Tools needed: the ImageJ scientific image-processing application, which happens to be written in Java.
It's available from

Step One: load your image into the application.

Here's a detail showing the pattern in the paper:

Step Two: Forward FFT.  Choose "Process | FFT | FFT" from the ImageJ menu.

This will create a bizarre image like the following:

Step Three: Remove as many of the star-shaped elements as you can.  First, select the brush tool, then change the brush size to about 30 or 40.  Then carefully black out the star-shaped elements.  Stay away from the very center of the image, if you touch that you'll destroy it.  In my example here I've been somewhat lazy and just dropped a big fat black circle in the center of each star.  If you're meticulous you'll get better results.

Also, you only need to do the work on one half of the image, since it is reflected around the center.

Step Four: Invert the FFT to get your original image back.  Choose "Process | FFT | Inverse FFT" from the menu.

As you can see, much of the pattern has been removed.  You might also consider doing a 'despeckle' operation,  "Process | Noise | Despeckle".

Step Five: Save your file.  "File | Save As...".


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