Deep Graph Laplacian Regularization

We propose to combine the robustness merit of model-based approaches and the learning power of data-driven approaches for image restoration. Specifically, by integrating graph Laplacian regularization as a trainable module into a deep learning framework, we are less susceptible to overfitting than pure CNN-based approaches, achieving higher robustness to small dataset and cross-domain denoising. First, a sparse neighborhood graph is built from the output of a convolutional neural network (CNN). Then the image is restored by solving an unconstrained quadratic programming problem, using a corresponding graph Laplacian regularizer as a prior term. The proposed restoration pipeline is fully differentiable and hence can be end-to-end trained. Experimental results demonstrate that our work avoids overfitting given small training data. It is also endowed with strong cross-domain generalization power, outperforming the state-of-the-art approaches by remarkable margin.