# Learning point spread function image processing

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.

• it's called de-convolution. if you have perfect measurements of the filtered image, you can directly compute the inverse filter, but in general you have only noisy measurement, and you'll have to write a model of noise, and you won't compute the exact inverse filter $\displaystyle\frac{1}{H(k)}$ but $\displaystyle\frac{1}{e^{i arg H(k)} (\alpha+|H(k)|)}$ the max-likelihood filter, where $\alpha$ depends on the variance of the noise (that you can estimate, or define a priori). – reuns May 2 '16 at 18:21
• the max-likelihood if your model is $s(n) = x \ast h(n) + w(n)$ (or $s(n) = (x+w) \ast h(n)$ but the result will be a little different) with $w(n)$ some Gaussian white noise; and you should get what I wrote when maximizing $\log L(s;x)$ . trying searching for en.wikipedia.org/wiki/Deconvolution and max-likelihood you should get results. – reuns May 2 '16 at 18:22
• I think there is a small difference between my question and deconvolution, that know the form of the kernel (Gaussian) and I have a lot of blurred images. – AnandJ May 4 '16 at 5:47