Kingsbury Q-shift 1-D inverse dual-tree complex wavelet transform
returns the inverse 1-D complex dual-tree transform of the final-level approximation
xrec = idualtree(
A, and cell array of wavelet coefficients,
D are outputs of
idualtree uses 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)
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')
A— Final-level approximation coefficients
Final-level approximation coefficients, specified as a real-valued vector or
real-valued matrix. The approximation coefficients are the output of
D— Wavelet coefficients
Approximation coefficients, specified as a cell array. The wavelet coefficients are
the output of
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
'LevelOneFilter'— Biorthogonal filter
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
'legall' — LeGall 5/3 filter
'nearsym13_19' — (13,19)-tap near-orthogonal
'nearsym5_7' — (5,7)-tap near-orthogonal filter
'antonini' — (9,7)-tap Antonini filter
'FilterLength'— Orthogonal Hilbert Q-shift synthesis filter pair length
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
'DetailGain'— Wavelet coefficients subband gains
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
DetailGain is the gain (weighting) applied to the
kth wavelet subband. By default,
DetailGain is a vector of L ones.
1(default) | real number
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.