Inthis supplemental material, wefirst present thedetailed networkarchitecture andparameters of the proposed approach in Sec. A. We further provide more analysis of the proposed method and ablation studies in Sec. B. Section C shows some qualitative results for potential applications of the proposed approach on medical imaging and imaging in astronomy. Figure 6: Illustration of learned deep features.(a) The blurry input and ground truth are shown in Figure 1(a)-(b). However, on may actually wonder whether the feature extraction network acts as a denoiser, leading to the observed robustness of the proposed method to various noise levels.

The proposed neural network is motivated by the low-rank property of pseudo-inverse kernels.

Neural Information Processing Systems http://nips.cc/

Blind image deblurring (BID) is an important yet challenging image recovery problem. Most existing deep learning methods require supervised training with ground truth (GT) images. This paper introduces a self-supervised method for BID that does not require GT images. The key challenge is to regularize the training to prevent over-fitting due to the absence of GT images. By leveraging an exact relationship among the blurred image, latent image, and blur kernel across consecutive scales, we propose an effective cross-scale consistency loss.

Moiré artifacts are common in digital photography, resulting from the interference between high-frequency scene content and the color filter array of the camera. Existing deep learning-based demoiréing methods trained on large scale datasets are limited in handling various complex moiré patterns, and mainly focus on demoiréing of photos taken of digital displays. Moreover, obtaining moiré-free ground-truth in natural scenes is difficult but needed for training. In this paper, we propose a self-adaptive learning method for demoiréing a high-frequency image, with the help of an additional defocused moiré-free blur image. Given an image degraded with moiré artifacts and a moiré-free blur image, our network predicts a moiré-free clean image and a blur kernel with a self-adaptive strategy that does not require an explicit training stage, instead performing test-time adaptation.

Deep-learning based Super-Resolution (SR) methods have exhibited promising performance under non-blind setting where blur kernel is known; however, blur kernels of Low-Resolution (LR) images in different practical applications are usually unknown. It may lead to a significant performance drop when degradation process of training images deviates from that of real images. In this paper, we propose a novel blind SR framework to super-resolve LR images degraded by arbitrary blur kernel with accurate kernel estimation in frequency domain. To our best knowledge, this is the first deep learning method which conducts blur kernel estimation in frequency domain. Specifically, we first demonstrate that feature representation in frequency domain is more conducive for blur kernel reconstruction than in spatial domain. Next, we present a Spectrum-to-Kernel (S$2$K) network to estimate general blur kernels in diverse forms. We use a conditional GAN (CGAN) combined with SR-oriented optimization target to learn the end-to-end translation from degraded images' spectra to unknown kernels. Extensive experiments on both synthetic and real-world images demonstrate that our proposed method sufficiently reduces blur kernel estimation error, thus enables the off-the-shelf non-blind SR methods to work under blind setting effectively, and achieves superior performance over state-of-the-art blind SR methods, averagely by 1.39dB, 0.48dB (Gaussian kernels) and 6.15dB, 4.57dB (motion kernels) for scales $2\times$ and $4\times$ respectively.

Previous methods decompose blind super resolution (SR) problem into two sequential steps: \textit{i}) estimating blur kernel from given low-resolution (LR) image and \textit{ii}) restoring SR image based on estimated kernel. This two-step solution involves two independently trained models, which may not well compatible with each other. Small estimation error of the first step could cause severe performance drop of the second one. While on the other hand, the first step can only utilize limited information from LR image, which makes it difficult to predict highly accurate blur kernel. Towards these issues, instead of considering these two steps separately, we adopt an alternating optimization algorithm, which can estimate blur kernel and restore SR image in a single model.