Non-blind deblurring of structured images with geometric deformation

Abstract

Non-blind deconvolution, which is to restore a sharp version of a given blurred image when the blur kernel is known, is a fundamental step in image deblurring. While the problem has been extensively studied, existing methods have conveniently ignored an important fact that deformation can significantly affect the statistical characteristics of an image and introduce additional blurring effect. In this paper, we show how to enhance non-blind deconvolution by recovering and undoing the deformation while deconvolving a given blurred image. We show that this is the case for almost all popular regularizers that have been proposed for image deblurring such as total variation and its variants. We conduct extensive simulations and experiments on real images and verify that the incorporation of geometric deformation in deconvolution can significantly improve the final deblurring results. Combined with existing blur kernel estimation techniques, our method can also be used to enhance blind image deblurring.