A new framework of designing iterative techniques for image deblurring. (April 2022) - Zhang, Min; Young, Geoffrey S.; Tie, Yanmei; Gu, Xianfeng; Xu, Xiaoyin
Highlights: We identified two aspects for improving iterative algorithms in deblurring. Proposed two modifications on existing methods for deblurring images. Testing showed that the new method can preserve fine details in deblurring. Abstract: 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.