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Thread Subject:
difference between wrcoef2 and appcoef2 in matlab

Subject: difference between wrcoef2 and appcoef2 in matlab

From: dhrub

Date: 17 Nov, 2012 06:00:12

Message: 1 of 2

what is the difference between wrcoef2 and appcoef2/detcoef2 in matlab ?


I mean in both cases, we get coefficients.
what is the difference then...

Subject: difference between wrcoef2 and appcoef2 in matlab

From: Wayne King

Date: 17 Nov, 2012 07:50:11

Message: 2 of 2

"dhrub " <dhruvkumar037@gmail.com> wrote in message <k8795b$ho4$1@newscl01ah.mathworks.com>...
> what is the difference between wrcoef2 and appcoef2/detcoef2 in matlab ?
>
>
> I mean in both cases, we get coefficients.
> what is the difference then...

Only in appcoef2 and detcoef2 do you actually get approximation or wavelet coefficients. With wrcoef2 you get a projection onto the subspace spanned by the particular wavelet or scaling function. There is a big difference between the coefficients and the projection. For one thing, the projection is the same size as the original image.

I'll give you a simple example with vectors in R^2 to illustrate the difference.

Assume you have an orthonormal basis for R^2: [1/sqrt(2) 1/sqrt(2)]', [1/sqrt(2) -1/sqrt(2)]'

Now take an arbitrary vector, [3 2]'. The expansion coefficients for [3 2]' in the basis are:

 5/sqrt(2)
 1/sqrt(2)

The orthogonal project of [3 2]' onto the space spanned by [1/sqrt(2) 1/sqrt(2)]' is

5/sqrt(2)*[1/sqrt(2) 1/sqrt(2)]'

2.5
2.5

The difference between appcoef2/detcoef2 and wrcoef2 is analogous to the difference between 5/sqrt(2) (the expansion coefficient) and [2.5 2.5], the projection onto the subspace spanned by [1/sqrt(2) 1/sqrt(2)]'

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