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*) > >

**References**:**FFT of a noisy image with weak periodic information***From:*Dave Martin <miltydcm@gmail.com>