Image inpainting using reproducing kernel Hilbert space and Heaviside functions

Image inpainting, a technique of repairing damaged images, is an important topic in image processing. In this paper, we solve the problem from an intensity function estimation perspective. We assume the underlying image is defined on a continuous domain and belongs to a space spanned by a basis of a reproducing kernel Hilbert space and some variations of the Heaviside function. The reproducing kernel Hilbert space is used to model the smooth component of the image while Heaviside function variations are used to model the edges. The coefficients of the redundant basis are computed by the discrete intensity at undamaged domain. We test the proposed model through various images. Numerical experiments show the effectiveness of the proposed method, especially in recovering edges.