The two-dimensional dual tree discrete wavelet transform (DTWT2d).

USAGE:

wavDTWT.2d( x, n.levels = 3, biorthogonal = ``nearsyma", qshift = ``a" )

DESCRIPTION:

The two-dimensional version of the dual-tree complex wavelet transform (DTWT) applies the DTWT to each column and to each row of the input matrix (e.g., an image).

REQUIRED ARGUMENTS:

x
A numeric matrix having an even number of rows and columns.

OPTIONAL ARGUMENTS:

n.levels
The number of decomposition levels. Default: min(logb(dim(x), base = 2)).
biorthogonal
A character string denoting the level one biorthogonal filter type. Supported types are ``antonini", ``legall", ``nearsyma", and ``nearsymb". Default: ``nearsyma".
qshift
A character string denoting the Q-Shift filter type used for levels greater than one. Supported types are ``a", ``b", ``c", and ``d". Default: ``a".

VALUE:

result
An object of class WaveletDualTree2d.

REFERENCES:

(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.

SEE ALSO:

, , .

EXAMPLES:

   ## 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)