idddtree2
Inverse dual-tree and double-density 2-D wavelet transform
Syntax
Description
Examples
Perfect Reconstruction Using Complex Oriented Dual-Tree Wavelet Filter Bank
Demonstrate perfect reconstruction of an image using a complex oriented dual-tree wavelet transform.
Load the image and obtain the complex oriented dual-tree wavelet transform down to level 5 using dddtree2
. Reconstruct the image using idddtree2
and demonstrate perfect reconstruction.
load woman; wt = dddtree2('cplxdt',X,5,'dtf2'); xrec = idddtree2(wt); max(max(abs(X-xrec)))
ans = 7.3896e-12
Input Arguments
wt
— Wavelet transform
structure
Wavelet transform, returned as a structure from dddtree2
with these fields:
type
— Type of wavelet decomposition (filter bank)
'dwt'
| 'ddt'
| 'realdt'
| 'cplxdt'
| 'realdddt'
| 'cplxdddt'
Type of wavelet decomposition (filter bank), specified as one
of 'dwt'
, 'ddt'
, 'realdt'
, 'cplxdt'
, 'realdddt'
,
or 'cplxdddt'
. 'dwt'
is the
critically sampled DWT. 'ddt'
produces a double-density
wavelet transform with one scaling and two wavelet filters for both
row and column filtering. 'realdt'
and 'cplxdt'
produce
oriented dual-tree wavelet transforms consisting of two and four separable
wavelet transforms. 'realdddt'
and 'cplxdddt'
produce
double-density dual-tree wavelet transforms consisting of two and
four separable wavelet transforms.
level
— Level of the wavelet decomposition
positive integer
Level of the wavelet decomposition, specified as a positive integer.
filters
— Decomposition (analysis) and reconstruction (synthesis) filters
structure
Decomposition (analysis) and reconstruction (synthesis) filters, specified as a structure with these fields:
Fdf
— First-stage analysis filters
matrix | cell array
First-stage analysis filters, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the first-stage analysis filters for the corresponding tree.
Df
— Analysis filters for levels > 1
matrix | cell array
Analysis filters for levels > 1, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the analysis filters for the corresponding tree.
Frf
— First-level reconstruction filters
matrix | cell array
First-level reconstruction filters, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the first-stage synthesis filters for the corresponding tree.
Rf
— Reconstruction filters for levels > 1
matrix | cell array
Reconstruction filters for levels > 1, specified as an N-by-2 or N-by-3 matrix for single-tree wavelet transforms, or a 1-by-2 cell array of two N-by-2 or N-by-3 matrices for dual-tree wavelet transforms. The matrices are N-by-3 for the double-density wavelet transforms. For an N-by-2 matrix, the first column of the matrix is the scaling (lowpass) filter and the second column is the wavelet (highpass) filter. For an N-by-3 matrix, the first column of the matrix is the scaling (lowpass) filter and the second and third columns are the wavelet (highpass) filters. For the dual-tree transforms, each element of the cell array contains the first-stage analysis filters for the corresponding tree.
cfs
— Wavelet transform coefficients
cell array of matrices
Wavelet transform coefficients, specified as a 1-by-(level
+1)
cell array of matrices. The size and structure of the matrix elements
of the cell array depend on the type of wavelet transform as follows:
'dwt'
—cfs{j}(:,:,d)
j = 1,2,...
level
is the level.d = 1,2,3 is the orientation.
cfs{level+1}(:,:)
are the lowpass, or scaling, coefficients.
'ddt'
—cfs{j}(:,:,d)
j = 1,2,...
level
is the level.d = 1,2,3,4,5,6,7,8 is the orientation.
cfs{level+1}(:,:)
are the lowpass, or scaling, coefficients.
'realddt'
—cfs{j}(:,:,d,k)
j = 1,2,...
level
is the level.d = 1,2,3 is the orientation.
k = 1,2 is the wavelet transform tree.
cfs{level+1}(:,:)
are the lowpass, or scaling, coefficients.
'cplxdt'
—cfs{j}(:,:,d,k,m)
j = 1,2,...
level
is the level.d = 1,2,3 is the orientation.
k = 1,2 is the wavelet transform tree.
m = 1,2 are the real and imaginary parts.
cfs{level+1}(:,:)
are the lowpass, or scaling, coefficients..
'realdddt'
—cfs{j}(:,:,d,k)
j = 1,2,...
level
is the level.d = 1,2,3 is the orientation.
k = 1,2 is the wavelet transform tree.
cfs{level+1}(:,:)
are the lowpass, or scaling, coefficients.
'cplxdddt'
—cfs{j}(:,:,d,k,m)
j = 1,2,...
level
is the level.d = 1,2,3 is the orientation.
k = 1,2 is the wavelet transform tree.
m = 1,2 are the real and imaginary parts.
cfs{level+1}(:,:)
are the lowpass, or scaling, coefficients.
Output Arguments
xrec
— Synthesized 2-D image
matrix
Synthesized image, returned as a matrix.
Data Types: double
Version History
Introduced in R2013b
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