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.

给定一个图像过滤器，去过滤是指从过滤后的版本恢复原始图像的问题，假设过滤器的内部结构是未知的。在本文中，我们提出了五种迭代图像去滤波方案，并将它们用于半盲图像去模糊问题。即，给定通过将被噪声破坏的模糊图像滤波器应用于干净图像而产生的图像，我们使用所提出的迭代方案来实现干净图像的恢复。特别是，对于运动去模糊问题，我们表明我们的去滤波方案在使用较少信息的情况下与现代非盲图像去卷积方法具有竞争力。这些方案受到解决逆问题的经典方法的启发，由 Van Cittert 迭代的适当修改和扩展版本组成，Levenberg-Marquardt 方法、Wiener 滤波器、Landweber 迭代和 Richardson-Lucy 算法。除了处理图像去模糊问题外，我们还展示了所提出的方案可用于反相非线性滤波器，并表明它们在这些问题上与最先进的黑盒去滤波方法具有竞争力。