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Re: backprojection [message #52165] Fri, 19 January 2007 01:52 Go to previous message
Wox is currently offline  Wox
Messages: 184
Registered: August 2006
Senior Member
On 18 Jan 2007 08:49:10 -0800, "Mike" <Michael.Miller5@gmail.com>
wrote:

> Don't forget that the inverse radon transform is not the inverse
> of forward projection. The filtered backprojection is the
> inverse. Filtered backprojection generally proceeds by four
> steps: 1) calculate the Fourier transform of the projection data,
> 2) apply the appropriate filter, 3) calculate the inverse Fourier
> transform to get filtered projections, 4) backproject the
> filtered projections to get an image.

<snip>

> ;; apply the filter to each row of the sinogram
> FOR a = 0,Nangles-1 DO BEGIN
> row = sgplane[*,a]
> ftrow = FFT(row)
> ftfilteredrow = ft_filter * ftrow
> filteredrow = FFT(ftfilteredrow, /INVERSE)
> sgplane[*,a] = filteredrow
> ENDFOR

<snip>

To clarify: the filter shown is similar to the RamLak filtering in
real space (using convolution instead of multiplication) on Mark
River's web-site:
http://www-fp.mcs.anl.gov/xray-cmt/tomo_filter.htm
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