  In this paper, we study the problem of recovering a sharp version of a given
blurry image when the blur kernel is unknown. Previous methods often introduce
an image-independent regularizer (such as Gaussian or sparse priors) on the
desired blur kernel. We shall show that the blurry image itself encodes rich
information about the blur kernel. Such information can be found through
analyzing and comparing how the spectrum of an image as a convolution operator
changes before and after blurring. Our analysis leads to an effective convex
regularizer on the blur kernel which depends only on the given blurry image. We
show that the minimizer of this regularizer guarantees to give good
approximation to the blur kernel if the original image is sharp enough. By
combining this powerful regularizer with conventional image deblurring
techniques, we show how we could significantly improve the deblurring results
through simulations and experiments on real images. In addition, our analysis
and experiments help explaining a widely accepted doctrine; that is, the edges
are good features for deblurring.
