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February  2016, 10(1): 195-225. doi: 10.3934/ipi.2016.10.195

## Preconditioned conjugate gradient method for boundary artifact-free image deblurring

 1 Department of Applied Mathematics, Inje University, Gimhae, Gyeongnam 621-749, South Korea 2 Department of Mathematics, Purdue University, West Lafayette, IN47906, United States

Received  May 2013 Revised  September 2015 Published  February 2016

Several methods have been proposed to reduce boundary artifacts in image deblurring. Some of those methods impose certain assumptions on image pixels outside the field-of-view; the most important of these assume reflective or anti-reflective boundary conditions. Boundary condition methods, including reflective and anti-reflective ones, however, often fail to reduce boundary artifacts, and, in some cases, generate their own artifacts, especially when the image to be deblurred does not accurately satisfy the imposed condition. To overcome these difficulties, we suggest using free boundary conditions, which do not impose any restrictions on image pixels outside the field-of-view, and preconditioned conjugate gradient methods, where preconditioners are designed to compensate for the non-uniformity in contributions from image pixels to the observation. Our simulation studies show that the proposed method outperforms reflective and anti-reflective boundary condition methods in removing boundary artifacts. The simulation studies also show that the proposed method can be applicable to arbitrarily shaped images and has the benefit of recovering damaged parts in blurred images.
Citation: Nam-Yong Lee, Bradley J. Lucier. Preconditioned conjugate gradient method for boundary artifact-free image deblurring. Inverse Problems & Imaging, 2016, 10 (1) : 195-225. doi: 10.3934/ipi.2016.10.195
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