Learning point spread function image processing

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Given a set of images, that are blurred by Gaussian point spread function, how can I learn the parameters of the PSF, i.e. standard deviation of the Gaussian kernel.

One way that I can think of is to consider Fourier transform of all the images. We know that these FFTs are all multiplied by a Gaussian window. Then perhaps take a log transform and the do PCA of all the images and the log of the Gaussian will be the principle component. Is there any other way?

I though there must be tons of literature on this subject, but somehow I didn't find much. Any pointers or ideas would be appreciated.