Background: Image inpainting is a technique that can be used to restore missing or damaged pixels in images. Owing to its high practical value, image inpainting has been a research field for many years. For image inpainting, the Total Variation (TV) model is always a powerful and popular tool. However, when TV norm is involved, most of the conventional image inpainting methods suffer from difficulty in the numerical solution.
Methods: To improve the speed and efficiency of handling TV-regularized image inpainting problem, this paper proposes a novel method that mainly employs variable splitting and alternating minimization. The proposed method first converts the classical TV model into an equivalent unconstrained minimization problem. Then, by applying variable splitting and alternating minimization, the minimization problem is decomposed into several subproblems with a smaller size. In an iterative process, by alternately addressing these subproblems with the help of corresponding appropriate methods, the optimal solution of the original problem can be efficiently obtained. In image inpainting application, the proposed method smoothly completes four damaged images with 50% of pixels lost, and the restored images illustrate good visual sense and high values of improved signal-to-noise ratio.
Conclusion: Using numerical experiments, the effectiveness of the proposed method is validated as well as the advantages of the proposed method over three similar state-of-the-art methods.