wavDTWT.2d( x, n.levels = 3, biorthogonal = ``nearsyma", qshift = ``a" )
(1) N. G. Kingsbury, ``The dual-tree complex wavelet transform: a new efficient tool for image restoration and enhancement'', Proc. EUSIPCO 98, Rhodes, Sept. 1998.
(2) N. G. Kingsbury, ``Image processing with complex wavelets'', Phil. Trans. Royal Society London A, Sept. 1999, pp. 2543-2560.
(3) N. G. Kingsbury, ``A dual-tree complex wavelet transform with improved orthogonality and symmetry properties'', Proc. IEEE Conf. on Image Processing, Vancouver, Sept. 11-13, 2000, Paper 1429.
(4) I. Daubechies, ``Orthonormal Bases of Compactly Supported Wavelets'', Communications on Pure and, Applied Mathematics, 41, 909-96.
## create an image
img <- make.image("flower", 128)
## calculate DTWT coefficients of an image x.img
## through level 3
y <- wavDTWT.2d(img, n.levels = 3, bior = "nearsymb",
+ qshift = "b", title.data = "Flower" )
## display results
print(y)
## plot complex magnitudes (decibels) of wavelet
## coefficients for all six angular orientations
## at level 1
plot(y, level=1)
## same plot, but showing actual magnitudes, not decibels
plot(y, decibels=F, level = 1)
## same plot, but with all magnitudes less than 60
## percent of maximum values set to zero
plot(y, decibels=F, level = 1, threshold=0.60)
## same type of plot, but showing an enlarged view of
## only the +15 deg plot
plot(y, decibels=F, level = 1, angle=15, threshold=0.60)
## same as above, but showing both the +15 deg and
## -15 deg plots
plot(y, decibels=F, level = 1, angle=c(15,-15),
+ threshold=0.60)
## reconstruct image from its 2D DTWT
img.recon <- reconstruct(y)
## verify reconstruction
vecnorm(img.recon - img)/vecnorm(img)