Image denoising using diffusion on curvelet-scaled Gabor filter responses

In [5], a general framework for adaptive function regularization was introduced, and this framework was demonstrated in several applications, including image denoising. The basic idea of the method applied to image denoising is to choose a set of features and consider the pixels of the image as lying in feature space. We then try to use the heat equation on the points in feature space to smooth the image. In this note, we would like to give a more in depth account of image denoising in this framework using curvelet scaled Gabor filter responses as features.