Image Deconvolution

Image Deconvolution is an amazing technique for focusing a blurry image. In order for this technique to work, the exact blurring function must be known. This technique can also be used for generating beautiful periodic textures.
(* runtime: 50 seconds *)
image = Import["C:/GrayPicture.jpg"][[1, 1]]; n = Length[image];
dx = 2.0/n; blurfunction = Fourier[Table[Exp[-(x^2 + y^2)/0.01^2], {y, -1, 1 - dx, dx}, {x, -1, 1 - dx, dx}]]^2;
blurryimage = Re[InverseFourier[Fourier[image]blurfunction]];
ListDensityPlot[blurryimage, Mesh -> False, Frame -> False];
restoredimage = Re[InverseFourier[Fourier[blurryimage]/blurfunction]];
ListDensityPlot[restoredimage, Mesh -> False, Frame -> False]

Link: Hubble telescope’s optical correction – M100 Galaxy before and after


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