We present a new method for blind motion deblurring that uses a neural network trained to compute estimates of sharp image patches from observations that are blurred by an unknown motion kernel. Instead of regressing directly to patch intensities, this network learns to predict the complex Fourier coefficients of a deconvolution filter to be applied to the input patch for restoration. For inference, we apply the network independently to all overlapping patches in the observed image, and average its outputs to form an initial estimate of the sharp image. We then explicitly estimate a single global blur kernel by relating this estimate to the observed image, and finally perform non-blind deconvolution with this kernel. Our method exhibits accuracy and robustness close to state-of-the-art iterative methods, while being much faster when parallelized on GPU hardware.
This is a review on blind image deblurring. First, we formulate the blind image deblurring problem and explain why it is challenging. Next, we bring some psychological and cognitive studies on the way our human vision system deblurs. Then, relying on several previous reviews, we discuss the topic of metrics and datasets, which is non-trivial to blind deblurring. Finally, we introduce some typical optimization-based methods and learning-based methods.
Northwestern Polytechnical University（西北工业大学）；University of Technology Sydney（悉尼科技大学）
Single image blind deblurring is highly ill-posed as neither the latent sharp image nor the blur kernel is known. Even though considerable progress has been made, several major difficulties remain for blind deblurring, including the trade-off between high-performance deblurring and real-time processing. Besides, we observe that current single image blind deblurring networks cannot further improve or stabilize the performance but significantly degrades the performance when re-deblurring is repeatedly applied. This implies the limitation of these networks in modeling an ideal deblurring process.…
PROBE (Progressive Removal of Blur Residual) is a recursive framework for blind deblurring. Using the elementary modified inverse filter at its core, PROBE's experimental performance meets or exceeds the state of the art, both visually and quantitatively. Remarkably, PROBE lends itself to analysis that reveals its convergence properties. PROBE is motivated by recent ideas on progressive blind deblurring, but breaks away from previous research by its simplicity, speed, performance and potential for analysis. PROBE is neither a functional minimization approach, nor an open-loop sequential method…
Faculty of Computer science, University of New Brunswick（新 Brunswick大学计算机科学学院）；Department of Computer Science, Brandon University（布兰顿大学计算机科学系）；Department of Applied Computer Science, University of Winnipeg（温尼伯大学应用计算机科学系）
University of California, Berkeley（加州大学伯克利分校）；University of California, San Diego（加州大学圣地亚哥分校）
We study the problem of deblurring light fields of general 3D scenes captured under 3D camera motion and present both theoretical and practical contributions. By analyzing the motion-blurred light field in the primal and Fourier domains, we develop intuition into the effects of camera motion on the light field, show the advantages of capturing a 4D light field instead of a conventional 2D image for motion deblurring, and derive simple methods of motion deblurring in certain cases. We then present an algorithm to blindly deblur light fields of general scenes without any estimation of scene geom…
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
The goal of this project is to build a deep-learning solution that deblurs cornea scans, used for medical examination. The spherical shape of the eye prevents ophtamologist from having completely sharp image. Provided with a stack of corneas from confocal images, our approach is to build a model that performs an upscaling of the images using an SR (Super Resolution) Network.
