       Re: FFT of a noisy image with weak periodic information

• To: mathgroup at smc.vnet.net
• Subject: [mg126807] Re: FFT of a noisy image with weak periodic information
• From: Dave Martin <miltydcm at gmail.com>
• Date: Fri, 8 Jun 2012 03:38:46 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jqn5gv\$hd3\$1@smc.vnet.net>

```On Wednesday, June 6, 2012 4:48:31 AM UTC-4, 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*)
>
> 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*)

Thanks to all of you for these different suggestions.  I actually figured out a reasonable solution on my own soon after posting my initial question, but have learned some useful things from these different alternatives, and so I appreciate the comments.  Here is my solution...

thresh = 1;
Do[If
[Abs[xf[[x1, y1]]] < thresh, xf[[x1, y1]] = 0,
xf[[x1, y1]] = xf[[x1, y1]]], {x1, 1, n}, {y1, 1, n}];

```

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