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_contents_.txt
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
PREREQUISITES: WAVELAB850, download at http://www-stat.stanford.edu/~wavelab/
NUFFT (for nonuniform sampling), download at http://web.eecs.umich.edu/~fessler/irt/irt/
SPGL1 (for compressed sensing), download at https://www.math.ucdavis.edu/~mpf/spgl1/
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
I. GS_handles: different reconstruction operators (handle functions)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Haar_Op_Handle.m %1D GS operator with Haar wavelets and uniform Fourier samples (acting on a vector)
Haar_Op_Handle_Scaling.m %1D GS operator with Haar scaling functions and uniform Fourier samples (acting on a vector)
Haar_Op2_VecHandle.m %2D GS operator with Haar wavelets and uniform Fourier samples (acting on a vector)
Haar_Op2_Wavelet.m %2D GS operator with Haar wavelets and uniform Fourier samples (acting on a matrix)
Haar_Op_Handle_NU.m %1D GS operator with Haar wavelets and arbitrary (nonuniform) Fourier samples (acting on a vector)
Haar_Op2_VecHandle_NU.m %2D GS operator with Haar wavelets and arbitrary Fourier samples (acting on a vector)
Haar_Op2_Handle_NU.m %2D GS operator with Haar wavelets and arbitrary Fourier samples (acting on a wavelet-matrix)
CDJV_Op_Handle.m %1D GS operator with CDJV (boundary-corrected) wavelets and uniform Fourier samples (acting on a vector)
CDJV_Op_Scaling.m %1D GS operator with CDJV scaling functions and uniform Fourier samples (acting on a vector)
CDJV_Op2_VecHandle.m %2D GS operator with CDJV wavelets and uniform Fourier samples (acting on a vector)
CDJV_Op2_Wavelet.m %2D GS operator with CDJV wavelets and uniform Fourier samples (acting on a matrix)
CDJV_Op_Handle_NU.m %1D GS operator with CDJV wavelets and arbitrary Fourier samples (acting on a vector)
CDJV_Op_Scaling_NU.m %1D GS operator with CDJV scaling functions and arbitrary Fourier samples (acting on a vector)
CDJV_Op2_VecHandle_NU.m %2D GS operator with CDJV wavelets and arbitrary Fourier samples (acting on a vector)
CDJV_Op2_Handle_NU.m %2D GS operator with CDJV wavelets and arbitrary Fourier samples (acting on a wavelet-matrix)
DFT_DWT_Op.m %2D operator corresponding to compressed sensing with DFT measurements and DWT as the sparsifying transform
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
II. Wavelet_tools: files for handling wavelets
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
haar_phi_ft.m %calculates the Fourier transform of Haar scaling function
haar_psi_ft.m %calculates the Fourier transform of Haar wavelet function
CDJV_Setup.m %returns the Fourier transforms of internal and boundary scaling functions for uniform samples
CDJV_Setup_NU1D.m %returns the Fourier transforms of internal and boundary scaling functions for arbitrary samples in 1D
CDJV_Setup_NU2D.m %returns the Fourier transforms of internal and boundary scaling functions for arbitrary samples in 2D
CDJV_FT_Vec.m %calculates pointwise evaluation of the Fourier transforms of internal (by calling FTfromFilter.m)
%and boundary scaling functions (by calling CDJV_FTfromFilter.m).
CDJV_FTfromFilter.m %see CDJV_FT_Vec.m
FTfromFilter.m %see CDJV_FT_Vec.m
get1DHaarReconstruction.m %evaluates 1D Haar reconstruction on a grid from given wavelet coefficients
get2DHaarReconstruction.m %evaluates 2D Haar reconstruction on a grid from given wavelet coefficients
get1DReconstruction.m %evaluates 1D CDJV reconstruction on a grid from given wavelet coefficients
get1DReconstruction.m %evaluates 2D CDJV reconstruction on a grid from given wavelet coefficients
getScalingMatrix.m %returns a matrix of pointwise evaluations of scaling functions
getScalingFn.m %computes pointwise evaluations of a scaling function on grid points
psi_jl.m %scales and shifts a given vector
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
III. Utilities: files for handling different sampling schemes
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Samples.m %calculates pointwise evaluations of the Fourier transform at equispaced points, for a given function
Samples_NU.m %calculates pointwise evaluations of the Fourier transform at arbitrary points, for a given function
jittered_sampling_1d.m %returns sampling points taken on 1D jittered sampling scheme
log_sampling_1d.m %returns sampling points taken on 1D log sampling scheme
jittered_sampling_2d.m %returns sampling points taken on 2D jittered sampling scheme
polar_sampling.m %returns sampling points taken on 2D radial sampling scheme
spiral_sampling.m %returns sampling points taken on 2D spiral sampling scheme
GetSampleMask1D.m %returns 1D sampling mask for compressed sensing, consisting of different levels
GetSampleMask2D.m %returns 2D sampling mask for compressed sensing, consisting of different levels
GetLinesMask.m %returns 2D sampling mask for compressed sensing, consisting of radial lines on an equispaced grid
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
IV. GS_matrices: files that produce GS matrices
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Haar_1DMatrix.m %generates 1D GS matrix with Haar and uniform Fourier samples
Haar_2DMatrix.m %generates 2D GS matrix with Haar and uniform Fourier samples
Haar_Scal_1DMatrix_jit.m %generates 1D GS matrix with Haar scaling functions and jittered Fourier samples
Haar_Scal_2DMatrix_NU.m %generates 2D GS matrix with Haar scaling functions and radial or spiral Fourier samples
CDJV_1DMatrix.m %generates 1D GS matrix with CDJV wavelets and uniform Fourier samples
CDJV_2DMatrix.m %generates 2D GS matrix with CDJV wavelets and uniform Fourier samples
CDJV_1DMatrix_jit.m %generates 1D GS matrix with CDJV wavelets and jittered Fourier samples
CDJV_1DMatrix_log.m %generates 1D GS matrix with CDJV wavelets and log Fourier samples
CDJV_2DMatrix_NU.m %generates 2D GS matrix with CDJV wavelets and radial or spiral Fourier samples
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
V. WaveLabFiles: updates of some Wavelab files
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MakeCDJVFilter.m %sets up filters for CDJV Wavelet Transform for orders 2-8
%NB: MakeCDJVFilter.m from Wavelab850 only supports CDJV filters up to order 3.
%Replace the MakeCDJVFilter.m from Wavelab with this file for higher wavelet orders.
CDJV_Filters %folder with text files for CDJV wavelet filters of order 2-8
IWT2_CDJV.m %IWT for 2D boundary-corrected wavelets
FWT2_CDJV.m %FWT for 2D boundary-corrected wavelets
FWT2_CDJV_noP.m %FWT for 2D boundary-corrected wavelets without preconditioning
IWT2_CDJV_noP.m %IWT for 2D boundary-corrected wavelets without postconditioning
FWT_CDJV_noP.m %FWT for 1D boundary-corrected wavelets without preconditioning
IWT_CDJV_noP.m %IWT for 1D boundary-corrected wavelets without postconditioning
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
VI. Examples: contains several example files
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
See _contents_examples_.m for more information.