Fast non-iterative single-blur 2-D blind deconvolution of separable and low-rank point-spread functions from finite-support images

摘要

The problem of 2-D blind deconvolution is to reconstruct an unknown image from its 2-D convolution with an unknown blur function. Motivated by the superior restoration quality achieved by the recently proposed nullspace-based multichannel image restoration methods, we propose a single-blur restoration approach that avoids the restrictive assumption of multichannel blurring and has the advantage of lower complexity. The assumption made about the image and the blur function is that they both have a finite spatial extent with that of the image being known. Also, the blur is assumed to be either separable or low-rank. If the blur is separable the image can be restored perfectly under noiseless conditions. When the blur is low-rank, favorable results can be achieved if the blur function has large spatial extent relative to the image. This requirement makes the proposed solution suitable for the cases where the degraded images are severely blurred.