A Patch-based Image Denoising Method Using Eigenvectors of the Geodesics' Gramian Matrix

With the proliferation of sophisticated cameras in modern society, the demand for accurate and visually pleasing images is increasing. However, the quality of an image captured by a camera may be degraded by noise. Thus, some processing of images is required to filter out the noise without losing vital image features. Even though the current literature offers a variety of denoising methods, the fidelity and efficacy of their denoising are sometimes uncertain. Thus, here we propose a novel and computationally efficient image denoising method that is capable of producing accurate images. To preserve image smoothness, this method inputs patches partitioned from the image rather than pixels. Then, it performs denoising on the manifold underlying the patch-space rather than that in the image domain to better preserve the features across the whole image. We validate the performance of this method against benchmark image processing methods.