Preconditioned conjugate gradient method for boundary artifact-free image deblurring
Nam-Yong Lee, Bradley J. Lucier · Inverse Problems and Imaging · 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-reflectiveboundary 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 pixelsoutside the field-of-view,and preconditioned conjugate gradient methods, wherepreconditioners are designedto compensate for the non-uniformity in contributions from image pixels to the observation.Our simulation studies show that the proposed methodoutperforms reflective and anti-reflective boundary condition methodsin removing boundary artifacts.The simulation studies also show that the proposed method canbe applicable to arbitrarily shaped images andhas the benefit of recovering damaged parts in blurred images.