Huazhong University of Science and Technology（华中科技大学）；University of California, Merced（加州大学默塞德分校）；Nanjing University of Science and Technology（南京理工大学）
We present an effective blind image deblurring method based on a data-driven discriminative prior.Our work is motivated by the fact that a good image prior should favor clear images over blurred images.In this work, we formulate the image prior as a binary classifier which can be achieved by a deep convolutional neural network (CNN).The learned prior is able to distinguish whether an input image is clear or not.Embedded into the maximum a posterior (MAP) framework, it helps blind deblurring in various scenarios, including natural, face, text, and low-illumination images.However, it is difficul…
Blind image deblurring is a particularly challenging inverse problem where the blur kernel is unknown and must be estimated en route to recover the deblurred image. The problem is of strong practical relevance since many imaging devices such as cellphone cameras, must rely on deblurring algorithms to yield satisfactory image quality. Despite significant research effort, handling large motions remains an open problem. In this paper, we develop a new method called Blind Image Deblurring using Row-Column Sparsity (BD-RCS) to address this issue. Specifically, we model the outer product of kernel a…
Peking University（北京大学）；National Institute of Informatics（国立信息学研究所）；Harbin Institute of Technology（哈尔滨工业大学）
Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel, de-convolve blurry input to restore the target image. In this paper, we propose a graph-based blind image deblurring algorithm by interpreting an image patch as a signal on a weighted graph. Specifically, we first argue that a skeleton image---a proxy that retains the strong gradients of the target but smooths out the details---can be used to accurately estimate…
School of Automation, Nanjing University of Information Science and Technology（南京信息工程大学自动化学院）；B-DAT（B-DAT（注：此处B-DAT为原文缩写，无更多上下文时保留英文））；Nanjing University of Information Science and Technology（南京信息工程大学）
Blind motion deblurring is one of the most basic and challenging problems in image processing and computer vision. It aims to recover a sharp image from its blurred version knowing nothing about the blur process. Many existing methods use Maximum A Posteriori (MAP) or Expectation Maximization (EM) frameworks to deal with this kind of problems, but they cannot handle well the figh frequency features of natural images. Most recently, deep neural networks have been emerging as a powerful tool for image deblurring. In this paper, we prove that encoder-decoder architecture gives better results for …
Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）
Blind motion deblurring involves reconstructing a sharp image from an observation that is blurry. It is a problem that is ill-posed and lies in the categories of image restoration problems. The training data-based methods for image deblurring mostly involve training models that take a lot of time. These models are data-hungry i.e., they require a lot of training data to generate satisfactory results. Recently, there are various image feature learning methods developed which relieve us of the need for training data and perform image restoration and image synthesis, e.g., DIP, InGAN, and SinGAN.…
We present a novel, blind, single image deblurring method that utilizes information regarding blur kernels. Our model solves the deblurring problem by dividing it into two successive tasks: (1) blur kernel estimation and (2) sharp image restoration. We first introduce a kernel estimation network that produces adaptive blur kernels based on the analysis of the blurred image. The network learns the blur pattern of the input image and trains to generate the estimation of image-specific blur kernels. Subsequently, we propose a deblurring network that restores sharp images using the estimated blur …
Peking University（北京大学）；Harbin Institute of Technology（哈尔滨工业大学）；National Institute of Informatics（国立信息学研究所）
Blind image deblurring, i.e., deblurring without knowledge of the blur kernel, is a highly ill-posed problem. The problem can be solved in two parts: i) estimate a blur kernel from the blurry image, and ii) given estimated blur kernel, de-convolve blurry input to restore the target image. In this paper, by interpreting an image patch as a signal on a weighted graph, we first argue that a skeleton image---a proxy that retains the strong gradients of the target but smooths out the details---can be used to accurately estimate the blur kernel and has a unique bi-modal edge weight distribution. We …
Recently, end-to-end learning-based methods based on deep neural network (DNN) have been proven effective for blind deblurring. Without human-made assumptions and numerical algorithms, they are able to restore images with fewer artifacts and better perceptual quality. However, in practice, we also find some of their drawbacks. Without the theoretical guidance, these methods can not perform well when the motion is complex and sometimes generate unreasonable results. In this paper, for overcoming these drawbacks, we integrate deep convolution neural networks into conventional deblurring framewor…
Ukrainian Catholic University（乌克兰天主教大学）；ELEKS Ltd.（ELEKS有限公司）；Visual Recognition Group, Center for Machine Perception, FEE, CTU in Prague（布拉格捷克技术大学（CTU）费尔学院（FEE）机器感知中心视觉识别小组）
