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dddtreecfs

Extract dual-tree/double-density wavelet coefficients or projections

Syntax

  • out = dddtreecfs(outputtype,wt,outputspec,outputindices) example
  • out = dddtreecfs(outputtype,wt,outputspec,outputindices,'plot') example

Description

example

out = dddtreecfs(outputtype,wt,outputspec,outputindices) extracts the coefficients or subspace projections from the 1-D or 2-D wavelet decomposition, wt. If outputtype equals 'e', out contains wavelet or scaling coefficients. If outputtype equals 'r', out contains wavelet or scaling subspace projections (reconstructions).

example

out = dddtreecfs(outputtype,wt,outputspec,outputindices,'plot') plots the signal or image reconstruction or specified analysis coefficients. You can include the 'plot' option anywhere after the wt input.

Examples

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Reconstruction from 1-D Complex Dual-Tree Wavelet Transform

Obtain the complex dual-tree wavelet transform of the 1-D noisy Doppler signal. Reconstruct an approximation based on the level-three detail coefficients

Load the noisy Doppler signal. Obtain the complex dual-tree transform down to level 3.

load noisdopp;
wt = dddtree('cplxdt',noisdopp,3,'dtf1');

Plot a reconstruction of the original signal based on the level-three detail coefficients

xr = dddtreecfs('r',wt,'scale',{3},'plot');

Coefficients from 1-D Complex Dual-Tree Wavelet Transform

Load the noisy Doppler signal. Obtain the complex dual-tree transform down to level 3.

load noisdopp;
wt = dddtree('cplxdt',noisdopp,3,'dtf1');

Create a cell array of vectors to obtain the second- and third-level detail coefficients from each of the wavelet filter bank trees.

outputindices = {[2 1]; [2 2]; [3 1]; [3 2]};

The first element of each vector in the cell array denotes the level, or stage. The second element denotes the tree.

Extract the detail coefficients.

out = dddtreecfs('e',wt,'ind',outputindices);

out is a 1-by-4 cell array. The cell array elements contain the wavelet coefficients corresponding to the elements in outputindices. For example, out{1} contains the level-two detail coefficients from the first tree.

1-D Complex Dual-Tree Wavelet Transform Structure

Load the noisy Doppler signal. Obtain the complex dual-tree transform down to level 3.

load noisdopp;
wt = dddtree('cplxdt',noisdopp,3,'dtf1');

Create a cell array of vectors to obtain the second- and third-level detail coefficients from each of the wavelet filter bank trees.

outputindices = {[2 1]; [2 2]; [3 1];[3 2]};

The first element of each vector in the cell array denotes the level, or stage. The second element denotes the tree.

Create a structure array identical to the wt output of dddtree with all the coefficients equal to zero except the first- and second-level detail coefficients.

out = dddtreecfs('e',wt,'cumind',outputindices);

Extract Diagonal Features from Image

Use the complex dual-tree wavelet transform to isolate diagonal features in an image at +45 and –45 degrees.

Load and display the xbox image.

load xbox;
imagesc(xbox)

Obtain the complex dual-tree wavelet transform down to level 3.

fdf = dtfilters('FSfarras');
df = dtfilters('qshift10');
wt = dddtree2('cplxdt',xbox,3,fdf,df);

Isolate the +45 and -45 diagonal image features in the level-one wavelet coefficients. Plot the result.

out = dddtreecfs('e',wt,'ind',{[1 3 1 2]; [1 3 2 2]},'plot');

Input Arguments

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outputtype — Output type'e' | 'r'

Output type, specified as 'e' or 'r'. Use 'e' to obtain the scaling or wavelet coefficients. Use 'r' to obtain a projection, or reconstruction, onto the appropriate scaling or wavelet subspace.

wt — Wavelet transformstructure

Wavelet transform, specified as a structure. The structure array is the output of dddtree or dddtree2.

outputspec — Output specification'lowpass' | 'scale' | 'ind' | 'cumind'

Output specification, specified as one of 'lowpass', 'scale', 'ind', or 'cumind'. The output specifications are defined as follows:

  • 'lowpass' — Outputs the lowpass, or scaling, coefficients or a signal/image approximation based on the scaling coefficients. If you set the output specification to 'lowpass', do not specify outputindices. If the outputtype is 'e', out is a structure array with fields identical to the input structure array wt except that all wavelet (detail) coefficients are equal to zero. If the outputtype is 'r', out is a signal or image approximation based on the scaling coefficients. The signal or image approximation is equal in size to the original input to dddtree or dddtree2.

  • 'scale' — Outputs the coefficients or a signal/image approximation based on the scales specified in outputindices. If the outputtype is 'e', out is a cell array of structure arrays. The fields of the structure arrays in out are identical to the fields of the input structure array wt. The coefficients in the cfs field are all equal to zero except the coefficients corresponding to the scales in outputindices. If the outputtype is 'r', out is a signal or image approximation based on the scales in outputindices. The signal or image approximation is equal in size to the original input to dddtree or dddtree2.

  • 'ind' — Outputs the coefficients or a signal/image approximation based on the tree-position indices specified in outputindices. If the outputtype is 'e', out is a cell array of vectors or matrices containing the coefficients specified by the tree-position indices in outputindices. If the outputtype is 'r', out is a cell array of vectors or matrices containing signal or image approximations based on the corresponding tree-position indices in outputindices.

  • 'cumind' — Outputs the coefficients or a signal/image approximation based on the tree-position indices specified in outputindices. If the outputtype is 'e', out is a structure array. The fields of the structure array are identical to the fields of the input structure array wt. The coefficients in the cfs field are all equal to zero except the coefficients corresponding to the tree positions in outputindices. If the outputtype is 'r', out is a signal or image approximation based on the coefficients corresponding to the tree-position indices in outputindices.

Example: 'ind',{[1 1]; [1 2]}

outputindices — Output indicescell array

Output indices, specified as a cell array with scalar or vector elements. If outputspec equals 'scale', a scalar element selects the corresponding element in the cfs field of wt. If outputspec equals 'ind' or 'cumind', the elements of outputspec are row vectors. The first element of the row vector corresponds to the element in the cfs field of wt. Subsequent elements in the row vector correspond to the indices of the array contained in the cell array element.

Example: 'scale',{1;2;3}

Output Arguments

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out — Signal or image reconstruction or coefficientscell array | structure | vector | matrix

Signal or image reconstruction or coefficients, returned as a vector, matrix, structure array, cell array of vectors or matrices, or cell array of structure arrays. The form of out depends on the value of outputspec and outputindices.

See Also

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