ABSTRACT

Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations.

摘要

盲图像反卷积从模糊图像中恢复去模糊图像和模糊核。从数学的角度来看，这是一个非常不适定的问题，并且已经提出了一些工作来解决它。Chan 和 Wong 提出的一种成功方法是使用总变差 (TV) 作为图像和内核的正则化。这些作者还引入了交替最小化 (AM) 算法来计算物理解决方案。不幸的是，Chan 的方法尤其受到 TV 正则化产生的振铃和阶梯效应的影响。为了解决这些问题，我们提出了一种基于图像双边总变差 (BTV) 正则化的新模型，该模型对内核保持相同的正则化。我们使用松弛过程证明了在合适空间中提出的变分问题的最小化存在。我们还提出了一种基于我们的模型的 AM 算法。通过数值模拟说明了我们模型的效率和鲁棒性，并与 TV 方法进行了比较。