A nonparametric procedure for blind image deblurring

Observed images are usually blurred versions of the true images, due to imperfections of the imaging devices, atmospheric turbulence, out of focus lens, motion blurs, and so forth. The major purpose of image deblurring is to restore the original image from its blurred version. A blurred image can be described by the convolution of the original image with a point spread function (psf) that characterizes the blurring mechanism. Thus, one essential problem for image deblurring is to estimate the psf from the observed but blurred image, which turns out to be a challenging task, due to the “ill-posed” nature of the problem. In the literature, most existing image deblurring procedures assume that either the psf is completely known or it has a parametric form. Motivated by some image applications, including handwritten text recognition and calibration of imaging devices, we suggest a method for estimating the psf nonparametrically, in cases when the true image has one or more line edges, which is usually satisfied in the applications mentioned above and which is not a big restriction in some other image applications, because it is often convenient to take pictures of objects with line edges, using the imaging device under study. Both theoretical justifications and numerical studies show that the proposed method works well in applications.