We present DeblurGAN, an end-to-end learned method for motion deblurring. The learning is based on a conditional GAN and the content loss . DeblurGAN achieves state-of-the art performance both in the structural similarity measure and visual appearance. The quality of the deblurring model is also evaluated in a novel way on a real-world problem -- object detection on (de-)blurred images. The method is 5 times faster than the closest competitor -- DeepDeblur. We also introduce a novel method for generating synthetic motion blurred images from sharp ones, allowing realistic dataset augmentation. …
Deep learning in motion deblurring: current status, benchmarks and future prospects
Institute of Systems Engineering, Academy of Military Science（军事科学院系统工程研究所）；School of Artificial Intelligence and Computer Science, Jiangnan University（江南大学人工智能与计算机学院）；School of Electronics Engineering and Computer Science, Peking University（北京大学电子工程与计算机科学学院）
Technion–Israel Institute of Technology（以色列理工学院）；KTH Royal Institute of Technology（瑞典皇家理工学院）
In blind motion deblurring, leading methods today tend towards highly non-convex approximations of the l0-norm, especially in the image regularization term. In this paper, we propose a simple, effective and fast approach for the estimation of the motion blur-kernel, through a bi-l0-l2-norm regularization imposed on both the intermediate sharp image and the blur-kernel. Compared with existing methods, the proposed regularization is shown to be more effective and robust, leading to a more accurate motion blur-kernel and a better final restored image. A fast numerical scheme is deployed for alter…
Centre for Quantum Computation & Intelligent Systems（量子计算与智能系统中心）；Faculty of Engineering & Information Technology（工程与信息技术学院）；University of Technology Sydney（悉尼科技大学）
This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, im…
INRIA（法国国家信息与自动化研究所）；Département d’informatique de l’ENS（巴黎高等师范学院计算机科学系）；ENS（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL University（巴黎文理研究大学）；Xi’an Jiaotong University（西安交通大学）
Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method with Richardson fixed-point iterations for its least-squares updates and a proximal operator for the auxiliary variable updates. We propose to precondition the Richardson solver using approximate inverse filters of the (known) blur and natural image prior kernels. Using convolutions instead of a generic linear preconditioner allows extremely efficient parameter…
In this paper, we study the problem of recovering a sharp version of a given blurry image when the blur kernel is unknown. Previous methods often introduce an image-independent regularizer (such as Gaussian or sparse priors) on the desired blur kernel. We shall show that the blurry image itself encodes rich information about the blur kernel. Such information can be found through analyzing and comparing how the spectrum of an image as a convolution operator changes before and after blurring. Our analysis leads to an effective convex regularizer on the blur kernel which depends only on the given…
Multi-scale Frequency Enhancement Network for Blind Image Deblurring
The Institute of Systems Engineering, Academy of Military Science（军事科学院系统工程研究所）；School of Artificial Intelligence and Computer Science, Jiangnan University（江南大学人工智能与计算机学院）；Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University（江南大学江苏省模式识别与计算智能工程实验室）；College of Artificial Intelligence, China University of Petroleum(beijing)（中国石油大学（北京）人工智能学院）；Beijing Key Laboratory of Petroleum Data Mining, China University of Petroleum(beijing)（中国石油大学（北京）北京市石油数据挖掘重点实验室）
Seoul National University（首尔大学）；Inha University（仁荷大学）
Removing camera motion blur from a single light field is a challenging task since it is highly ill-posed inverse problem. The problem becomes even worse when blur kernel varies spatially due to scene depth variation and high-order camera motion. In this paper, we propose a novel algorithm to estimate all blur model variables jointly, including latent sub-aperture image, camera motion, and scene depth from the blurred 4D light field. Exploiting multi-view nature of a light field relieves the inverse property of the optimization by utilizing strong depth cues and multi-view blur observation. The…
The goal of blind image deblurring is to recover a sharp image from a motion blurred one without knowing the camera motion. Current state-of-the-art methods have a remarkably good performance on images with no noise or very low noise levels. However, the noiseless assumption is not realistic considering that low light conditions are the main reason for the presence of motion blur due to requiring longer exposure times. In fact, motion blur and high to moderate noise often appear together. Most works approach this problem by first estimating the blur kernel $k$ and then deconvolving the noisy b…
Blind image deblurring (BID) is an ill-posed inverse problem, usually addressed by imposing prior knowledge on the (unknown) image and on the blurring filter. Most of the work on BID has focused on natural images, using image priors based on statistical properties of generic natural images. However, in many applications, it is known that the image being recovered belongs to some specific class (e.g., text, face, fingerprints), and exploiting this knowledge allows obtaining more accurate priors. In this work, we propose a method where a Gaussian mixture model (GMM) is used to learn a class-adap…
Northwestern Polytechnical University（西北工业大学）；Microsoft Research Asia（微软亚洲研究院）
