A second-order approach for blind motion deblurring by normalized l₁ regularization

We propose a second-order approach for blind motion deblurring. Our idea is to define an energy functional, and the convolution kernel corresponds to the minimum of the functional. After the kernel is obtained, the problem is solved by existing non-blind deconvolution algorithms. To avoid that the minimizer of energy functional does not correspond to the unblurred image, which is often encountered in many algorithms, in the literature the normalized l₁ norm regularization term for the original or first-order gradient image was adopted. We further extend the idea using the second-order gradient image, which is the main novelty of the paper. This method favours a piecewise linear transition in the unblurred image, and thus efficiently attenuates the staircase and ring effects in the original or first-order case. Comparing with other stateof- the-art algorithms, the proposed method is effective in estimating the blur-kernel and restoring the unblurred image.