Image restoration is a long-standing problem in low-level computer vision
with many interesting applications. We describe a flexible learning framework
based on the concept of nonlinear reaction diffusion models for various image
restoration problems. By embodying recent improvements in nonlinear diffusion
models, we propose a dynamic nonlinear reaction diffusion model with
time-dependent parameters (\ie, linear filters and influence functions). In
contrast to previous nonlinear diffusion models, all the parameters, including
the filters and the influence functions, are simultaneously learned from
training data through a loss based approach. We call this approach TNRD --
\textit{Trainable Nonlinear Reaction Diffusion}. The TNRD approach is
applicable for a variety of image restoration tasks by incorporating
appropriate reaction force. We demonstrate its capabilities with three
representative applications, Gaussian image denoising, single image super
resolution and JPEG deblocking. Experiments show that our trained nonlinear
diffusion models largely benefit from the training of the parameters and
finally lead to the best reported performance on common test datasets for the
tested applications. Our trained models preserve the structural simplicity of
diffusion models and take only a small number of diffusion steps, thus are
highly efficient. Moreover, they are also well-suited for parallel computation
on GPUs, which makes the inference procedure extremely fast.

使用非线性反应扩散模型的 TNRD 方法，通过动态学习参数从训练数据中同时学习滤波器和影响函数，实现图像恢复任务，包括高斯图像去噪、单图像超分辨率和 JPEG 去块，显示训练模型可以在保持扩散模型结构简单的同时，具有高效的运算速度，并在测试中取得最佳性能表现。

可训练非线性反应扩散：快速有效图像恢复的灵活框架

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast  and Effective Image Restoration

For several decades, image restoration remains an active research topic in
low-level computer vision and hence new approaches are constantly emerging.
However, many recently proposed algorithms achieve state-of-the-art performance
only at the expense of very high computation time, which clearly limits their
practical relevance. In this work, we propose a simple but effective approach
with both high computational efficiency and high restoration quality. We extend
conventional nonlinear reaction diffusion models by several parametrized linear
filters as well as several parametrized influence functions. We propose to
train the parameters of the filters and the influence functions through a loss
based approach. Experiments show that our trained nonlinear reaction diffusion
models largely benefit from the training of the parameters and finally lead to
the best reported performance on common test datasets for image restoration.
Due to their structural simplicity, our trained models are highly efficient and
are also well-suited for parallel computation on GPUs.

本论文介绍一种高效且高质量的图像修复方法，通过引入多个参数化的滤波器和函数对传统非线性反应扩散模型进行扩展，并采用基于损失的方法训练其参数。实验证明，训练后的非线性反应扩散模型的性能得以极大提升，且具有高效，适用于 GPU 的特点。