A Wiener filtering scheme in graph Fourier domain is proposed for
improving image denoising performance achieved by various spectral
graph based denoising methods. The proposed Wiener filter is
estimated by using graph Fourier coefficients of the noisy image after
they are processed for denoising, to further improve the already
achieved denoising accuracy as a post-processing step. It can be estimated
from and applied to the entire image, or can be used patchwise
in a locally adaptive manner. Our results indicate that the proposed
step yields consistent accuracy improvement for different choices of
weighted adjacency and graph Laplacian matrices used in computing
the graph Fourier transform and for different processing methods
used to denoise obtained transform coefficients. We obtain higher
peak signal-to-noise ratio values than the BM3D method for some
images.
Index Terms— Signal processing on graphs, spectral graph
methods, graph Fourier transform, image denoising, Wiener filter.