Non-Redundant Shift-Invariant Complex Wavelet Transform

2 m-file functions for applying complex wavelet and inverse complex wavelet transforms.

Description

This transformation is non-redundant, approximately shift-invariant and produces oriented filters in 2D and 3D. There is a m-file called 'example.m' which shows how one can use this package.
For more information see the following paper:
Hosseini, Vafadust : "Almost Perfect Reconstruction Filter Bank for Non-redundant ,Approximately Shift-Invariant, Complex Wavelet Transforms"

• MATLAB release: MATLAB 6.0 (R12)

[Alex Kolesov]

Reshad, thank you for publishing this code!
Questions:
1) why 2 different wavelet filters are used in coding/decoding?
2) where is "magic" low-pass filter? (the code doesn't contain it).
3) whether is absence of the this filter the reason of inadmissible reconstruction error? - even abs(max(input(:)-output(:)) is too far from value x*10^-9.
Thank you for support.

[Reshad Hosseini]

Alex, thanks for your questions. I think it helps for clarifying the code also for the others.
++++++++++ Regarding Q.1 and Q.2 ++++++++++
It is because of this low-pass filter that I have two different filters in the code. As I mentioned in the paper there is a low-pass filter before applying the filter-bank. Instead of applying a low-pass filter and then the filter bank, I included this low-pass filter in the filters of the first level (With just convolving the low-pass filter with the filters of the filter bank).
++++++++++ Regarding Q.3 ++++++++++
Because of the low-pass filter, one does not have perfect-reconstruction property. If your input signal does not decay fast enough, you need to increase the sampling rate before applying the filter-bank.
For increasing the sampling rate, the typical method is first upsampling the input signal and then low-passing this up-sampled signal. The low-pass filter of the filter bank can be considered as the low-pass filter in the interpolation. In other words, you do not need two low-pass filters.
++++++++++ One more comment ++++++++++
Instead of comparing the maximum magnitude of the error, I would suggest to check PSNR.

[ruman sarkar]

Sir I am very beginner in image processing field, so I am very much interested to know what is the advantages for applying complex wavelet transform over face image's

[Goutam]

Sir I am very beginner in image processing field, so I am very much interested to know what is the advantages for applying complex wavelet transform over face image's specially illumination invariant and expression changes

[Reshad Hosseini]

I am sorry but I do not have real experience in face recognition. However, I did a quick search on the internet and I found that maybe the following papers are of interest for you:
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5161305

http://www.ubicc.org/files/pdf/UBICC-455-kjayapriya_455.pdf

I would guess that the choice of complex wavelets in those papers could be changes and you could also use the complex wavelet code here, instead of Dual-tree complex-wavelet.