3d_cylind_shear

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.

3d Cylindrical Shearlet transform for Matlab

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.

Additional literature

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

Credits

• 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