Black-box image deblurring and defiltering

Given an image filter, defiltering refers to the problem of recovering an original image from its filtered version, assuming that the internal structure of the filter is not known. In this paper, we propose five iterative image defiltering schemes and use them for a semi-blind image deblurring problem. Namely, given an image resulting from applying a blurring image filter corrupted by noise to a clean image, we use the proposed iterative schemes to achieve a restoration of the clean image. In particular, for the motion deblurring problem, we show that our defiltering schemes are competitive with modern non-blind image deconvolution methods while using less information. The schemes are inspired by classical methods solving inverse problems and consist of properly modified and extended versions of the Van Cittert iterations, Levenberg–Marquardt method, Wiener filter, Landweber iterations, and Richardson–Lucy algorithm. In addition to dealing with image deblurring problems, we show that the proposed schemes can be used for inverting non-linear filters, and show that they are competitive with state-of-the-art black-box defiltering methods for these problems.