[Insight-users] Is there an Inverse FFT in ITK ? (IFFT)

[Luis Ibanez]

Hi Robert,

In order to get the Inverse Fourier Transform you should
apply the direct transform first and then flip the output.

So, your pipeline will look like:

  1) A = (image/volume from disk)
  2) B = VnlFFTRealToComplexConjugateImageFilter(A)
  3) [do some operation on B in Fourier space]
  5) C = VnlFFTComplexConjugateToRealImageFilter(B)
  4) E = FlipImageFilter(D) [with all dimensions
                             set to true]


Note, that in order to make sure that your "Inverse
Transform will map fine into a Real Image your operations
in point (3) *must* be symmetric.  E.g. any Function F(x)
that you use for filtering at that level must be such that
it respects

                  F(x) == F(-x)


Otherwise, the result of the Inverse Transform should be
another complex image.



Regards,


    Luis




======================
Robert Maroon wrote:

> Hi Luis,
> 
> 
>>However, note that you can easily get the 
>>equivalent of the Inverser FFT by running a 
>>*direct* FFT and then Flipping the outptut image.
> 
> 
> Sure, I implemented this successfully in Matlab, but
> I'm having trouble making the same pipeline work in
> ITK. Here's pseudocode of how I'm attempting it:
> 
> 1) A = (image/volume from disk)
> 2) B = VnlFFTRealToComplexConjugateImageFilter(A)
> 3) [do some operation on B in Fourier space]
> 4) C = FlipImageFilter(B) [with all dimensions set to
> true]
> 5) D = VnlFFTComplexConjugateToRealImageFilter(C)
> 
> Was this what you had in mind? Thanks,
> 
> Robert
> 
> 
> 
> 		
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