Publications

In recent years shearlet analysis has become a mature research field with a variety of interesting results. Below we try to give an overview of all publications that have contributed to this theory. If you spot a paper we have missed, please feel free to contact our team.

ShearLab

Shearlet Theory - Recommended reading

Shearlet Theory and Applications

  • J. Ma, M. März
    A multilevel based reweighting algorithm with joint regularizers for sparse recovery.
    Submitted (2016)
  • A. Pein, S. Loock, G. Plonka, T. Salditt
    Using sparsity information for iterative phase retrieval in x-ray propagation imaging.
    Opt. Express 24 (2016), 8332-8343.
  • R. Reisenhofer, E. King, J. Kiefer
    Shearlet-Based Detection of Flame Fronts.
    Exp. Fluids 57 (2016), 41:1-41:14.
  • W. Dahmen, G. Kutyniok, W.-Q. Lim, C. Schwab, G. Welper
    Adaptive Anisotropic Petrov-Galerkin Methods for First Order Transport Equations.
    Submitted (2015).
  • S. Pejoski, V. Kafedziski, D. Gleich
    Compressed Sensing MRI Using Discrete Nonseperable Shearlet Transform and FISTA.
    IEEE Signal Process Lett. 22 (2015), 1566-1570.
  • M. Cotronei, D. Ghisi, M. Rossini, T. Sauer
    An anisotropic directional multiresolution and subdivision scheme.
    Adv. Comput. Math. (2015) 41, 709-726.
  • C. Sun, C. Tang, X. Zhu, X. Li, L. Wang
    An efficient method for salt-and-pepper noise removal based on shearlet transform and noise detection.
    AEU Int. J. Electron. Commun. 69 (2015), 1823-1832
  • J.-L. Starck, F- Murtagh, J. M. Fadili
    Sparse Image and Signal Processing. Wavelets and Related Geometric Multiscale Analysis.
    Cambridge University Press (2015).
  • Y. Li, L.-M. Po, C.-H. Cheung, X. Xu, L. Feng, F. Yuan, K.-W. Cheung
    No-Reference Video Quality Assesment with 3D Shearlet Transform and Convolutional Neural Networks
    IEEE Trans. Circuits Syst. Video Technol. PP (2015),
  • P. Grohs, G. Kutyniok, J. Ma, P. Petersen
    Anisotropic Multiscale Systems on Bounded Domains.
    Submitted (2015)
  • G. Kutyniok, W.-Q. Lim
    Optimal Compressive Imaging of Fourier Data.
    Submitted (2015).
  • E. King, G. Kutyniok, W.-Q. Lim
    Image Inpainting: Theoretical Analysis and Comparison of Algorithms.
    Wavelets and Sparsity XV (San Diego, CA, 2013), 885802-1-885802-11, SPIE Proc. 8858, SPIE, Bellingham, WA, 2013.
  • G. Kutyniok
    Geometric Separation by Single-Pass Alternating Thresholding.
    Appl. Comput. Harmon. Anal. 36 (2014), 23-50.
  • G. Kutyniok, P. Petersen.
    Classification of Edges using Compactly Supported Shearlets.
    Appl. Comput. Harmon. Anal., to appear
  • G. Kutyniok, W.-Q. Lim
    Dualizable Shearlet Frames and Sparse Approximation.
    Constr. Approx., to appear
  • G. Kutyniok, V. Mehrmann, P. Peterson.
    Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames.
    submitted (2014).
  • J. Ma, P. Petersen
    Linear independence of compactly supported separable shearlet systems.
    J. Math. Anal. Appl., 428(1): 238-257, 2015..
  • W. Dahmen, C. Huang, G. Kutyniok, W.-Q. Lim, C. Schwab, G. Welper
    Efficient Resolution of Anisotropic Structures.
    Extraction of Quantifiable Information from Complex Systems, 25-21, Springer, 2014.
  • P. Grohs, S. Keiper, G. Kutyniok, M. Schäfer
    alpha-Molecules
    Appl. Comput. Harmon. Anal., to appear.
  • M. Genzel, G. Kutyniok
    Asymptotic Analysis of Inpainting via Universal Shealet Systems
    SIAM J. Imaging Sci. 7 (2014), 2301-2339.
