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

• G. Kutyniok, W.-Q Lim, and R. Reisenhofer.
  ShearLab 3D: Faithful Digital Shearlet Transforms Based on Compactly Supported Shearlets.
  ACM Trans. Math. Software 42 (2016), Article No.: 5.
  Download numerical experiments.
• G. Kutyniok, M. Shahram, and X. Zhuang.
  ShearLab: A Rational Design of a Digital Parabolic Scaling Algorithm.
  SIAM J. Imaging Sci. 5 (2012), 1291–1332.

Shearlet Theory - Recommended reading

• G. Kutyniok, D. Labate
  Introduction to Shearlets.
  Shearlets: Multiscale Analysis for Multivariate Data, Springer, 2012.
• G. Kutyniok, J. Lemvig, W.-Q. Lim.
  Shearlets and Optimally Sparse Approximations.
  Shearlets: Multiscale Analysis for Multivariate Data, Springer, 2012.
• G. Kutyniok, W.-Q. Lim, X. Zhuang.
  Digital Shearlet Transforms.
  Shearlets: Multiscale Analysis for Multivariate Data, Springer, 2012

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.
  J. Comput. Appl. Math. 340 (2018), 191-220.
• 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.
  SIAM J. Imaging Sciences 11 (1) , 507-546 (2018).
• 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.
  J. of Inv. and Ill-Posed Prob. 25(3), 287-309 (2014).
• J. Ma, P. Petersen
  Linear independence of compactly supported separable shearlet systems.
  J. Math. Anal. Appl., 428(1): 238-257 (2017)
• 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).