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.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper tackles the problem of blind image deconvolution and proposes an alternative approach to the commonly employed coarse-to-fine scheme in existing state-of-the-art methods. Instead of performing kernel estimation at different resolution scales, the authors suggest to apply Gaussian blur of various widths to yield different scales, each of which accentuates complementary image features. Kernel estimation at all scales is performed simultaneously rather than successively such that kernel information revealed in different scales can be combined in the estimation process. The weights that determine how much information each scale contributes to kernel estimation are chosen adaptively.

We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax-kernels.

Single Image Super-Resolution (SISR) is a low-level visual task to recover High-Resolution (HR) images from its degraded Low-Resolution (LR) counterparts.

Most motion deblurring algorithms rely on spatial-domain convolution models, which struggle with the complex, non-linear blur arising from camera shake and object motion. In contrast, we propose a novel single-image deblurring approach that treats motion blur as a temporal averaging phenomenon. Our core innovation lies in leveraging a pre-trained video diffusion transformer model to capture diverse motion dynamics within a latent space. It sidesteps explicit kernel estimation and effectively accommodates diverse motion patterns. We implement the algorithm within a diffusion-based inverse problem framework. Empirical results on synthetic and real-world datasets demonstrate that our method outperforms existing techniques in deblurring complex motion blur scenarios. This work paves the way for utilizing powerful video diffusion models to address single-image deblurring challenges.

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.

Greedy algorithms, particularly the orthogonal greedy algorithm (OGA), have proven e ff ective in training shallow neural networks for fitting functions and solving partial di fferential equations (PDEs). In this paper, we extend the application of OGA to the tasks of linear operator learning, which is equivalent to learning the kernel function through integral transforms. Firstly, a novel greedy algorithm is developed for kernel estimation rate in a new semi-inner product, which can be utilized to approximate the Green's function of linear PDEs from data. Secondly, we introduce the OGA for point-wise kernel estimation to further improve the approximation rate, achieving orders of accuracy improvement across various tasks and baseline models. In addition, we provide a theoretical analysis on the kernel estimation problem and the optimal approximation rates for both algorithms, establishing their e fficacy and potential for future applications in PDEs and operator learning tasks. Introduction In recent years, deep neural networks have emerged as a powerful tool for solving partial di ff erential equations (PDEs) in a wide range of scientific and engineering domains [1]. Approaches in this area can be broadly classified into two main categories: (1) single PDE solvers and (2) operator learning. Single PDE solvers, such as physics-informed neural networks(PINNs)[2], the deep Galerkin method[3], the deep Ritz method[4], optimize the deep neural network by minimizing a given loss function related to the PDE. These methods are specifically designed to solve a given instance of the PDE. In contrast, operator learning involves using deep neural networks to learn operators between function spaces, allowing for the learning of solution operators of PDEs from data pairs. Recently, several operator learning methods have been proposed, including deep Green networks (DGN)[5], deep operator networks (DON)[6], and neural operators (NOs)[7].

The presence of noise and small scale structures usually leads to large kernel estimation errors in blind image deblurring empirically, if not a total failure. We present a scale space perspective on blind deblurring algorithms, and introduce a cascaded scale space formulation for blind deblurring. This new formulation suggests a natural approach robust to noise and small scale structures through tying the estimation across multiple scales and balancing the contributions of different scales automatically by learning from data. The proposed formulation also allows to handle non-uniform blur with a straightforward extension. Experiments are conducted on both benchmark dataset and real-world images to validate the effectiveness of the proposed method. One surprising finding based on our approach is that blur kernel estimation is not necessarily best at the finest scale.