  Image diffusion plays a fundamental role for the task of image denoising.
Recently proposed trainable nonlinear reaction diffusion (TNRD) model defines a
simple but very effective framework for image denoising. However, as the TNRD
model is a local model, the diffusion behavior of which is purely controlled by
information of local patches, it is prone to create artifacts in the homogenous
regions and over-smooth highly textured regions, especially in the case of
strong noise levels. Meanwhile, it is widely known that the non-local
self-similarity (NSS) prior stands as an effective image prior for image
denoising, which has been widely exploited in many non-local methods. In this
work, we are highly motivated to embed the NSS prior into the TNRD model to
tackle its weaknesses. In order to preserve the expected property that
end-to-end training is available, we exploit the NSS prior by a set of
non-local filters, and derive our proposed trainable non-local reaction
diffusion (TNLRD) model for image denoising. Together with the local filters
and influence functions, the non-local filters are learned by employing
loss-specific training. The experimental results show that the trained TNLRD
model produces visually plausible recovered images with more textures and less
artifacts, compared to its local versions. Moreover, the trained TNLRD model
can achieve strongly competitive performance to recent state-of-the-art image
denoising methods in terms of peak signal-to-noise ratio (PSNR) and structural
similarity index (SSIM).
