Bi-l0-l2-Norm Regularization for Blind Motion Deblurring

Wen-Ze Shao, Hai-Bo Li, Michael Elad

Published 2014-08-20Version 1

In blind motion deblurring, a commonly practiced approach is to perform the restoration in two stages: first, the blur-kernel is estimated along with a temporal restored image, and then a regular image deblurring algorithm is applied with the found kernel. This work addresses the first stage, for which a great deal of effort has been placed on the choice of the image and the blur-kernel priors. Leading methods today tend towards highly non-convex approximations of the l0-norm, especially in the image regularization term. In this paper, an effective approach is proposed for the estimation of the motion blur-kernel, through a bi-l0-l2-norm regularization, imposed on both the image and the blur-kernel. Compared with existing methods, the proposed regularization is shown to be more effective and robust in improving the accuracy of the estimated motion blur-kernel, thereby leading to a better final restored image. Our approach has the capability of genera- ting a higher quality intermediate sharp image with more accu- rate salient edges and less staircase and ringing artifacts, as well as an ability of reducing the possible isolated points and weak components in the estimated blur-kernel. We derive a fast nume- rical algorithm for computing alternatingly the sharp image and the motion blur-kernel, by coupling the operator splitting and the augmented Lagrangian methods, as well as using the fast Fourier transform (FFT). We also use a continuation strategy that dimi- nishes the strength of the regularization over the iterations, which we demonstrate to be beneficial to the motion-blur kernel estima- tion accuracy. Extensive experiments on a benchmark dataset and real-world motion blurred images demonstrate that the proposed approach is highly competitive with state-of-the-art methods in both deblurring effectiveness and computational efficiency.