I would really like to fix this image!

Clare aged around 15

This is a blurred image. I would really like to unblur it.

What is blurring? It is an artefact of the imaging process. If the image is out of focus, each point in the original is replaced (in the image) by an average value of neighbouring points. This process is called convolution, and blurring is sometimes modelled by a Gaussian point-spread function (PSF).

Pixelation is also a convolutional process. Here there is a uniformity of image value across the pixel; the pixel is formed via a uniform PSF. Both effects are present on the the picture above of the young Clare.

The process of restoring the orginal image is called deconvolution. It's complicated by three problems: (i) we normally don't know the exact PSF; (ii) the image always has added noise; (iii) information is thrown away in the blurred-imaging process. Recovery is inevitably somewhat speculative.

If the PSF is not known, it can be estimated in a process known as blind convolution. If the nature of the image is known (Clare's face) then model-based recovery could be used, particularly if we have other images of the subject (we do!).

This is an area where deep learning is very, very applicable; a spin-off from facial recognition systems. There are a large number of papers on the topic but I have failed to find an online website where I can simply upload the picture (and maybe some unblurred pictures of the subject) and get a restored, sharp picture to download.

Perhaps an iteration of Google Photos at some point? Like this:

State of the art (PDF)

The above images are from a team including Beijing Institute of Technology, Nvidia and Google Cloud. When can I get to use it?

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Update: June 15th 2020: There's a system online and I've tried it.