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371:(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.
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0.0434526754612290872323451760615, -0.0956472641201940521884294720076, 0.000354892813233037828625936077981, 0.0316241658525117260250768298826, -0.00667962022627715496448604519801, -0.00605496057509013186633408627538, 0.00261296728049449139578039971105, 0.000325814671352184426090225377209, -0.000356329759021555335019716207419, 5.56455140343097156546388203637E-5
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If there are other libraries or extensions necessary to make the code run, or if the user needs to run any preliminary expressions, then that should be stated clearly. Likewise it should also be indicated if any of the functions or variables in the code refer to any possible user-defined functions
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Upon trying the code (direct copy/paste) in Matlab with S being a column vector of 512 elements between 0-255 (e.g., image row), the result (after transform and inverse transform) did not come anywhere close to being the original array. In my most recent attempt the sum of the absolute values
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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
162:
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
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There are more problems. The article claims that the detail coefficients are , but if you look at the output from the code (I could not understand the code itself at all, it does way too much magic for me) and scale it by sqrt(2) you can see that the coefficients used are , ie. the signs are
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0.0538503495893256002938669913355, 0.344834303813955884022358807362, 0.855349064359415132589782756294, 0.929545714366294680245423892326, 0.188369549506367558166635349778, -0.414751761801876984688928276295, -0.136953549024766197207530847836, 0.210068342279012384309087440949,
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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)
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I'm to lazy to read all of the article, but I can see directly that it's missing a section about the applications of
Daubechies wavelets. That's probably what is the most interesting to read about, so they should be mentioned in the article.
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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.
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I have another question about this tutorial. The analysis coefficients are given in the page, however is it possible to derive the corresponding coefficients for synthesis filter banks from the coefficients already given?
368:(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.
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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,
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Hi, please read again the article, the algorithm for the synthesis coefficients is already there. In short, one just has to reverse the analysis sequence. That's why the
Daubechies wavelets are orthogonal (or
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PS: Sorry, the wavelet part of WP was messed around by different authors without ever getting into a consistent state. The part that is refered to as "above" dealing with this problem is now in an extra page
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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)
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so far, the third is slightly wrong. An e-4 should have been an e-3. If the values in the table were just copied from "ten lectures", then perhaps the correction shortly after publication was missed.--
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The provided code does not work "as is" in Matlab as the paragraph above it would lead you to believe. Matlab does not come with a function 'S' by default, so some further explanation is needed.
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The article should state that this is the LIFTING SCHEME implementation of the D4 wavelet transform and refer to the paper of
Sweldens and Daubechies where the lifting coefficients are given.
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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.
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I presume the scaling filter D18 in the table is wrong. The sum of the function is 2.00589431 and it is extremely away from 2 compared with other filters in the table.
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Did more testing on this code. Forward transform was good, inverse transform needed some minor changes. I have verified the changes with Octave. Found this link
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between the original S and final S (after forward and inverse transform) was 10703. My best guess is that there are some issues with the ends of the arrays.
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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.
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Both sign versions are correct, one only needs to take care when implementing the inverse transform. There is no way to decide which version is better.--
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Related: It's unclear what "tap" is even referring to. The article simply starts using the word "tap" without providing a defintion. What is a tap?
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You're right, I meant it isnt orthogonal, not it isn't symetric. But it does have lower processing requirements.
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Ehm, S is the input Signal? A simple array of length N (even)? Nevertheless, it should be explained.--
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Thanks a lot LutzL - the answer helped. But just to clarify, please answer the following:
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overlaps the pictures. Probably, the pictures should all be aligned to the right. Comments?
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0.4829629131445341, 0.83651630373780772, 0.22414386804201339, -0.12940952255126034
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The support of dbN is (2N - 1). See
Daubechies' Ten Lectures on Wavelets, p. 194.
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Actually, WT and IWT with the filter have not made a round-trip.--
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scaling filter has 7 taps and the wavelet filter 9 taps. --
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and tell there (and if necessary here) what is missing.--
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reversed. Which is "wrong" -- the code or the article? -
673:{\displaystyle {\frac {1+{\sqrt {(}}3)}{4{\sqrt {2}}}}}
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A question about coefficients of
Synthesis filter banks
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A section about the applications is what is missing. —
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202:Cohen-Daubechies-Feauveau wavelets
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109:and see a list of open tasks.
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395:FOLLOW UP 2 - 25 Sept. 2006
338:FOLLOW UP 1 - 22 Sept. 2006
247:05:39, 21 October 2023 (UTC)
741:21:00, 29 August 2011 (UTC)
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260:ORIGINAL Q - 21 Sept. 2006
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