# idualtree3

3-D dual-tree complex wavelet reconstruction

## Description

example

xrec = idualtree3(a,d) returns the inverse 3-D dual-tree complex wavelet transform of the final-level approximation coefficients, a, and cell array of wavelet coefficients, d.

xrec = idualtree3(a,d,Name,Value) specifies options using name-value pair arguments.

## Examples

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Generate all-zero sets of scaling and wavelet coefficients by computing the 3-D dual-tree complex wavelet transform of an array of zeros.

zr = zeros(64,64,64);

[a,d] = dualtree3(zr,4);

Find the real (4,5) wavelet coefficient of the 19th subband of the third level by assigning 1 to the corresponding array element and inverting the transform.

d{3}(4,5,19) = 1;

xr = idualtree3(a,d);

Find the corresponding imaginary coefficient assigning the imaginary unit to the array element and then inverting the transform.

[a,d] = dualtree3(zr,4);

d{3}(4,5,19) = 1j;

xi = idualtree3(a,d);

Display the 18th page of the real and imaginary reconstructions.

subplot(1,2,1)
surf(xr(:,:,18))
view(0,0)
zlim([-0.02 0.02])

subplot(1,2,2)
surf(xi(:,:,18))
view(0,0)
zlim([-0.02 0.02])

## Input Arguments

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Final-level scaling coefficients, specified as a real-valued matrix. a is an output of dualtree3.

Data Types: single | double

Wavelet coefficients, specified as a cell array. d is an output of dualtree3.

Data Types: single | double
Complex Number Support: Yes

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'LevelOneFilter','legall','FilterLength',6 inverts a transform using LeGall synthesis filters with scaling length 3 and wavelet length 5 at level 1, and length-6 Q-shift filters at levels 2 and greater.

Hilbert Q-shift filter-pair length, specified as the comma-separated pair consisting of 'FilterLength' and one of 6, 10, 14, 16, or 18. The synthesis filters used by idualtree3 must match the analysis filters used by dualtree3.

Data Types: double | single

First-level biorthogonal analysis filter, specified as the comma-separated pair consisting of 'LevelOneFilter' and a character vector or string. By default, idualtree3 uses the near-symmetric biorthogonal wavelet filter with lengths 7 (scaling synthesis filter) and 5 (wavelet synthesis filter) in the reconstruction.

Data Types: char | string

Size of the original data, specified as the comma-separated pair consisting of 'OriginalDataSize' and a three-element vector of even integers. This vector must match the size of the original input to the 3-D dual-tree wavelet transform. When the first-level wavelet coefficients are not available, the reconstructed data size can differ from the original input data size. If you call dualtree3 with the 'excludeL1' option, then 'OriginalDataSize' adjusts the size of xrec to match the size of the original input data. If you do not use the 'excludeL1' option, then this argument is ignored.

Data Types: double | single

## Output Arguments

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Inverse 3-D dual-tree complex wavelet transform, returned as a 3-D array.

## References

[1] Chen, H., and N. G. Kingsbury. “Efficient Registration of Nonrigid 3-D Bodies.” IEEE® Transactions on Image Processing. Vol 21, January 2012, pp. 262–272.

[2] Kingsbury, N. G. “Complex Wavelets for Shift Invariant Analysis and Filtering of Signals.” Journal of Applied and Computational Harmonic Analysis. Vol. 10, May 2001, pp. 234–253.

## Version History

Introduced in R2017a