[Insight-developers] FFT implementations handle spacing differently

[Cartik Sharma]

Dear Kevin:

Please see attached comments. Disclaimer: Some of the notes we have in
this thread
really are sensitive to SNR (signal from data relative to noise).

On 9/28/12, Kevin H. Hobbs <hobbsk at ohio.edu> wrote:
>>>             On 9/27/12 7:13 AM, "Bradley Lowekamp"
>>>             <blowekamp at mail.nih.gov <mailto:blowekamp at mail.nih.gov>>
>>>             wrote:
>>>             However, I am
>>>             >uncertain that this actually make sense, as the
>>>             FFTForward filter does
>>>             >converts from the spacial domain to the frequency this
>>>             physical
>>>             >information may not be very logical.
>>>             >
>
>
> It would be really nice if the transformed image had frequency units, or
> log2 frequency units.
Measures of entropy count :)

> I for one do not know enough to calculate the precise meaning of a
> position on the transformed image.
Tough to predict position and momentum (pixel intensities) at the same
time. Essentially, capture the error envelope in predicting pos,
directionality.

> I do know that artifacts that show up in repeating patterns will show up
> as a blob on the transformed image, and I can high or low pass filter an
> image with a circular mask, after applying itkFFTShiftImageFilter.

> What I cannot do is use the current units on the transformed image to
> confirm that the blob I mask corresponds to the artifact that repeats
> every 10mm.
>
> I also cannot compare two FFTs of repeating structures, I'm thinking
> sarcomeres, and say anything quantitative about what's different.

Nice example..for repeating structures, I'd say impulse response studies for
neurological phenomena that have repetitive patterns and can be simulated
with FFTs. Similar manner, filtering or transformation of octaves.
(musical notes)

>
-Cartik