Talk:Daubechies wavelet

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[edit] Formatting issues

Should the table of the "Orthogonal Daubechies Coefficients" have several fewer columns? The way it is now, the table does not fit in my browser window (on a 19" screen), and I doubt having that many numbers adds any value to the article. Also, maybe only on my screen, the table at the bottom overlaps the pictures. Probably, the pictures should all be aligned to the right. Comments? Oleg Alexandrov 18:49, 8 Mar 2005 (UTC)

[edit] A question

What means the two parameters 7/9 in Daubechies 7/9? anybody knows? I think it should be explained in the article. I cannot find anything about it in the web tutorials.

It means that the Wavelet isn't symmetric. The Scaling Function has 9 coefficients (9-Tap), and the Wavelet Function has 7 (7-Tap). Non-symetric wavelets are useful in image processing because they require less processing. Seabhcán 10:27, 31 Mar 2005 (UTC)

In fact, the 5/3 and 9/7 biorthogonal wavelets are widely used exactly because they are symmetric/antisymmetric and so have linear phase filter banks. In the analysis filter bank, the scaling low pass filter has 9 taps, the wavelet band pass filter has 7 taps. In the synthesis filter bank, the scaling filter has 7 taps and the wavelet filter 9 taps. --LutzL 11:48, 27 May 2005 (UTC)

I think Daubechies 7/9 refers to the Cohen-Daubechies-Feauveau wavelets, which is not orthogonal and which is symmetric and it is used because of its symmetry. This has nothing to do amount of processing, but symmetry is wanted because this guarants an equal treatment e.g. of left and right edges.

You're right, I meant it isnt orthogonal, not it isn't symetric. But it does have lower processing requirements. Seabhcán 14:06, 29 March 2006 (UTC)

[edit] A question (wrt. the 2D wavelet)

??? >>>ORIGINAL Q - 21 Sept. 2006

Why, in the article, a 3 dimensional picture of a D(20) referred to as a 2-d wavelet? Is this a misprint or are the two not related to one another? Please explain? Thanks... Yaroslav (21 September 2006)

For the same reason that there is a 2 dimensional picture for the 1D wavelets: It's a functions graph. The 2D wavelets are nothing but the product of a wavelet function in x and a wavelet funktion in y dirction, . However, the graph is not very good since the used approximation of the wavelet function is very coarse.--LutzL 15:00, 21 September 2006 (UTC)

??? >>>FOLLOW UP 1 - 22 Sept. 2006

Thanks a lot LutzL - the answer helped. But just to clarify, please answer the following:

(1) Does 1D and 2D refer to Wavelet (Mother) and Scaling (Father) Functions, where 1D (Mother) and 2D (Mother and Father)?

(2) Is 1D and 2D wavelets are a form of wavelet classification?

(3) Is it applicable only to Daubechies wavelet transforms?

(4) Is there such a thing as a 3D wavelet?

Thanks again. Yaroslav (22 September 2006)

(1) No, 1D, 2D, 3D,... refers to the dimension of the domain space of the wavelet and scaling functions.

(2) Yes, one can classify wavelets by the dimension of their domain space, and further if they are non-separable or are tensor-wavelets.

(3) The Daubechies series of wavelet transforms is purely 1D. From every 1D wavelet on can construct tensor wavelets for any dimension of the domain space, one applies the 1D-transform to each dimension seperately.

(4) Yes, but either it is (trivial and) a tensor wavelet or heavily complicated. The design (of the filter sequences) of higher dimensional non-sep smooth wavelets is a heavy theoretical and computational task, the implementation of a multidimensional filter mask is equally heavy to execute, the neat tricks of 1D transforms such as lifting do not carry over easyly.

--You can sign with ~~~~ for name/IP and date or ~~~~~ to add the date to your name.

--LutzL 16:02, 22 September 2006 (UTC)

??? >>>FOLLOW UP 2 - 25 Sept. 2006

From FOLLOW UP 1: '(1) No, 1D, 2D, 3D,... refers to the dimension of the domain space of the wavelet and scaling functions'. As an example, if we assume a 3D space of XYZ, then would the 'domain space' be X & Y (2D)? Yaroslav (25 September 2006)