Edge adaptive hybrid regularization model for image deblurring

Abstract Parameter selection is crucial to regularization-based image restoration methods. Generally speaking, a spatially fixed parameter for the regularization term does not perform well for both edge and smooth areas. A larger parameter for the regularization term reduces noise better in smooth areas but blurs edge regions, while a small parameter sharpens edge but causes residual noise. In this paper, an automated spatially adaptive regularization model, which combines the harmonic and total variation (TV) terms, is proposed for the image reconstruction from noisy and blurred observation. The proposed model detects the edges and then spatially adjusts the parameters of Tikhonov and TV regularization terms for each pixel according to the edge information. Accordingly, the edge information matrix will also be dynamically updated during the iterations. Computationally, the newly-established model is convex, which can be solved by the semi-proximal alternating direction method of multipliers with a linear convergence rate. Numerical simulation results demonstrate that the proposed model effectively preserves the image edges and eliminates the noise and blur at the same time. In comparison to state-of-the-art algorithms, it outperforms other methods in terms of peak signal to noise ratio, structural similarity index and visual quality.