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idualtree2

Kingsbury Q-shift 2-D inverse dual-tree complex wavelet transform

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Syntax

imrec = idualtree2(A,D)
imrec = idualtree2(___,Name,Value)

Description

imrec= idualtree2(A,D)returns the inverse 2-D complex dual-tree transform of the final-level approximation coefficients,A, and cell array of wavelet coefficients,D.AandDare outputs ofdualtree2. For the reconstruction,idualtree2uses two sets of filters:

  • Orthogonal Q-shift filter of length 10

  • Near-symmetric biorthogonal filter pair with lengths 7 (scaling synthesis filter) and 5 (wavelet synthesis filter)

example

imrec= idualtree2(___,Name,Value)specifies additional options using name-value pair arguments. For example,'LowpassGain',0.1applies a gain of 0.1 to the final-level approximation coefficients.

Examples

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Open Live Script

This example shows how to reconstruct an approximation based on a subset of the wavelet subbands.

加载一个128 -by-128 grayscale image.

loadxboximagesc(xbox) colormapgray

Figure contains an axes object. The axes object contains an object of type image.

Obtain the dual-tree wavelet transform of the image down to level 2

lev = 2; [a,d] = dualtree2(xbox,'Level',lev);

Since there are six wavelet subbands in each level of the decomposition, create a 2-by-6 matrix of zeros.

dgains = zeros(lev,6);

To reconstruct an approximation based on the 2nd and 5th wavelet subbands, set the second and fifth rows ofdgainsequal to 1. The 2nd and 5th wavelet subbands correspond to the highpass filtering of the rows and columns of the image.

dgains(:,[2 5]) = 1;

Obtain two reconstructions using the specified wavelet subbands. Include the scaling (lowpass) coefficients only in the first reconstruction.

imrec = idualtree2(a,d,'DetailGain',dgains); imrec2 = idualtree2(a,d,'DetailGain',dgains,'LowpassGain',0); figure subplot(2,1,1) imagesc(imrec) title('With Lowpass Coefficients') subplot(2,1,2) imagesc(imrec2) title('Without Lowpass Coefficients') colormapgray

Figure contains 2 axes objects. Axes object 1 with title With Lowpass Coefficients contains an object of type image. Axes object 2 with title Without Lowpass Coefficients contains an object of type image.

Input Arguments

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Final-level approximation coefficients, specified as a real-valued array. The approximation coefficients are the output ofdualtree2.

Data Types:double|single

Approximation coefficients, specified as a cell array. The wavelet coefficients are the output ofdualtree2.

Data Types:double|single

Name-Value Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

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 indualtree2.

  • '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 indualtree2.

Wavelet coefficients subband gains, specified as a real-valued matrix with a row dimension ofL, whereLis the number of elements inD. There are six columns inDetailGainfor each of the six wavelet subbands. The elements ofDetailGain是重新al numbers in the interval [0, 1]. Thekthcolumn elements ofDetailGainare the gains (weightings) applied to thekthwavelet subband. By default,DetailGainis aL-by-6 matrix of ones.

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

References

[1] Antonini, M., M. Barlaud, P. Mathieu, and I. Daubechies. “Image Coding Using Wavelet Transform.”IEEE Transactions on Image Processing1, no. 2 (April 1992): 205–20. https://doi.org/10.1109/83.136597.

[2] Kingsbury, Nick. “Complex Wavelets for Shift Invariant Analysis and Filtering of Signals.”应用和计算谐波分析10, no. 3 (May 2001): 234–53. https://doi.org/10.1006/acha.2000.0343.

[3] Le Gall, D., and A. Tabatabai. “Sub-Band Coding of Digital Images Using Symmetric Short Kernel Filters and Arithmetic Coding Techniques.” InICASSP-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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

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