An Efficient Iterative Convolution-Thresholding Method for Image Inpainting (CSIAM Transactions on Applied Mathematics, 2025)
Variational methods have been developed for image inpainting, which involve minimizing an objective functional consisting of the regularization term and the fidelity term. The fidelity term controls the consistency of the restored region with the original image, while the regularization term smooths the boundary of the region. In this paper, we develop an efficient iterative convolution-thresholding method to solve variational approach-based image inpainting problems. In the proposed method, the region is represented by its indicator function, and the regularization term is approximated by the heat kernel convolution with the indicator function. Based on this approximation, we derive an efficient iterative method to update the indicator function only within the damaged region by alternating the convolution and thresholding steps, relying on a relaxation and linearization procedure. Extensive numerical experiments demonstrate the simplicity and efficiency of the proposed method.