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Re: FFT of a noisy image with weak periodic information
*To*: mathgroup at smc.vnet.net
*Subject*: [mg126790] Re: FFT of a noisy image with weak periodic information
*From*: Matthias Odisio <matthias at wolfram.com>
*Date*: Thu, 7 Jun 2012 05:22:06 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201206060851.EAA17867@smc.vnet.net>
Dave,
On 6/6/12 3:51 AM, Dave Martin wrote:
> I'm trying to accomplish what should be a relatively simple frequency
> domain filtering of a noisy input image with with some weak, periodic
> signals (a low dose transmission electron microscope image of some
> organic crystals). Using the commands below, I've been able to input
> the image (x), convert it to data (xi), and calculate the FFT (fx).
> Now what I want to do is to set the FFT to zero for all values below
> some threshold, and then inverse transform back to a filtered image.
> My stumbling block is a simple means to set the values of the array fx
> to zero below some threshold, before I perform InverseFourier.
>
> x=Import["data.tif"] (*import the file as an image*)
> xi=ImageData[x]; (*convert image to array data*)
> x1=xi[[All,All,1]]; (*extract one of the three color channels from
> the RGB image*)
> fx=Fourier[x1]; (*calculate the FFT of x1*)
This sets to zero the complex numbers for which the magnitude is less
than a threshold:
thr = 2;
m = Threshold[Abs[fx], thr];
z = InverseFourier[m*Exp[I*Arg[fx]]];
To "chop" the tiny values of z, I suggest using again Threshold
instead of Chop. Threshold does not unpack so it is more efficient.
With[{r = Re[z], i = Im[z]},
newz = Threshold@r + I*Threshold@i]
Matthias Odisio
Wolfram Research
>
> Some other commands I've found useful...
>
> pfx=fx*Conjugate[fx]; (*calculate power spectrum = fx^2*)
> n=Length[pfx] (*determine size of arrays*)
> pxr=RotateRight[pfx, {n/2,n/2}]; (*put origin in center of PS
> image*)
> pi = Image[pxr] (*convert PS to image for display*)
>
> Inverse transforming...
>
> rx=Chop[InverseFourier[fx]]; (*convert fx back to a real space data
> set rx*)
> ri=Image[rx] (*convert rx to an image ri for
> display*)
>
>
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