meyer.pyramid(x, wavelet="s8", n.levels=NULL, boundary="periodic", dual=F, analysis.filter=NULL, synthesis.filter=NULL)
"d4", "s8"
,
see
wavelet
for all available wavelet names.
If the length of
wavelet
is one, the same wavelet is used for both
row and column. See
wavelet
for details.
For user-provided filter, input the values in
analysis.filter
below.
boundary
is one, the same boundary rule is used for both
row and column.
The only available rule currently is:
`"periodic".
wavelet
for details.
filter
argument in
wave.filter
for
details.
filter
argument in
wave.filter
for
details. When
analysis.filter
is provided, then the default
synthesis.filter
is also
analysis.filter
.
meyer.pyramid
, inheriting from the classes
dwt.2d
,
wpt.2d
, and
crystal.matrix
.
See
crystal.matrix.object
for details.
This transform was develoed by Meyer and Coifman and used for motion
estimation. This non-decimated two dimensional discrete wavelet transform is
non-orthogonal variant of the classical 2-D DWT and also a variant of the
highly oversampled non-decimated nd.dwt.2d. Unlike the dwt.2d or the nd.dwt.2d
function, the low-pass coefficients are subsampled at each level while the
high-pass coeficients are not.
With the Meyer pyramid, starting with
nr x nc
sample values,
you end up with
4.nr.nc
coefficients.
The non-decimated wavelet
transform can be inverted using the
reconstruct
function.
Refer to the section "Non-Decimated Wavelets" in the
S+WAVELETS User's Manual
for more details about the
meyer.pyramid
function.
The forward and the inverse transform work only for image size that is multiple
of 2^J where J is the number of levels. For other image sizes while the forward
transform works, the inverse transform does not.
All the default optional arguments can be reset using function
wavelet.options
. See
wavelet.options
for details.
Under
"periodic"
boundary rule (the only boundary rule currently supported),
matrix
x
is assumed to be periodic.
Meyer, F.G., Averbuch, A. Z., and Coifman, R.R. (1997). Motion Compenstaion of Wavelet Coeficients with Wavelet Packet Based Motion Residual Coding. IEEE Transactions on Circuits and Systems for Video Technology, October 1997. Mallat, S. and Hwang, W. L. (1992). Singularity Detection and Processing with Wavelets. IEEE Transactions on Information Theory, 38 (2), 617-643.
nd.brain <- meyer.pyramid(brain, n.levels=2) image(nd.brain[["s1-s1"]])