Zhang Min, Young Geoffrey S, Tie Yanmei, Gu Xianfeng, Xu Xiaoyin
Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, USA.
Pattern Recognit. 2022 Apr;124. doi: 10.1016/j.patcog.2021.108463. Epub 2021 Nov 27.
In this work we present a framework of designing iterative techniques for image deblurring in inverse problem. The new framework is based on two observations about existing methods. We used Landweber method as the basis to develop and present the new framework but note that the framework is applicable to other iterative techniques. First, we observed that the iterative steps of Landweber method consist of a constant term, which is a low-pass filtered version of the already blurry observation. We proposed a modification to use the observed image directly. Second, we observed that Landweber method uses an estimate of the true image as the starting point. This estimate, however, does not get updated over iterations. We proposed a modification that updates this estimate as the iterative process progresses. We integrated the two modifications into one framework of iteratively deblurring images. Finally, we tested the new method and compared its performance with several existing techniques, including Landweber method, Van Cittert method, GMRES (generalized minimal residual method), and LSQR (least square), to demonstrate its superior performance in image deblurring.
在这项工作中，我们提出了一种用于逆问题中图像去模糊的迭代技术设计框架。新框架基于对现有方法的两点观察。我们以Landweber方法为基础来开发和展示新框架，但请注意该框架适用于其他迭代技术。首先，我们观察到Landweber方法的迭代步骤包含一个常数项，它是已模糊观测值的低通滤波版本。我们提出了一种修改方法，直接使用观测图像。其次，我们观察到Landweber方法使用真实图像的估计值作为起始点。然而，这个估计值在迭代过程中不会更新。我们提出了一种修改方法，随着迭代过程的推进更新这个估计值。我们将这两种修改整合到一个图像迭代去模糊的框架中。最后，我们测试了新方法，并将其性能与几种现有技术进行比较，包括Landweber方法、Van Cittert方法、GMRES（广义极小残差法）和LSQR（最小二乘法），以证明其在图像去模糊方面的优越性能。
