wt = dwt3(x,wname)
returns the single-level three-dimensional wavelet decomposition
wt of the input data x using the
wname wavelet. The default extension mode of the 3-D
discrete wavelet transform (DWT) is "sym" (see dwtmode).
wt = dwt3(x,w,___)
specifies three wavelets, one for each direction. w is a cell
array, string array, or structure, and can be followed by
"mode",extmode.
wt = dwt3(x,wf,___)
specifies four filters, two for decomposition and two for reconstruction, or 3
× 4 filters (one quadruplet by direction). wf is a cell
array or structure, and can be followed by
"mode",extmode..
Analyzing wavelet used to compute the 3-D DWT, specified as a character
vector or string scalar. The analyzing wavelet is from one of the following
wavelet families: Best-localized Daubechies, Beylkin, Coiflets, Daubechies,
Fejér-Korovkin, Haar, Han linear-phase moments, Morris minimum-bandwidth,
Symlets, Vaidyanathan, Discrete Meyer, Biorthogonal, and Reverse
Biorthogonal. See wfilters for the wavelets
available in each family.
Analyzing wavelets to use in the 3-D wavelet decomposition, one for each
direction, specified as a cell array of character vectors, a string array,
or a structure. w = {'wname1','wname2','wname3'}, or
w = ["wname1","wname2","wname3"], or
w is a structure with three fields,
"w1", "w2", and
"w3", containing character vectors or string scalars
that are the names of wavelets.
Example: wt =
dwt3(x,["db2","db4","db6"]);
Wavelet filters to use in the 3-D wavelet decomposition, specified as
either a cell array or structure. wf specifies four
filters, two for decomposition and two for reconstruction, or 3 × 4
filters (one quadruplet by direction). wf is either a
cell array (1-by-4) or (3-by-4) : {LoD,HiD,LoR,HiR} or a
structure with the four fields "LoD",
"HiD", "LoR",
"HiR".
Extension mode used when performing the wavelet decomposition, specified as:
extmode
DWT Extension Mode
"zpd"
Zero padding
"sp0"
Smooth extension of order 0
"spd" (or "sp1")
Smooth extension of order 1
"sym" or "symh"
Symmetric extension (half point): boundary value symmetric replication
"symw"
Symmetric extension (whole point): boundary value symmetric replication
"asym" or "asymh"
Antisymmetric extension (half point): boundary value antisymmetric replication
"asymw"
Antisymmetric extension (whole point): boundary value antisymmetric replication
"ppd", "per"
Periodized extension
If the signal length is odd and
mode is "per", an extra sample
equal to the last value is added to the right and the extension is performed
in "ppd" mode. If the signal length is even,
"per" reduces to "ppd". This rule
also applies to images.
The global variable managed by dwtmode specifies the default extension
mode.
Structure with four fields:
LoD, HiD,
LoR, HiR,
which are the filters used for DWT.
dec
2-by-2-by-2 cell array containing the
coefficients of the
decomposition.
dec{i,j,k},
i,j,k
= 1 or 2 contains the
coefficients obtained by lowpass filtering (for
i or j or
k = 1) or highpass filtering
(for i or j or
k = 2).
The
i element filters along the
rows of x, the
j element filters along the
columns, and the k element
filters along the third dimension. For example,
dec{1,2,1} is obtained by
filtering x along the rows with
the lowpass (scaling) filter, along the columns with
the highpass (wavelet) filter, and along the third
dimension with the lowpass (scaling)
filter.
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