PDE-based non-linear diffusion techniques for denoising scientific and industrial images: an empirical study

摘要

Removing noise from data is often the first step in data analysis. Denoising techniques should not only reduce the noise, but do so without blurring or changing the location of the edges. Many approaches have been proposed to accomplish this; in this paper, we focus on one such approach, namely the use of non-linear diffusion operators. This approach has been studied extensively from a theoretical viewpoint ever since the 1987 work of Perona and Malik showed that non-linear filters outperformed the more traditional linear Canny edge detector. We complement this theoretical work by investigating the performance of several isotropic diffusion operators on test images from scientific domains. We explore the effects of various parameters such as the choice of diffusivity function, explicit and implicit methods for the discretization of the PDE, and approaches for the spatial discretization of the non-linear operator etc. We also compare these schemes with simple spatial filters and the more complex wavelet-based shrinkage techniques. Our empirical results show that, with an appropriate choice of parameters, diffusion-based schemes can be as effective as competitive techniques.