  • S. Dahlke, F. De Mari, E. De Vito, S. Häuser, G. Steidl, G. Teschke
    Different faces of the shearlet group
    J. Geom. Anal., DOI 10.1007/s12220-015-9605-7, 2015.
  • P. Grohs, S. Vigogna
    Intrinsic Localization of Anisotropic Frames II: alpha-Molecules
    J. Fourier Anal. Appl., to appear.
  • P. Grohs, S. Keiper, G. Kutyniok, M. Schäfer.
    alpha-Molecules: Curvelets, Shearlets, Ridgelets, and Beyond.
    to appear in Wavelets and Sparsity XV (San Diego, CA, 2013), SPIE Proc. 8858, SPIE, Bellingham, WA, (2013).
  • H. Lakshman, W.-Q. Lim, H. Schwarz, D. Marpe, G. Kutyniok, T. Wiegand
    Image interpolation using Shearlet based iterative refinement
    Signal. Proc. Image. Comm., to appear.
  • B.G. Bodmann, G. Kutyniok, X. Zhuang
    Gabor Shearlets
    Appl. Comput. Harmon. Anal. 38 /2015, 87-114.
  • W.-Q. Lim
    Nonseparable Shearlet Transform.
    to appear in IEEE Trans. Image Process. (2013)
  • S. Häuser, G. Steidl
    Convex Multiclass Segmentation with Shearlet Regularization.
    International Journal of Computer Mathematics. 90 pp. 62-81 (2013)
  • E.J. King, G. Kutyniok, X. Zhuang
    Analysis of Inpainting via Clustered Sparsity and Microlocal Analysis.
    J. Math. Imaging Vis. 48 (2014), 205-234.
  • P. Grohs and G. Kutyniok
    Parabolic Molecules.
    Found. Comput. Math. 14 (2014), 299-337.
  • D. Labate, L. Mantovani, and P. S. Negi
    Shearlet smoothness spaces.
    J. Fourier Anal. Appl. 19(3), 577-611, 2013.
  • K. Guo, and D. Labate
    The construction of smooth Parseval frames of shearlets
    Math. Model. Nat. Phenom 8(1), 82-105, 2013.
  • G. Kutyniok, J. Lemvig, and W.-Q Lim.
    Optimally Sparse Approximations of 3D Functions by Compactly Supported Shearlet Frames.
    SIAM J. Math. Anal. 44 pp. 2962-3017 (2012).
  • S. Häuser, J.Ma
    Seismic Data Reconstruction via Shearlet-Regularized Directional Inpainting
    Preprint
  • B. G. Bodmann, G. Kutyniok and X. Zhunag
    Coarse Qunatization with the Fast Digital Shearlet Transform.
    Wavelets and Sparsity XIV (San Diego, CA, 2009), SPIE Proc. 8138, SPIE, Bellingham, WA, (2011).
  • B. Han, G. Kutyniok, and Z. Shen
    Adaptive Multiresolution Analysis Structures and Shearlet Systems.
    SIAM J. Numer. Anal. 49 pp. 1921-1946, (2011).
  • G. Kanghui and D. Labate.
    Optimally Sparse Representations of 3D Data with C2 Surface Singularities using Parseval Frames of Shearlets.
    SIAM J Math. Anal. 44 p. 851-886 (2012).
  • G. Kutyniok, J. Lemvig and W.-Q Lim.
    Optimally Sparse Approximations of Multivariate Functions Using Compactly Supported Shearlet Frames.
    SampTA'11 (Singapore, 2011), Proc., (2011).
  • G. Kanghui and D. Labate.
    Analysis and Detection of Surface Discontinuities using the 3D Continuous Shearlet Transform.
    Appl. Comput. Harmon. Anal., 30 p. 231-242 (2011).
  • G. Kanghui and D. Labate.
    Optimally Sparse 3D Approximations using Shearlet Representations.
    Electronic Research Announcements in Mathematical Sciences, 17 pp 126-138, (2010).
  • G. Kutyniok and D. Labate.
    Shearlets. The First Five Year.
    Oberwolfach Report No. 44/2010 (2010).
  • G. Kutyniok and W.-Q Lim.
    Image Separation Using Wavelets and Shearlets.
    Curves and Surfaces (Avignon, France, 2010), Lecture Notes in Computer Science 6920, Springer, (2011).
  • G. Kutyniok, J. Lemvig and W.-Q Lim.
    Compactly Supported Shearlets.
    Approximation Theory XIII (San Antonio, TX, 2010), Springer Proc. Math. 13, 187-206, Springer,(2012).
