Dualtree: Dual-tree Complex Discrete Wavelet Transform

In neuroconductor/waveslim: Basic Wavelet Routines for One-, Two-, and Three-Dimensional Signal Processing

Dual-tree Complex Discrete Wavelet Transform

Description

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

Usage

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.
J	number of stages.
Faf	analysis filters for the first stage.
af	analysis filters for the remaining stages.
w	DWT coefficients.
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

See Also

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

Examples

## 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)

neuroconductor/waveslim documentation built on Feb. 6, 2023, 6:56 a.m.