Typical blur from camera shake often deviates from the standard uniform convolutional script, in part because of problematic rotations which create greater blurring away from some unknown center point. Consequently, successful blind deconvolution requires the estimation of a spatially-varying or non-uniform blur operator. Using ideas from Bayesian inference and convex analysis, this paper derives a non-uniform blind deblurring algorithm with several desirable, yet previously-unexplored attributes. The underlying objective function includes a spatially adaptive penalty which couples the latent …
Blind Image deblurring tries to estimate blurriness and a latent image out of a blurred image. This estimation, as being an ill-posed problem, requires imposing restrictions on the latent image or a blur kernel that represents blurriness. Different from recent studies that impose some priors on the latent image, this paper regulates the structure of the blur kernel. We propose a kernel mixture structure while using the Gaussian kernel as a base kernel. By combining multiple Gaussian kernels structurally enhanced in terms of scales and centers, the kernel mixture becomes capable of modeling nea…
In this paper, we address the problem of blind deblurring with high efficiency. We propose a set of lightweight deep-wiener-network to finish the task with real-time speed. The Network contains a deep neural network for estimating parameters of wiener networks and a wiener network for deblurring. Experimental evaluations show that our approaches have an edge on State of the Art in terms of inference times and numbers of parameters. Two of our models can reach a speed of 100 images per second, which is qualified for real-time deblurring. Further research may focus on some real-world application…
Many deep learning based methods are designed to remove non-uniform (spatially variant) motion blur caused by object motion and camera shake without knowing the blur kernel. Some methods directly output the latent sharp image in one stage, while others utilize a multi-stage strategy (\eg multi-scale, multi-patch, or multi-temporal) to gradually restore the sharp image. However, these methods have the following two main issues: 1) The computational cost of multi-stage is high; 2) The same convolution kernel is applied in different regions, which is not an ideal choice for non-uniform blur. Henc…
Dalian University of Technology（大连理工大学）；Guilin University of Electronic Technology（桂林电子科技大学）
Blind image deblurring plays a very important role in many vision and multimedia applications. Most existing works tend to introduce complex priors to estimate the sharp image structures for blur kernel estimation. However, it has been verified that directly optimizing these models is challenging and easy to fall into degenerate solutions. Although several experience-based heuristic inference strategies, including trained networks and designed iterations, have been developed, it is still hard to obtain theoretically guaranteed accurate solutions. In this work, a collaborative learning framewor…
Hebei University of Technology（河北工业大学）；Australian National University（澳大利亚国立大学）；Tencent（腾讯）
Single-image super-resolution (SR) and multi-frame SR are two ways to super resolve low-resolution images. Single-Image SR generally handles each image independently, but ignores the temporal information implied in continuing frames. Multi-frame SR is able to model the temporal dependency via capturing motion information. However, it relies on neighbouring frames which are not always available in the real world. Meanwhile, slight camera shake easily causes heavy motion blur on long-distance-shot low-resolution images. To address these problems, a Blind Motion Deblurring Super-Reslution Network…
Image blurring refers to the degradation of an image wherein the image's overall sharpness decreases. Image blurring is caused by several factors. Additionally, during the image acquisition process, noise may get added to the image. Such a noisy and blurred image can be represented as the image resulting from the convolution of the original image with the associated point spread function, along with additive noise. However, the blurred image often contains inadequate information to uniquely determine the plausible original image. Based on the availability of blurring information, image deblurr…
Australian National University（澳大利亚国立大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Northwestern Polytechnical University（西北工业大学）
The image blurring process is generally modelled as the convolution of a blur kernel with a latent image. Therefore, the estimation of the blur kernel is essentially important for blind image deblurring. Unlike existing approaches which focus on approaching the problem by enforcing various priors on the blur kernel and the latent image, we are aiming at obtaining a high quality blur kernel directly by studying the problem in the frequency domain. We show that the auto-correlation of the absolute phase-only image can provide faithful information about the motion (e.g. the motion direction and m…
This paper proposes a novel approach to regularize the \textit{ill-posed} and \textit{non-linear} blind image deconvolution (blind deblurring) using deep generative networks as priors. We employ two separate generative models --- one trained to produce sharp images while the other trained to generate blur kernels from lower-dimensional parameters. To deblur, we propose an alternating gradient descent scheme operating in the latent lower-dimensional space of each of the pretrained generative models. Our experiments show promising deblurring results on images even under large blurs, and heavy no…
