Image Deblurring with Deconvolution
We’ve all probably seen the old ‘Zoom, ENHANCE…’ meme from a variety of crime dramas, where they take an unbelievably blurry or destroyed photo and make it crystal clear in order to extract key evidence. In most cases, this is indeed impossible, as there is no INFORMATION to even begin trying to extract any meaningful definition. But for more reasonable cases, this is a real process:
What we do is utilize a point spread function, which is a smearing distribution of sorts for each point on a photo. We can represent the general brightness on a point in a photo as a convolution of the photo with the point spread function. We can represent the brightness with a Fourier series. In short, the Fourier transform of the blurred photo is the product of the Fourier transforms of the point spread function and the point spread function.
To deblur our picture, we can divide the transform of the blurred photo by the transform of the point spread function. This gives us the Fourier transform of our unblurred photo, which we can inverse transform to obtain the unburied image. Evidently, the point spread function must be known pretty accurately, but the result is extremely cool.