Fast restoration approach for rotational motion blurred image based on deconvolution along the blurring paths

Abstract

We present a novel approach to restoring images blurred by rotational motions, without experiencing geometric coordinate transformations as in traditional restoration. The space-variant blur is decomposed into a series of space-invariant blurs along the blurring paths. By incorporating Bresenham's algorithm into our work, the blurred gray values of the discrete pixels can be fetched along the blurring paths in real time. Thus, the space-variant blur can be quickly removed along the blurring paths. We apply a two-stage process to restore the rectangular blurred image, which results in the proposal of two corresponding restoration algorithms. One removes the blur by deconvolution along the blurring paths, which are completely inside the rectangular image. The other is used in the case when only some of the pixels of some blurring paths are inside the rectangular image, so based on a neighborhood knowledge guide, the information of these pixels is restored with the least cost in terms of the constrained optimization estimation theory. Furthermore, these two restoration algorithms avoid iteration calculations and some time-consuming operations. To determine the blur center and the blur extents from the blurred image in a case of not knowing the rotational motion parameters, we present, based on cross correlation, an effective blur identification method, which becomes an integral part of the proposed approach. The experimental results demonstrate the efficiency of the proposed restoration algorithms and the effectiveness of the blur identification method.