Dual-tree Complex 2D Discrete Wavelet Transform

Dual-tree complex 2D discrete wavelet transform (DWT).

cplxdual2D(x, J, Faf, af)
icplxdual2D(w, J, Fsf, sf)

Arguments

x	2D array.
w	wavelet coefficients.
J	number of stages.
Faf	first stage analysis filters for tree \(i\).
af	analysis filters for the remaining stages on tree \(i\).
Fsf	last stage synthesis filters for tree \(i\).
sf	synthesis filters for the preceeding stages.

Value

For the analysis of x, the output is

w

wavelet coefficients indexed by [[j]][[i]][[d1]][[d2]], where \(j=1,\ldots,J\) (scale), \(i=1\) (real part) or \(i=2\) (imag part), \(d1=1,2\) and \(d2=1,2,3\) (orientations).

For the synthesis of w, the output is

y

output signal.

References

WAVELET SOFTWARE AT POLYTECHNIC UNIVERSITY, BROOKLYN, NY
http://taco.poly.edu/WaveletSoftware/

See also

FSfarras, farras, afb2D, sfb2D.

Author

Matlab: S. Cai, K. Li and I. Selesnick; R port: B. Whitcher

Examples

if (FALSE) {
## EXAMPLE: cplxdual2D
x = matrix(rnorm(32*32), 32, 32)
J = 5
Faf = FSfarras()$af
Fsf = FSfarras()$sf
af = dualfilt1()$af
sf = dualfilt1()$sf
w = cplxdual2D(x, J, Faf, af)
y = icplxdual2D(w, J, Fsf, sf)
err = x - y
max(abs(err))
}