The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for solving this problem. In particular, we start by carefully describing how to represent images, the process of blurring an image and modeling different kind of added noise. Then, we present regularization methods such as Tikhonov (on the standard and general form), Total Variation and other variations with sparse and edge preserving properties. Additionally, we briefly overview some of the main matrix structures for the blurring operator and finalize presenting multilevel methods that preserve such structures. Numerical examples are used to illustrate the techniques described.
翻译：图像分流问题包括从模糊和噪音污染的可用数据中重建图像。 在本 AMS 通告文章中,我们概述了用于解决这一问题的一些众所周知的数字线性代数技术。特别是,我们首先仔细描述如何显示图像,模糊图像的过程和制作不同类型添加的噪音的模型。然后,我们介绍规范化方法,如Tikhonov(标准形式和一般形式)、总变化和其他变化,包括稀疏和边缘保护特性。此外,我们简要概述了模糊操作员的一些主要矩阵结构,并最后确定了保护这些结构的多层次方法。我们用数字例子来说明所描述的技术。
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