Detailed construction and numerical tests in:
T. A. Bubba, G. Easley, T. Heikkilä, D. Labate and J. P. Rodriguez Ayllon. "Efficient representation of spatio-temporal data using cylindrical shearlets" (2023). Journal of Computational and Applied Mathematics, Volume 429, 115206.
Please cite the above article if you use these codes in your own projects.
Root: Readme and license files and the following 4 folders.
main: Simple test script testMain.m to try some of the properties, including forming the directional filters and computing forward, inverse and adjoint transforms of a simple 4d object. hypercube.m is a helper function for creating a semi-random 4d phantom. cartoonPhantom.m is the custom ellipsoid phantom used for the dynamic tomography tests.
BP: Short for bandpass, this folder contains the necessary routines and functions to perform the Laplacian pyramid decomposition and its inverse (reconstruction).
dirFilters: Contains the GetMeyerBasedFilter.m routine for creating the directional filters and all of the additional functions for splitting the Fourier domain to pyramids and sampling on polar and cartesian grids.
4dCylShearTrans: Contains the routines for the forward, inverse and adjoint transforms and the function cylconv3d.m which performs 3d cylindrical convolution using Fourier transform along the first 3 coordinates/components.
Decomposition, inverse and adjoint transforms, and extension of (pseudo)4d directional filters by Tommi Heikkilä.
This work is based on the 3d Cylindrical Shearlet implementation by Glenn Easley:
G. Easley, K. Guo, D. Labate and B. Pahari. "Optimally sparse representation of cartoon-like cylindrical data" (2020). The Journal of Geometric Analysis, pages 1-21.
Matlab implementation of the 3d cylindrical shearlet transform is available here.
Generation of 3d Meyer-like directional filters by Pooran Negi, with contributions of D. Labate:
P. Negi and D. Labate. "3-d discrete shearlet transform and video processing" (2021). IEEE transactions on Image Processing, 21(6):2944-2954.
Laplacian pyramid decomposition scheme is part of Surfacelet Toolbox for Matlab (SurfBox) by Yue Lu and Minh N. Do:
Y. M. Lu and M. N. Do. "Multidimensional Directional Filter Banks and Surfacelets" (2007). IEEE Transactions on Image Processing, 16(4):918-931.
Extended array indexing function exindex.m by David Young:
D. Young. "Extended array indexing" (2010). MATLAB Central File Exchange, (https://www.mathworks.com/matlabcentral/fileexchange/27117-extended-array-indexing).
Some functions in dirFilters -folder are still missing their original authors.