  • G. Kutyniok, and W.-Q Lim.
    Shearlets on Bounded Domains.
    Approximation Theory XIII (San Antonio, TX, 2010), Springer Proc. Math. 13, 187-206, Springer, (2012).
  • P. Kittipoom, G. Kutyniok, and W.-Q Lim.
    Construction of Compactly Supported Shearlet Frames.
    Constr. Approx. 35 pp. 21-72 (2012).
  • G. Kutyniok and W.-Q Lim.
    Compactly Supported Shearlets are Optimally Sparse
    J. Approx. Theory 163 pp. 1564-1589, (2011).
  • P. Kittipoom, G. Kutyniok, and W.-Q Lim.
    Irregular Shearlet Frames: Geometry and Approximation Properties.
    J. Fourier Anal. Appl. 17 pp. 604-639, (2011).
  • D. L. Donoho and G. Kutyniok.
    Geometric Separation using a Wavelet-Shearlet Dictionary.
    SAMPTA'09, Marseille : France (2009).
  • S. Dahlke, G. Kutyniok, G. Steidl, and G. Teschke.
    Shearlet Coorbit Spaces and associated Banach Frames.
    Appl. Comput. Harmon. Anal. 27 pp. 195-214, (2009).
  • G. Kutyniok and T. Sauer.
    Adaptive Directional Subdivision Schemes and Shearlet Multiresolution Analysis.
    SIAM J. Math. Anal. 41 pp. 1436-1471, (2009).
  • F. Colonna, G. R. Easley, K. Guo, and D. Labate.
    Radon Transform Inversion using the Shearlet Representation.
    Appl. Comput. Harmon. Anal., 29(2), pp. 232-250, (2010)
  • K. Guo, and D. Labate.
    Characterization and analysis of edges using the Continuous Shearlet Transform.
    SIAM on Imaging Sciences 2, pp. 959-986, (2009).
  • S. Yi, D. Labate, G. R. Easley, and H. Krim.
    A Shearlet Approach to Edge Analysis and Detection.
    IEEE Trans. Image Process. 18 (5) pp. 929-941, (2009).
  • K. Guo, D. Labate and W. Lim.
    Edge Analysis and identification using the Continuous Shearlet Transform.
    Appl. Comput. Harmon. Anal., pp. 31, (2009).
  • G. R. Easley, D. Labate, and F. Colonna.
    Shearlet Based Total Variation for Denoising.
    IEEE Trans. Image Process. 18 (2) pp. 260-268, (2009).
  • G. Easley, W.-Q Lim and D. Labate.
    Sparse Directional Image Representations using the Discrete Shearlet Transform.
    Appl. Comput. Harmon. Anal. 25 pp. 25-46, (2008).
  • G. Kutyniok and D. Labate.
    Resolution of the Wavefront Set using Continuous Shearlets.
    Trans. Amer. Math. Soc. 361 pp. 2719-2754, (2009).
  • G. Kutyniok and T. Sauer.
    From Wavelets to Shearlets and back again.
    Approximation Theory XII (San Antonio, TX, 2007), Nashboro Press, Nashville, TN (2007)
  • K. Guo and D. Labate.
    Representation of Fourier Integral Operators using Shearlets.
    J. Fourier Anal. Appl. 14 pp. 327-371, (2008)
  • S. Dahlke, G. Kutyniok, P. Maass, C. Sagiv, H.-G. Stark, and G. Teschke.
    The Uncertainty Principle associated with the Continuous Shearlet Transform.
    Int. J. Wavelets Multiresolut. Inf. Process., to appear.
  • K. Guo and D. Labate.
    Optimally Sparse Multidimensional Representation using Shearlets.
    SIAM J. Math Anal. 39 pp. 298-318, (2007).
  • G. Kutyniok and D. Labate.
    Construction of Regular and Irregular Shearlets.
    J. Wavelet Theory and Appl. 1 pp. 1-10, (2007).
  • K. Guo, G. Kutyniok, and D. Labate.
    Sparse Multidimensional Representations using Anisotropic Dilation and Shear Operators.
    Wavelets and Splines (Athens, GA, 2005), Nashboro Press, Nashville, TN pp. 189-201, (2006).
  • D. Labate, W.-Q Lim, G. Kutyniok, and G. Weiss.
    Sparse multidimensional representation using shearlets.
    Wavelets XI (San Diego, CA, 2005), 254-262, SPIE Proc. 5914, SPIE, Bellingham, WA, (2005).