fld2dt: transform a field into an array of spectral energies

In dualtrees: Decimated and Undecimated 2D Complex Dual-Tree Wavelet Transform

transform a field into an array of spectral energies

Description

Handles the transformation itself, boundary conditions and bias correction and returns the unbiased local wavelet spectrum at each grid-point.

Usage

fld2dt(fld, Nx = NULL, Ny = NULL, J = NULL, correct = TRUE,
  rsm = 0, verbose = FALSE, boundaries = "pad",
  fb1 = near_sym_b_bp, fb2 = qshift_b_bp)

Arguments

fld	a real matrix
Nx	size to which the field is padded in x-direction
Ny	size to which the field is padded in y-direction
J	number of levels for the decomposition
correct	logical, whether or not to apply the bias correction
rsm	number of pixels to be linearly smoothed along each edge before applying the boundary conditions (see smooth_borders).
verbose	whether or not you want the transform to talk to you
boundaries	how to handle the boundary conditions, either "pad", "mirror" or "periodic"
fb1	filter bank for level 1
fb2	filter bank for all further levels

Details

The input is blown up to Nx x Ny and transformed by dtcwt(..., dec=FALSE). Then the original domain is cut out, the coefficients are squared and the bias is corrected (for details on the bias, see A).

Value

an array of size J x nx x ny x 6 where dim(fld)=c(nx,ny)

References

Nelson, J. D. B., A. J. Gibberd, C. Nafornita, and N. Kingsbury (2018) <doi:10.1007/s11222-017-9784-0>

See Also

A

Examples

oldpar <- par( no.readonly=TRUE )
dt <- fld2dt( blossom )
par( mfrow=c(2,2), mar=rep(2,4) )
for( j in 1:4 ){
    image( blossom, col=gray.colors(128, 0,1), xaxt="n", yaxt="n" )
    for(d in  1:6) contour( dt[j,,,d], levels=quantile(dt[,,,], .995), 
                            col=d+1, add=TRUE, lwd=2, drawlabels=FALSE )
    title( main=paste0("j=",j) )
} 
x0  <- seq( .1,.5,,6 )
y0  <- rep( 0.01,6 )
a   <- .075
phi <- seq( 15,,30,6 )*pi/180
x1  <- x0 + a*cos( phi )
y1  <- y0 + a*sin( phi )
rect( min(x0,x1)-.05, min(y0,y1)-.05, 
      max(x0,x1)+.05, max(y0,y1), col="black", border=NA )
arrows( x0, y0, x1, y1, length=.05, col=2:7, lwd=2, code=3 )
par( oldpar )

dualtrees documentation built on Oct. 4, 2023, 5:10 p.m.