Page - 53 - in Proceedings - OAGM & ARW Joint Workshop 2016 on "Computer Vision and Robotics“

RobustBlindDeconvolutionUsingConvolution Spectraof Images PhilippMoser1 andMartinWelk1 Biomedical ImageAnalysisDivision University forHealth Sciences,Medical Informaticsand Technology (UMIT), Hall/Tyrol,Austria philipp.moser@hotmail.com,martin.welk@umit.at Abstract We present a method for blind image deconvolution that acts by alternating optimisation of image and point-spread function. The approach modifies a variational model recently published by Liu et al.whichcombinesaquadraticdata termwitha total variationregulariser for the imageandaregu- lariserforthepoint-spreadfunctionthatisconstructedfromconvolutioneigenvaluesandeigenvectors of the blurred input image. We replace the image estimation component with a robust modification of Richardson-Lucy deconvolution, and introduce a robust data term into the point-spread function estimation. We present experiments on images with synthetic and real-world blur that indicate that themodifiedmethodhasadvantages in the reconstruction offine imagedetails. 1. Introduction Blur is, second to noise, one of the major sources of degradations in digital images. Its removal has therefore been a subject of intense investigation since the beginnings of digital image processing. If for each location the intensity is smeared across a neighbourhood in the same way, this spatially invariantblur ismathematicallymodelledbyaconvolutionwithakernel,calledpoint-spreadfunction (PSF). Describing the observed blurred image f, the unobservable sharp imageu and the PSFh as functions fromsuitable functionspaces, and assumingadditivenoisen, onehas f=u∗h+n . (1) SpatiallyvariantblurcanbemodelledsimilarlyusingFredholmintegraloperators. Themathematical problemofapproximate inversionof these bluroperations is termeddeconvolution. In this paper, we focus on the spatially invariant case. In non-blind deconvolution problems, both the blurred image f and the PSFh are available as input; in contrast, blind deconvolution aims at recovering the PSFh along with the sharp imageu from the input imagef. Both kinds of problems are severely ill-posed; inparticular, deconvolutionalgorithmsarehighly sensitive tonoise. Non-blind deconvolution can nowadays be performed efficiently with favourable quality, with meth- ods ranging from the time-proven Wiener filter [15] and Richardson-Lucy deconvolution [6, 10] up to the performant iterative algorithm by Krishnan and Fergus [4], to name a few representatives. Recentlyalsoneural network techniques havebeenused, see [12,17]. For blind deconvolution, a straightforward approach proceeds in two steps: first, estimating the PSF, 53