Manifold regularization model for image deblurring: A point integral approach to Laplace-Beltrami equation

This paper introduces the Manifold Regularization Model (MRM), a new approach to image deblurring. The observation that the patch manifolds of many natural images have a low-dimensional structure is the basis of MRM. With this information, we can use the patch manifold dimension as a regularization technique to fix blurred images. The point integral approach solves the Laplace-Beltrami equation on a point cloud, which is the main objective of MRM. This approach is advantageous compared to the conventional graph Laplacian methodology, since it accurately applies restrictions to the sample points, improving deblurring performance. Through extensive numerical tests on deblurring tasks, we demonstrate that MRM greatly improves image clarity, demonstrating its efficacy as a reliable image restoration technique.