Gaussian mixture diffusion
Jeremias Sulam, Yaniv Romano, Michael Elad · 2016
Most state-of-the-art denoising algorithms employ a patch-based approach by enforcing a local model or prior, such as self similarity, sparse representation, or Gaussian Mixture Model (GMM). While applying these models, these algorithms implicitly build a notion of similarity between the image pixels. This can be formulated as an image-adaptive linear-filter which is then used to denoise or restore the degraded image. In this work we focus on such a filter emerging from the GMM, study its properties and construct a graph Laplacian from it. Focusing on a variational denoising formulation, we incorporate a graph-based regularization term by leveraging the corresponding GMM Laplacian. The resulting algorithm extends and improves the non-local diffusion algorithm by replacing the Non-Local Means kernel with a GMM one. Our results indicate that this approach, termed Gaussian Mixtures Diffusion (GMD), consistently improves over both the original GMM scheme and the non-local diffusion algorithm. Furthermore, GMD is competitive or even better than the state-of-the-art method of EPLL.