Dualtree: Dual-tree Complex Discrete Wavelet Transform

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

One- and two-dimensional dual-tree complex discrete wavelet transforms developed by Kingsbury and Selesnick et al.

Usage

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dualtree(x, J, Faf, af)
idualtree(w, J, Fsf, sf)
dualtree2D(x, J, Faf, af)
idualtree2D(w, J, Fsf, sf)

Arguments

x

N-point vector or MxN matrix.

w

DWT coefficients.

J

number of stages.

Faf

analysis filters for the first stage.

af

analysis filters for the remaining stages.

Fsf

synthesis filters for the last stage.

sf

synthesis filters for the preceeding stages.

Details

In one dimension N is divisible by 2^J and N≥2^{J-1}\cdot\mbox{length}(\mbox{\code{af}}).

In two dimensions, these two conditions must hold for both M and N.

Value

For the analysis of x, the output is

w

DWT coefficients. Each wavelet scale is a list containing the real and imaginary parts. The final scale (J+1) contains the low-pass filter coefficients.

For the synthesis of w, the output is

y

output signal

Author(s)

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

References

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

See Also

FSfarras, farras, convolve, cshift, afb, sfb.

Examples

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## EXAMPLE: dualtree
x = rnorm(512)
J = 4
Faf = FSfarras()$af
Fsf = FSfarras()$sf
af = dualfilt1()$af
sf = dualfilt1()$sf
w = dualtree(x, J, Faf, af)
y = idualtree(w, J, Fsf, sf)
err = x - y
max(abs(err))

## Example: dualtree2D
x = matrix(rnorm(64*64), 64, 64)
J = 3
Faf = FSfarras()$af
Fsf = FSfarras()$sf
af = dualfilt1()$af
sf = dualfilt1()$sf
w = dualtree2D(x, J, Faf, af)
y = idualtree2D(w, J, Fsf, sf)
err = x - y
max(abs(err))

## Display 2D wavelets of dualtree2D.m

J <- 4
L <- 3 * 2^(J+1)
N <- L / 2^J
Faf <- FSfarras()$af
Fsf <- FSfarras()$sf
af <- dualfilt1()$af
sf <- dualfilt1()$sf
x <- matrix(0, 2*L, 3*L)
w <- dualtree2D(x, J, Faf, af)
w[[J]][[1]][[1]][N/2, N/2+0*N] <- 1
w[[J]][[1]][[2]][N/2, N/2+1*N] <- 1
w[[J]][[1]][[3]][N/2, N/2+2*N] <- 1
w[[J]][[2]][[1]][N/2+N, N/2+0*N] <- 1
w[[J]][[2]][[2]][N/2+N, N/2+1*N] <- 1
w[[J]][[2]][[3]][N/2+N, N/2+2*N] <- 1
y <- idualtree2D(w, J, Fsf, sf)
image(t(y), col=grey(0:64/64), axes=FALSE)

andrewzm/waveslim documentation built on May 10, 2019, 11:16 a.m.