dst.q

Implementation of the discrete shearlet transform, according to our LNLA 2009 Paper:

B. Goossens, J. Aelterman, H. Q. Luong, A. Pizurica and W. Philips, “Efficient Design of a Low Redundant Discrete Shearlet Transform, “ in 2009 International Workshop on Local and Non-Local Approximation in Image Processing (LNLA2009), August 19-21, 2009, Tuusula, Finland (invited paper)

Summary

dst.q	Implementation of the discrete shearlet transform, according to our LNLA 2009 Paper:
Functions
pseudo_polargrid	Constructs of a pseudo-polar grid
wedge_filter	Computes shearlet wedge filters
meyer_radial_wavelet_filters	Computes Meyer radial wavelet filters used in the implementation of the discrete shearlet transform.
subsample_fft	Computes a subsampling operation in FFT domain
upsample_fft	Computes an upsampling operation in FFT domain
pyramid_fft	Pyramid decomposition in FFT domain
ipyramid_fft	Pyramid reconstruction in FFT domain
shearlet_analysis	Computes the discrete shearlet transform
shearlet_synthesis	Computes the inverse discrete shearlet transform
shearlet_compute_energy_per_subband	Computes the energy per subband, useful for subband normalization.

Constructs of a pseudo-polar grid

[r, theta] = pseudo_polargrid(M : int, N : int)

M	the height of the grid (# samples in the y-direction)
N	the width of the grid (# samples in the x-direction)
r	the radial components
theta	the angular components

Computes shearlet wedge filters

function G = wedge_filter(sz,K,bw)

sz	the size of the input image
K	the number of orientations
bw	the transition bandwidth (pi/32..pi/2)

Computes Meyer radial wavelet filters used in the implementation of the discrete shearlet transform.

function H=meyer_radial_wavelet_filters(sz,J)

sz	the size of the input images
J	the number of scales of the transform

Computes a subsampling operation in FFT domain

subsample_fft(x, D)

Computes an upsampling operation in FFT domain

function y = upsample_fft(x, D)

Pyramid decomposition in FFT domain

function w = pyramid_fft(x, af, df)

x	DFT coefficients of the input image
af	DFT coefficients of the analysis/synthesis filters
df	the decimation factors for each filter

Pyramid reconstruction in FFT domain

function y = ipyramid_fft(w, af, df)

w	FFT pyramid coefficients
af	DFT coefficients of the analysis/synthesis filters
df	the upsampling factors for each filter

Computes the discrete shearlet transform

function w = shearlet_analysis(x, J, K, af, G, decimate=1)

x	input image (real-valued or complex-valued)
J	number of scales
K	number of orientations
af	analysis wavelet filters
G	analysis shearing filters
decimate	perform radial decimation (to reduce the redunancy without loss of information).

Computes the inverse discrete shearlet transform

function y = shearlet_synthesis(w, J, K, af, G, decimate=1)

w	shearlet/scaling coefficients
J	number of scales
K	number of orientations
af	synthesis wavelet filters
G	synthesis shearing filters
decimate	shearlet coefficients are computed with radial decimation

Computes the energy per subband, useful for subband normalization.

function e = shearlet_compute_energy_per_subband(J, K, af, G)