  Image denoising is a fundamental operation in image processing and holds
considerable practical importance for various real-world applications. Arguably
several thousands of papers are dedicated to image denoising. In the past
decade, sate-of-the-art denoising algorithm have been clearly dominated by
non-local patch-based methods, which explicitly exploit patch self-similarity
within image. However, in recent two years, discriminatively trained local
approaches have started to outperform previous non-local models and have been
attracting increasing attentions due to the additional advantage of
computational efficiency. Successful approaches include cascade of shrinkage
fields (CSF) and trainable nonlinear reaction diffusion (TNRD). These two
methods are built on filter response of linear filters of small size using feed
forward architectures. Due to the locality inherent in local approaches, the
CSF and TNRD model become less effective when noise level is high and
consequently introduces some noise artifacts. In order to overcome this
problem, in this paper we introduce a multi-scale strategy. To be specific, we
build on our newly-developed TNRD model, adopting the multi-scale pyramid image
representation to devise a multi-scale nonlinear diffusion process. As
expected, all the parameters in the proposed multi-scale diffusion model,
including the filters and the influence functions across scales, are learned
from training data through a loss based approach. Numerical results on Gaussian
and Poisson denoising substantiate that the exploited multi-scale strategy can
successfully boost the performance of the original TNRD model with single
scale. As a consequence, the resulting multi-scale diffusion models can
significantly suppress the typical incorrect features for those noisy images
with heavy noise.
