# How to remove circled noise from image

Consider a simplified example:

noise

noise = Table[
RandomVariate[
NormalDistribution[1, 0.2]] Sin[Sqrt[x^2 + y^2]]^8, {x, -16,
16 - 16/512, 32/512}, {y, -16, 16 - 16/512, 32/512}];


original image

img1 = ExampleData[{"TestImage", "Mandrill"}];


image with noise

img2 = ImageAdd[img1, Image[0.2 noise]]

Row[{img1,img2}]


Is it possible to remove the noise and reconstruct the original image just from the noised image, assuming that the circles are all centered at the center of the image?

• I would make a histogram of pixel values versus radius, which will surely reveal the periodic noise structure, then balance and project back to the original pixel space. – David G. Stork Oct 19 '17 at 0:13