Dear Subhamoy. Thanks for the reply and good references.

I shall specify my question.

I'm interested in research on the choice of of different wavelets for image processing (eg. enhances the outline image).

Which wavelet choose, given the type of image. How to do it. What methods are used for this purpose.

Its all about decomposing the image into several frequency sub-bands. For general purpose processing the Haar wavelet is suitable, Matlab offers loads of different wavelet functions that can be easily implemented under the DWT function. You can simply build a Matlab GUIDE interface and try different mother wavelets in order to visually decide on which one is more appropriate. 

The multiresolution property is an interesting tool for different image processing application either compression, noise reduction, watermarking in wavelet domain. It provides good time frequency representation. The important thing is to select appropriate wavelet family inorder to perform suitable filter-bank decomposition. It depends for which perporse wavelet is used for image processing. The details of wavelet is at the following link;

http://users.rowan.edu/~polikar/WAVELETS/WTpart1.html

Part 3 & Part 4 for CWT, DWT.

Dear Nijad. Such an experiment I did and wrote an article. But I want to know - there is such studies.

Dear Sujan. You gave a good and correct answer. But how to choose the appropriate wavelet. There are such procedures (choice of a wavelet) for image processing?

Actually, there is different test to do that. First of all, need to analysis the test image/data characteristics. Based on some analysis results, it is required to observe the characteristics of wavelet family (check biorthogonality, orthogonality, etc.).

In some cases, researcher generate their own wavelet family for any new kind of image (eg. MRI, CT scan image etc). In general application, like compression, noise reduction using wavelet filter-bank, some people use the existing family. eg. symlet, db 1-8 etc.

The simpleast one is Haar. The best way is to test the filter-bank characteristics with some family with the test image. The results not vary too much. Thanks.

Dear Sujan. Thanks for the detailed answer. Do you have links to the studies that you have listed.

Actually, I read some papers and follow the characteristics of wavelet filterbank. Based on some knowledge and multiresolution property, I used wavelet for speech , image denoising recently and got got result. In my case, symlet family was suited well. I have added a link in the first reply, there is something details about some property that I am talking.

You can check the paper of image denoising using wavelet. There is some details discussion regarding this.

Thanks.

The beauty of wavelet transform appears after applying wavelet on an image, where we get LL,LH,HL and HH sub bands, the distribution of the non-LL sub bands is Laplacian, the redundant data or non feature data are normally around the mean of the distribution, and the features (e.g. edges) are on both tails of the distribution, now it is a matter of shareholding, some people argue that the features reside outside the area of mean+-Standard deviation,  others used the area outside mean +- (2 standard deviation)

  source of image: professor Sabah Jassim lectures notes.

this tutorial might be interesting for you 

http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html

firstly wavelet is a  combination between LPF and HPF.

To select the filter type depends on your application.

To select the number of levels depend on the compression that you need, which affected the losses in data.

Dear Muzhir. How to choose the type of filter. Concretely. Can you give me links to do this (for image processing).

Dear Vyacheslav

There is no exact filter selection type but any how it depend on the image  details, this link may help you

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.301.4400

www.e-ijaet.org/media/2I15-IJAET0715522_v6_iss3_1055to1062.pdf

Regards

Dear Muzhir and Subhamoy. Thank you very much. I got the answer to the question.

Each wavelet is constructed with constraints. Number of moments, smoothness, polinomial representation, etc. 

You have to cross these properties with the needs of your application.

Dear Henrique. Thanks for the addition. But the question is - are there any procedures that bind:

Image and Number of moments,

image and polinomial representation,

etc.

Sir the choice for the  wavelets can be made in different ways. You can either use the properties of the image you are interested in . e.g. for the case of compression the sparsity of the wavelet domain representation would be the key factor. An example of similar methods is basis pursuit.An other one is known as matching pursuit.

Another method particularly for image processing is selection based on the entropy of the wavelet representation. This was proposed by coifman et al.

If you are interested in classification problems then an optimization based approach is used. For this you can refer to the "Wavelet subspace decomposition of thermal infrared images for defect detection in artworks" attached below. An earlier version of the article hosted on RG is also attached for reference.

Moreover there are adaptive wavelet basis techniques such as the empirical wavelet and curvelet transforms and the lifting schemes. The papers are attached for reference. Hope this helps!!!!

http://redwood.psych.cornell.edu/discussion/papers/chen_donoho_BP_intro.pdf

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=119732&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D119732

blanche.polytechnique.fr/~mallat/papiers/MallatPursuit93.pdf

http://www.sciencedirect.com/science/article/pii/S1350449515302024

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4360002&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4360002

ftp://ftp.math.ucla.edu/pub/camreport/cam13-35.pdf

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1257383&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1257383

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1257384&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1257384

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4060933&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4060933

http://en.cnki.com.cn/Article_en/CJFDTotal-SXZZ20050200D.htm

Research Wavelet subspace decomposition of thermal infrared images fo...