We propose extrapolation boundary conditions(BCs) for blurring removal.They lead to C¹ continuity for one-dimensional signals and C⁰ continuity with normal derivative continuity for images.Two models and two kinds of blurring operators are used in the extrapolation BCs with Dirichlet,Neumann and antireflective BCs.We apply extrapolation BCs to fast algorithms for total variation-based image deblurring and denoising.Numerical results illustrate efficiency of the extrapolation BCs.

Weighted essentially non-oscillatory schemes are described in detail for a total variation-based image restoration problem with Gaussian kernel at different boundary conditions.Numerical results with three methods (weighted essentially non-oscillatory schemes,wiener algorithm and a combination of them) are compared. Experimental results demonstrate effectiveness of the combination of weighted essentially non-oscillatory schemes and wiener algorithm.