Group-Based Sparse Representation Based on lp-Norm Minimization for Image Inpainting

As a powerful statistical image modeling technique, sparse representation has been successfully applied in various image restoration applications. Most traditional methods depend on ℓ
₁
-norm optimization and patch-based sparse representation models. However, these methods have two limits: high computational complexity and the lack of the relationship among patches. To solve the above problems, we choose the group-based sparse representation models to simplify the computing process and realize the nonlocal self-similarity of images by designing the adaptive dictionary. Meanwhile, we utilize Ipnorm minimization to solve nonconvex optimization problems based on the weighted Schatten p-norm minimization, which can make the optimization model more flexible. Experimental results on image inpainting show that the proposed method has a better performance than many current state-of-the-art schemes, which are based on the pixel, patch, and group respectively, in both peak signal-to-noise ratio and visual perception.