  One popular approach for blind deconvolution is to formulate a maximum a
posteriori (MAP) problem with sparsity priors on the gradients of the latent
image, and then alternatingly estimate the blur kernel and the latent image.
While several successful MAP based methods have been proposed, there has been
much controversy and confusion about their convergence, because sparsity priors
have been shown to prefer blurry images to sharp natural images. In this paper,
we revisit this problem and provide an analysis on the convergence of MAP based
approaches. We first introduce a slight modification to a conventional joint
energy function for blind deconvolution. The reformulated energy function
yields the same alternating estimation process, but more clearly reveals how
blind deconvolution works. We then show the energy function can actually favor
the right solution instead of the no-blur solution under certain conditions,
which explains the success of previous MAP based approaches. The reformulated
energy function and our conditions for the convergence also provide a way to
compare the qualities of different blur kernels, and we demonstrate its
applicability to automatic blur kernel size selection, blur kernel estimation
using light streaks, and defocus estimation.
