Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. We propose an alternative approach, shifting the paradigm towards regularization at the level of the probability distribution on the space of images. Our method is based upon the idea of maximum entropy on the mean wherein we work at the level of the probability density function of the image whose expectation is our estimate of the ground truth. Using techniques from convex analysis and probability theory, we show that the method is computationally feasible and amenable to very large blurs. Moreover, when images are imbedded with symbology (a known pattern), we show how our method can be applied to approximate the unknown blur kernel with remarkable effects. While our method is stable with respect to small amounts of noise, it does not actively denoise. However, for moderate to large amounts of noise, it performs well by preconditioned denoising with a state of the art method.

中文翻译：

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图像去模糊均值法的最大熵

图像去模糊是一个众所周知的具有挑战性的不适定逆问题。近年来，基于图像级别的正则化或机器学习技术提出了各种各样的方法。我们提出了一种替代方法，将范式转移到图像空间概率分布级别的正则化。我们的方法基于均值的最大熵的思想，其中我们在图像的概率密度函数级别工作，其期望是我们对基本事实的估计。使用来自凸分析和概率论的技术，我们表明该方法在计算上是可行的，并且适用于非常大的模糊。此外，当图像嵌入符号系统（一种已知模式）时，我们展示了如何将我们的方法应用于具有显着效果的未知模糊核的近似。虽然我们的方法对于少量噪声是稳定的，但它不会主动降噪。然而，对于中到大量的噪声，它通过使用最先进的方法进行预处理去噪表现良好。