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convolve mystery [message #86413]

Wed, 06 November 2013 07:13

Mats Löfdahl
Messages: 263
Registered: January 2012

Senior Member

I found something surprising (to me) with the convolve() IDL function. There is something strange about how it does its Fourier wrap-around of an image from one side of the array to the other.

Here is a simple example. First define a simple image where half is unity and half is zero:

sz = 10
im = [replicate(1., sz/2), replicate(0., sz/2)] # replicate(1., sz)
print, 'Original:'
print,im[*,sz/2], format = '(f5.2)'

This gives the output:

Original:
1.00
1.00
1.00
1.00
1.00
0.00
0.00
0.00
0.00
0.00

Then define a point spread function and do the convolution:

psf1 = [[1., 1., 1.], [1., 5., 1.], [1., 1., 1.]]
psf1 = psf1/total(psf1)
imc1 = convolve(im, psf1)
print, 'With convolve:'
print,imc1[*,sz/2], format = '(f5.2)'

The output I get is:

With convolve:
0.77
1.00
1.00
1.00
0.77
0.23
-0.00
0.00
-0.00
-0.00

See how the wrap-around reduced the 1.00 in the first pixel to 0.75 but the last pixel does not get the corresponding increase?

Whereas if I do the equivalent operation explicitly with FFT, I do get the expected 0.23 in the last pixel:

psf2 = fltarr(sz, sz)
psf2[sz/2-1:sz/2+1, sz/2-1:sz/2+1] = psf1*sz*sz
psf2 = shift(psf2, sz/2, sz/2)
imc2 = float(fft(fft(im)*fft(psf2), /inv))
print, 'With fft:'
print,imc2[*,sz/2], format = '(f5.2)'

With fft:
0.77
1.00
1.00
1.00
0.77
0.23
-0.00
-0.00
-0.00
0.23

I've looked at the code in http://www.astro.washington.edu/docs/idl/cgi-bin/getpro/libr ary21.html?CONVOLVE and as far as I can see (due to various options the code is not entirely straight forward to read), the fft convolution has no reason to do give any different result from what I do explicitly with fft.

Does anybody know what is going on?

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[Message index]

		convolve mystery By: Mats Löfdahl on Wed, 06 November 2013 07:13
		Re: convolve mystery By: Helder Marchetto on Wed, 06 November 2013 07:27
		Re: convolve mystery By: Mats Löfdahl on Wed, 06 November 2013 07:53
		Re: convolve mystery By: David Fanning on Wed, 06 November 2013 08:03
		Re: convolve mystery By: Mats Löfdahl on Wed, 06 November 2013 08:14
		Re: convolve mystery By: wlandsman on Wed, 06 November 2013 08:54
		Re: convolve mystery By: Mats Löfdahl on Wed, 06 November 2013 12:00
		Re: convolve mystery By: David Fanning on Wed, 06 November 2013 12:20
		Re: convolve mystery By: Mats Löfdahl on Wed, 06 November 2013 13:22

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