Publishers
Bibliometrics:
Citation Count: 2

Recently, compressed sensing techniques in combination with both wavelet and directional representation systems have been very effectively applied to the problem of image inpainting. However, a mathematical analysis of these techniques which reveals the underlying geometrical content is missing. In this paper, we provide the first comprehensive analysis in the ...
Keywords: Sparse representation, Inpainting, Cluster coherence, Meyer wavelets, Shearlets, ℓ1 minimization, Data recovery, Parseval frames

10
September 2012
Bibliometrics:
Citation Count: 3

Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own ...

11
March 2012
Bibliometrics:
Citation Count: 9

Over the last20 years, multiscale methods and wavelets have revolutionized the field of applied mathematicsby providing an efficient means ofencoding isotropic phenomena. Directional multiscale systems, particularly shearlets,are now having the same dramatic impact on the encoding of multidimensional signals. Since its introduction about five years ago, the theory of shearlets ...

12
November 2011 Journal of Approximation Theory: Volume 163 Issue 11, November, 2011
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 13

Cartoon-like images, i.e., C^2 functions which are smooth apart from a C^2 discontinuity curve, have by now become a standard model for measuring sparse (nonlinear) approximation properties of directional representation systems. It was already shown that curvelets, contourlets, as well as shearlets do exhibit sparse approximations within this model, which ...
Keywords: Edges, Wavelets, Curvilinear discontinuities, Thresholding, Nonlinear approximation, Optimal sparsity, Shearlets

13
November 2011 IEEE Transactions on Information Theory: Volume 57 Issue 11, November 2011
Publisher: IEEE Press
Bibliometrics:
Citation Count: 2

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of the frame measurements of a signal typically requires a large number of additions and multiplications, ...

14
September 2011 SIAM Journal on Numerical Analysis: Volume 49 Issue 5, September 2011
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 1

In this paper, we first introduce the concept of an adaptive multiresolution analysis (AMRA) structure, which is a variant of the classical MRA structure well suited to the main goal of a fast flexible decomposition strategy adapted to the data at each decomposition level. We then study this novel methodology ...
Keywords: adaptive multiresolution analysis, shearlets, fast decomposition algorithm, affine systems, tight frames

15
July 2011 Advances in Computational Mathematics: Volume 35 Issue 1, July 2011
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 5

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert space, and thereby generalizes the concept of a frame for signal representation. However, when the signal and/or ...
Keywords: Fusion frames, Primary 94A12; Secondary 42C15, 68P30, Signal processing, 46C99, Frames, Hilbert spaces, Self-adjoint operators, Sparsity

16
June 2011 IEEE Transactions on Information Theory: Volume 57 Issue 6, June 2011
Publisher: IEEE Press
Bibliometrics:
Citation Count: 3

Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as compressed sensing (CS). Fusion frames are very rich new signal representation methods that use collections of subspaces instead of vectors to represent signals. This work ...

17
June 2010 Proceedings of the 7th international conference on Curves and Surfaces
Publisher: Springer-Verlag
Bibliometrics:
Citation Count: 1

In this paper, we present an image separation method for separating images into point- and curvelike parts by employing a combined dictionary consisting of wavelets and compactly supported shearlets utilizing the fact that they sparsely represent point and curvilinear singularities, respectively. Our methodology is based on the very recently introduced ...
Keywords: shearlets, wavelets, l1 minimization, geometric separation, sparse approximation

18
July 2007 Journal of Approximation Theory: Volume 147 Issue 1, July, 2007
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 5

An irregular wavelet frame has the form W(@j,@L)={a^-^1^/^[email protected](xa-b)}"("a","b")"@?"@L, where @[email protected]?L^2(R) and @L is an arbitrary sequence of points in the affine group A=R^+xR. Such irregular wavelet frames are poorly understood, yet they arise naturally, e.g., from sampling theory or the inevitability of perturbations. This paper proves that irregular wavelet frames ...
Keywords: 46C99, Affine systems, Frames, 42C15, Amalgam spaces, Density, Homogeneous Approximation Property, Time-scale shifts, Wavelets, 42C40, Riesz bases



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