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

With the sophisticated modern technology in the camera industry, the demand for accurate and visually pleasing images is increasing. However, the quality of images captured by cameras are inevitably degraded by noise. Thus, some processing on images is required to filter out the noise without losing vital image features such as edges, corners, etc. Even though the current literature offers a variety of denoising methods, fidelity and efficiency of their denoising are sometimes uncertain. Thus, here we propose a novel and computationally efficient image denoising method that is capable of producing an accurate output. This method inputs patches partitioned from the image rather than pixels that are well known for preserving image smoothness. 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.