To try out the decomposition and reconstruction algorithms simply run example1.m.
3DBP contains the Laplacian pyramid decomposition codes and Util the other utility files. StarSize128.mat is a 3d example volume.
Numerical implementation of the cylindrical shearlet decomposition and reconstruction schemes for 3-dimensional data as described in
- "Optimally sparse representations of cartoon-like cylindrical data",
Glenn R. Easley, Kanghui Guo, Demetrio Labate & Basanta R. Pahari.
The Journal of Geometric Analysis 31: 8926-8946, (2021).
DOI: 10.1007/s12220-020-00493-0
Please cite the above article if you use these codes in your own projects.
Cylindrical shearlets are first introduced in
- "Smooth projections and the construction of smooth parseval frames of shearlets",
B. G. Bodmann, D. Labate & B. R. Pahari.
Advances in Computational Mathematics, 45(5):3241–3264, (2019).
DOI: 10.1007/s10444-019-09736-3
Extension to 4D described in
- "Efficient representation of spatio-temporal data using cylindrical shearlets",
T. A. Bubba, G. Easley, T. Heikkilä, D. Labate & J. P. Rodriguez Ayllon.
Journal of Computational and Applied Mathematics, Volume 429, 115206, (2023).
DOI: 10.1016/j.cam.2023.115206
Codes available in Github
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Filter setup, decomposition and reconstruction algorithms by Glenn Easley.
Directional 2d shearlet filters described in:
"Sparse Directional Image Representations using the Discrete Shearlet Transform", G. Easley, D. Labate & W. Q. Lim. Applied and Computational Harmonic Analysis, 25.1: 25-46, (2008). -
Laplacian pyramid decomposition scheme is part of SurfBox, the Surfacelet Toolbox for Matlab by Yue Lu and Minh N. Do:
"Multidimensional Directional Filter Banks and Surfacelets", Y. M. Lu & M. N. Do. IEEE Transactions on Image Processing, 16(4):918-931, (2007). -
Adjoint algorithm by Tommi Heikkilä