Gradient-based image deconvolution

Heyan Huang, Hang Yang, Siliang Ma

Abstract: Image restoration and deconvolution from blurry and noisy observation is known to be ill-posed. To stabilize the recovery, total variation (TV) regularization is often utilized for its beneficial edge in preserving the image’s property. We take a different approach of TV regularization for image restoration. We first recover horizontal and vertical differences of images individually through some successful deconvolution algorithms. We restore horizontal and vertical difference images separately so that each is more sparse or compressible than the corresponding original image with a TV measure. Then we develop a novel deconvolution method that recovers the horizontal and vertical gradients, respectively, and then estimate the original image from these gradients. Various experiments that compare the effectiveness of the proposed method against the traditional TV methods are presented. Experimental results are provided to show the improved performance of our method for deconvolution problems.