# idualtree

Kingsbury Q-shift 1-D inverse dual-tree complex wavelet transform

## Syntax

``xrec = idualtree(A,D)``
``xrec = idualtree(___,Name,Value)``

## Description

````xrec = idualtree(A,D)` returns the inverse 1-D complex dual-tree transform of the final-level approximation coefficients, `A`, and cell array of wavelet coefficients, `D`. `A` and `D` are outputs of `dualtree`. For the reconstruction, `idualtree` uses two sets of filters: Orthogonal Q-shift filter of length 10Near-symmetric biorthogonal filter pair with lengths 7 (scaling synthesis filter) and 5 (wavelet synthesis filter) ```

example

````xrec = idualtree(___,Name,Value)` specifies additional options using name-value pair arguments. For example, `'LowpassGain',0.1` applies a gain of 0.1 to the final-level approximation coefficients.```

## Examples

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Load a signal, and obtain its dual-tree transform.

```load noisdopp [a,d] = dualtree(noisdopp);```

Reconstruct an approximation using all but the two finest-detail wavelet subbands.

```dgain = ones(numel(d),1); dgain(1:2) = 0; xrec = idualtree(a,d,'DetailGain',dgain); plot(noisdopp) hold on plot(xrec,'LineWidth',2); legend('Original','Reconstruction')``` ## Input Arguments

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Final-level approximation coefficients, specified as a real-valued vector or real-valued matrix. The approximation coefficients are the output of `dualtree`.

Data Types: `double` | `single`

Approximation coefficients, specified as a cell array. The wavelet coefficients are the output of `dualtree`.

Data Types: `double` | `single`

### 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','antonini','LowpassGain',0.5`

Biorthogonal filter to use in the first-level synthesis, specified by one of the values listed here. For perfect reconstruction, the first-level synthesis filters must match the first-level analysis filters used in `dualtree`.

• `'legall'` — LeGall 5/3 filter

• `'nearsym13_19'` — (13,19)-tap near-orthogonal filter

• `'nearsym5_7'` — (5,7)-tap near-orthogonal filter

• `'antonini'` — (9,7)-tap Antonini filter

Orthogonal Hilbert Q-shift synthesis filter pair length to use for levels 2 and higher, specified as one of the listed values. For perfect reconstruction, the filter length must match the filter length used in `dualtree`.

Wavelet coefficients subband gains, specified as a real-valued vector of length L, where L is the number of elements in `D`. The elements of `DetailGain` are real numbers in the interval [0, 1]. The kth element of `DetailGain` is the gain (weighting) applied to the kth wavelet subband. By default, `DetailGain` is a vector of L ones.

Gain to apply to final-level approximation (lowpass, scaling) coefficients, specified as a real number in the interval [0, 1].

 Antonini, M., M. Barlaud, P. Mathieu, and I. Daubechies. “Image Coding Using Wavelet Transform.” IEEE Transactions on Image Processing 1, no. 2 (April 1992): 205–20. https://doi.org/10.1109/83.136597.

 Kingsbury, Nick. “Complex Wavelets for Shift Invariant Analysis and Filtering of Signals.” Applied and Computational Harmonic Analysis 10, no. 3 (May 2001): 234–53. https://doi.org/10.1006/acha.2000.0343.

 Le Gall, D., and A. Tabatabai. “Sub-Band Coding of Digital Images Using Symmetric Short Kernel Filters and Arithmetic Coding Techniques.” In ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 761–64. New York, NY, USA: IEEE, 1988. https://doi.org/10.1109/ICASSP.1988.196696.