Blind image deblurring with a difference of the mixed anisotropic and mixed isotropic total variation regularization

This paper proposes a simple model for image deblurring with a new total variation regularization. Classically, the L_1-21 regularizer represents a difference of anisotropic (i.e. L₁) and isotropic (i.e. L₂₁) total variation, so we define a new regularization as L_e-2e, which is the weighted difference of the mixed anisotropic (i.e. L₀ + L₁ = L_e) and mixed isotropic (i.e. L₀ + L₂₁ = L_2e), and it is characterized by sparsity-promoting and robustness in image deblurring. Then, we merge the L₀-gradient into the model for edge-preserving and detail-removing. The union of the L_e-2e regularization and L₀-gradient improves the performance of image deblurring and yields high-quality blur kernel estimates. Finally, we design a new solution format that alternately iterates the difference of convex algorithm, the split Bregman method, and the approach of half-quadratic splitting to optimize the proposed model. Experimental results on quantitative datasets and real-world images show that the proposed method can obtain results comparable to state-of-the-art works.