In this paper, we propose a partial convolution model for image delburring and denoising. We also devise a new linearized alternating direction method of multipliers (ADMM) with extension step. On one hand, the computation of its subproblem is dominated by several FFTs, hence its per-iteration cost is low, on the other hand, the relaxed parameter condition together with the extra extension step inspired by Ye and Yuan's ADMM enables faster convergence than the original linearized ADMM. Preliminary experimental results show that our algorithm can produce a result with better quality than some existing efficient algorithms while the computation time is competitive. Specially, the advantage of our algorithm can be more evident when the noise ratio is high.
Tech Report 0702, Nanjing, May 2017