A Necessary Condition for a Shearlet System to be a Frame via Admissibility

Document Type: Research Paper

Authors

1 Department of Applied Mathematics, Faculty of Sciences and new Technologies, Graduate University of Advanced Technology, P. O. Box 76315-115, Kerman, Iran.

2 Shahid Bahonar University of Kerman

3 Ferdowsi University of Mashhad

10.22072/wala.2017.59948.1105

Abstract

    Necessary conditions for  shearlet  and cone-adapted shearlet systems to be frames are presented with respect to the admissibility condition of generators.

Keywords


[1] 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., 6(2) (2008), 157-181.
[2] S. Dahlke, G. Kutyniok, G. Steidl and G. Teschke, Shearlet coorbit spaces and associated Banach frames, Appl. Comput. Harmon. Anal., 27(2) (2009), 195-214.
[3] S. Dahlke, G. Steidl and G. Teschke, The continuous shearlet transform in arbitrary space dimensions, J. Fourier Anal. Appl., 16(3) (2010), 340-364.
[4] S. Dahlke, G. Steidl and G. Teschke, Multivariate shearlet transform, shearlet coorbit spaces and their structural properties, Shearlets: Multiscale Analysis for Multivariate Data, Springer, (2012), 105-144.
[5] S. Dahlke, G. Steidl and G. Teschke, Shearlet coorbit spaces: compactly supported analyzing shearlets traces and embeddings, J. Fourier Anal. Appl., 17(6) (2011), 1232-1255.
[6] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis, IEEE Trans. Inf. Theory}, 36(5), (1990), 961-1005.
[7] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
[8] 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, (2006), 189-201.
[9] S. Häuser and G. Steidl, Convex multiclass segmentation with shearlet regularization, Int. J. Comput Math., 90(1) (2013), 62-81.
[10] P. Kittipoom, G. Kutyniok and W.-Q. Lim, Construction of compactly supported shearlet frames, Constr. Approx., 35(1) (2012), 21-72.
[11] G. Kutyniok and D. Labate, Construction of regular and irregular shearlet frames, J. Wavelet Theory and Appl., 1(1) (2007), 1-12.
[12] G. Kutyniok and D. Labate, Resolution of the wavefront set using continuous shearlets, Trans. Am. Math. Soc., 361(5) (2009), 2719-2754.
[13] G. Kutyniok and D. Labate, Shearlets: Multiscale Analysis for Multivariate Data, Birkh"auser, Basel, 2012.
[14] D. Labate, W.-Q Lim, G. Kutyniok and G. Weiss, Sparse multidimensional representation using shearlets,
 Proceedings Volume 5914, Wavelets XI; 59140U, 2005.