FT math (motion blur removal)

[Roger Bourne]

How do I divide an FT by another FT (or the image of its power spectrum)?

I am trying to demonstrate removal of motion blur by division of the
blurred image FT by the FT of the blur vector.

Thanks
Roger Bourne

--
___________________________
Dr Roger Bourne
Medical Radiation Sciences
Faculty of Health Sciences
University of Sydney
Tel: [phone]
[hidden email]
__________________________

[Filip Rooms]

On 5/8/07, roger bourne <[hidden email]> wrote:
> How do I divide an FT by another FT (or the image of its power spectrum)?
>
> I am trying to demonstrate removal of motion blur by division of the
> blurred image FT by the FT of the blur vector.

That's what is called the inverse filter. This only works in complete
absence of any noise (sensor, discretization, ...), but is a highly
unstable computation, since you will divide the highest frequencies by
very small numbers (dividing by e.g. 0.001 is in fact multiplying with
1000, thus amplifying noise). If I am not mistaken, a motion blur
point spread function even has zero's in its spectrum, so for those
frequencies you divide by 0 (and every one knows that dividing by 0 is
not a good thing).

The simplest way to stabilize this is to add a small number to the
denominator, but better yet is to apply a Wiener filter instead,
taking into account the estimated spectra of the image and the noise.

Of course there are still better techniques involving other sharpening
procedures and stabilization methods... See my thesis, e.g., for more
explanation: http://www.filiprooms.be/frooms-phd.pdf

Kind regards,

Filip Rooms

[Thomas Boudier]

Hi Roger,

You can use FD Math in FFT with the operations "convolve" and "deconvolve".

Thomas

> How do I divide an FT by another FT (or the image of its power spectrum)?
>
> I am trying to demonstrate removal of motion blur by division of the
> blurred image FT by the FT of the blur vector.
>
> Thanks
> Roger Bourne
>


--
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 Thomas Boudier, MCU Université Pierre et Marie Curie
 UMR 7101 / IFR 83. Bat A 328, Campus Jussieu
 Tél : [phone]  Fax : [phone]
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[Gabriel Landini]

On Tuesday 08 May 2007 05:59:45 roger bourne wrote:
> How do I divide an FT by another FT (or the image of its power spectrum)?
>
> I am trying to demonstrate removal of motion blur by division of the
> blurred image FT by the FT of the blur vector.

There is this macro that shows blurring/deblurring:

http://rsbweb.nih.gov/ij/macros/MotionBlurRemoval.txt

I have tried to deblur other images by specfying the blur vector as in the
program above, but I cannot make it work. (I must be missing something quite
obvious).

Please post here if you find a way of doing motion deblurring this way.

Cheers,

Gabriel

[Gluender]

Dear Roger Bourne,

for the mentioned purpose (inverse filtering) I fear you need to
divide complex Fourier spectra.

I doubt that this is possible with the built-in FT of ImageJ, but you
may have a look at the FFTJ plug-in.

>How do I divide an FT by another FT (or the image of its power spectrum)?
>
>I am trying to demonstrate removal of motion blur by division of the
>blurred image FT by the FT of the blur vector.
>
>Thanks
>Roger Bourne
>
>--
>___________________________
>Dr Roger Bourne
>Medical Radiation Sciences
>Faculty of Health Sciences
>University of Sydney
>Tel: [phone]
>[hidden email]
>__________________________

HTH

Best


--


                   Herbie

          ------------------------

          <http://www.gluender.de>

[Michael Schmid]

High Gabriel,

maybe it is the "divide by zero" problem mentioned by Filip
Rooms that causes your problems?
If I run the MotionBlurRemoval macro as it is, it works perfectly.

If I add "Specified Noise" with a standard deviation of 2800
on the "Motion Blurred" image, the result looks awful.
2800 is roughly the sum of the PSF pixels, and thus it is the
factor that "Motion Blurred" is multiplied by with respect to
the input image. So this amount of noise only corresponds to
one grayscale step of the input image, and it completely kills
the result.

Thus, for a "real world" pictures, where noise and
nonlinearities are present and where the point spread function
(PSF) is not exactly known, one has to use more elaborate
methods (Wiener Filter, Maximum Entropy...)

Michael
________________________________________________________________

On 8 May 2007, at 10:11, Gabriel Landini wrote:

> On Tuesday 08 May 2007 05:59:45 roger bourne wrote:
>> How do I divide an FT by another FT (or the image of its power  
>> spectrum)?
>>
>> I am trying to demonstrate removal of motion blur by division of the
>> blurred image FT by the FT of the blur vector.
>
> There is this macro that shows blurring/deblurring:
>
> http://rsbweb.nih.gov/ij/macros/MotionBlurRemoval.txt
>
> I have tried to deblur other images by specfying the blur vector as  
> in the
> program above, but I cannot make it work. (I must be missing  
> something quite
> obvious).
>
> Please post here if you find a way of doing motion deblurring this  
> way.
>
> Cheers,
>
> Gabriel

[Joachim Wesner]

HI

The noise-free case works so nicely especially because the assumed "1d
spread function" has a sudden onset and
end, i.e. sharp edges, which mean it´s FT has still some sizeable spatial
frequency content up to half the pixel spacing.

For real world blurring with fuzzy,  smooth onset and ending of the
blurring kernel, noise senitivity will be
even worse than the noisy, otherwise perfect case discussed here

Joachim

ImageJ Interest Group <[hidden email]> schrieb am 08.05.2007 10:47:22:

> High Gabriel,
>
> maybe it is the "divide by zero" problem mentioned by Filip
> Rooms that causes your problems?
> If I run the MotionBlurRemoval macro as it is, it works perfectly.
>
> If I add "Specified Noise" with a standard deviation of 2800
> on the "Motion Blurred" image, the result looks awful.
> 2800 is roughly the sum of the PSF pixels, and thus it is the
> factor that "Motion Blurred" is multiplied by with respect to
> the input image. So this amount of noise only corresponds to
> one grayscale step of the input image, and it completely kills
> the result.
>
> Thus, for a "real world" pictures, where noise and
> nonlinearities are present and where the point spread function
> (PSF) is not exactly known, one has to use more elaborate
> methods (Wiener Filter, Maximum Entropy...)
>
> Michael
> ________________________________________________________________
>
> On 8 May 2007, at 10:11, Gabriel Landini wrote:
>
> > On Tuesday 08 May 2007 05:59:45 roger bourne wrote:
> >> How do I divide an FT by another FT (or the image of its power
> >> spectrum)?
> >>
> >> I am trying to demonstrate removal of motion blur by division of the
> >> blurred image FT by the FT of the blur vector.
> >
> > There is this macro that shows blurring/deblurring:
> >
> > http://rsbweb.nih.gov/ij/macros/MotionBlurRemoval.txt
> >
> > I have tried to deblur other images by specfying the blur vector as
> > in the
> > program above, but I cannot make it work. (I must be missing
> > something quite
> > obvious).
> >
> > Please post here if you find a way of doing motion deblurring this
> > way.
> >
> > Cheers,
> >
> > Gabriel

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