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What is deconvolution?

Figure 1: Left: original, properly focused photograph. Right: blurred (misfocused) and noisy photograph.

Image deconvolution is a fundamental inverse problem, where an unknown picture is blurred by a point spread function (PSF) and further degraded by random noise. In practice, images are often blurred by camera shake (curve-like PSF), by poor focusing (disc-like PSF) or by bad optical quality (more complicated PSF). See Figure 1 for an example of blur resulting from misfocus. The goal of deconvolution is to recover the original picture from the blurred and noisy image.

On one hand, deconvolution is a simple inverse problem since it is linear and can be accurately described with the help of the Fourier transform (FT) as severe damping of high-frequency components of the image. This is because FT turns convolution into point-wise multiplication in the frequency domain, and because the FTs of typical PSFs are close to zero at high frequencies.

On the other hand, image deconvolution is very ill-posed and difficult to solve when the PSF has wide extent and decays rapidly in the frequency domain.

The HDC2021 competition is based on real-world disc-like PSFs of increasing sizes, realized by misfocusing a digital camera. We produced a large set of photographic data with both sharp and blurred image of the same target. This allows development and testing of deconvolution methods, including approaches based on supervised machine learning.

In a data challenge it is important to have an objective and quantitative measure for reconstruction quality. We chose strings of random characters of the latin (roman) alphabet as targets in our images. The success of a deconvolution algorithm can then be measured by applying an Optical Character Recognition (OCR) software that turns the photograph into a text file. The resulting text can be compared to the original text, leading to a discrete error measure that is same for all participants of the challenge.

Organising Committee

  • Samuli Siltanen - University of Helsinki, Finland
  • Markus Juvonen - University of Helsinki, Finland
  • Fernando Moura - University of Helsinki, Finland; Federal University of ABC, Brazil