Deep Convolutional Primal-Dual Network for Image Deblurring

Image deblurring is a challenging image task, which is regarded as a classical inverse problem. Deep primal-dual proximal network (DeepPDNet) is recently proposed which unrolls the Condat-Vũ primal-dual splitting algorithm as a feed-forward network and it has demonstrated excellent restoration performance. However, the feature patterns in the DeepPDNet are well manually designed and thus the network is not implemented in an efficient convolutional fashion. In this work, we revisit the DeepPDNet and extend it in three respects: i) the convolution and pooling operators as well as their associating adjoint operations are studied in the primal-dual algorithm, and then a deep convolutional primal-dual network (DeepConvPDNet) and its full variant with skips are proposed to preserve the optimization consistence of primal-dual Condat-Vũ algorithm; ii) two (cascade vs parallel) variants of the networks are designed according to the structure of convolutional kernels; iii) rather than that the blur kernels are given as prior knowledge, they can be encoded by a set of convolutional layers and deconvolutional layers for their conjugate, resulting to a full learnable deep convolutional primal-dual neural network.We investigate the proposed networks on the MNIST dataset, the grayscale and color version of BSD dataset and GoPro dataset for image deblurring. Extensive experiments are conducted to validate the performance of the proposed networks, and promising results in term of PSNR and SSIM are obtained in comparison with twelve methods including state-of-the-art methods (e.g. Restormer, DRUNet, and DeblurGAN), which validated its effectiveness.