# How do I reconstruct a covered-over part of a regular pattern

I have a set of images which consist of a fairly regular pattern - essentially a set of roughly concentric distorted ellipses - with a small area (<1% of the total image area) obscured by a circular disk. I'd like to be able, digitally, to reconstruct the part of the pattern which is hidden by the disk and produce an image which is 'complete', as it would look if the disk were not there.

Although the pattern is not completely regular (the ellipses are distorted and the centre moves around from image to image), it's pretty obvious to a human observer what the obscured part of the pattern would look like - one could draw it in with a pencil in a moment! I wonder therefore if there exists an image-processing algorithm which would enable me to do this automatically - for example, transforming the image into some suitable space that separates the circular disk from the rest of the pattern, filtering out the disk, then doing the inverse transform to reconstruct the image. Not being a specialist in this field, however, I don't really know what I'm looking for. Does anyone have any suggestions?

• Could you provide a sample image or two?
– user42
Nov 7, 2011 at 21:40
• I could, if I knew how to upload images to this site. I'm afraid I haven't been able to figure that out, either. Nov 7, 2011 at 21:54
• @EosPengwern when you edit your question there's an icon of a photo/image, when you click it you get an upload dialog and through that you can add an image Nov 7, 2011 at 23:22
• 2D Fourier extrapolation might work dsp.stackexchange.com/questions/101/… Nov 8, 2011 at 5:08
• @Ivo Flipse, Thank you, see image added above. These are laser interference patterns, so there's some speckle noise there as well. The disk is right at the centre of the frame, cutting what would otherwise be the innermost complete ellipse. Nov 8, 2011 at 19:36