In this paper, we introduce an end-to-end generative adversarial network (GAN) based on sparse learning for single image blind motion deblurring, which we called SL-CycleGAN. For the first time in blind motion deblurring, we propose a sparse ResNet-block as a combination of sparse convolution layers and a trainable spatial pooler k-winner based on HTM (Hierarchical Temporal Memory) to replace non-linearity such as ReLU in the ResNet-block of SL-CycleGAN generators. Furthermore, unlike many state-of-the-art GAN-based motion deblurring methods that treat motion deblurring as a linear end-to-end …
We inspect all the deep learning based solutions and provide holistic understanding of various architectures that have evolved over the past few years to solve blind deblurring. The introductory work used deep learning to estimate some features of the blur kernel and then moved onto predicting the blur kernel entirely, which converts the problem into non-blind deblurring. The recent state of the art techniques are end to end, i.e., they don't estimate the blur kernel rather try to estimate the latent sharp image directly from the blurred image. The benchmarking PSNR and SSIM values on standard…
Peking University（北京大学）；Cooperative Media-net Innovation Center（协同媒体网创新中心）；Beida (Binhai) Information Research（北大（滨海）信息研究院）；Harbin Institute of Technology（哈尔滨工业大学）
Blind image deblurring is a challenging problem in computer vision, which aims to restore both the blur kernel and the latent sharp image from only a blurry observation. Inspired by the prevalent self-example prior in image super-resolution, in this paper, we observe that a coarse enough image down-sampled from a blurry observation is approximately a low-resolution version of the latent sharp image. We prove this phenomenon theoretically and define the coarse enough image as a latent structure prior of the unknown sharp image. Starting from this prior, we propose to restore sharp images from t…
DWDN: Deep Wiener Deconvolution Network for Non-Blind Image Deblurring
School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Department of Computer Science, TU Darmstadt（达姆施塔特工业大学计算机科学系）
Centro de Informática, Universidade Federal de Pernambuco（伯南布哥联邦大学信息中心）；Motorola Mobility LLC (a Lenovo Company)（摩托罗拉移动有限责任公司（联想旗下公司））
We propose a new incremental aggregation algorithm for multi-image deblurring with automatic image selection. The primary motivation is that current bursts deblurring methods do not handle well situations in which misalignment or out-of-context frames are present in the burst. These real-life situations result in poor reconstructions or manual selection of the images that will be used to deblur. Automatically selecting best frames within the burst to improve the base reconstruction is challenging because the amount of possible images fusions is equal to the power set cardinal. Here, we approac…
This paper proposes a novel approach to regularize the ill-posed blind image deconvolution (blind image deblurring) problem using deep generative networks. We employ two separate deep generative models - one trained to produce sharp images while the other trained to generate blur kernels from lower dimensional parameters. To deblur, we propose an alternating gradient descent scheme operating in the latent lower-dimensional space of each of the pretrained generative models. Our experiments show excellent deblurring results even under large blurs and heavy noise. To improve the performance on ri…
Chongqing University of Posts and Telecommunications（重庆邮电大学）；Chongqing University（重庆大学）
Most existing deep-learning-based single image dynamic scene blind deblurring (SIDSBD) methods usually design deep networks to directly remove the spatially-variant motion blurs from one inputted motion blurred image, without blur kernels estimation. In this paper, inspired by the Projective Motion Path Blur (PMPB) model and deformable convolution, we propose a novel constrained deformable convolutional network (CDCN) for efficient single image dynamic scene blind deblurring, which simultaneously achieves accurate spatially-variant motion blur kernels estimation and the high-quality image rest…
Beijing Jiaotong University（北京交通大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Xpeng Motors（小鹏汽车）
Non-uniform blur, mainly caused by camera shake and motions of multiple objects, is one of the most common causes of image quality degradation. However, the traditional blind deblurring methods based on blur kernel estimation do not perform well on complicated non-uniform motion blurs. Recent studies show that GAN-based approaches achieve impressive performance on deblurring tasks. In this letter, to further improve the performance of GAN-based methods on deblurring tasks, we propose an edge heuristic multi-scale generative adversarial network(GAN), which uses the "coarse-to-fine" scheme to re…
In recent years, deep neural network-based restoration methods have achieved state-of-the-art results in various image deblurring tasks. However, one major drawback of deep learning-based deblurring networks is that large amounts of blurry-clean image pairs are required for training to achieve good performance. Moreover, deep networks often fail to perform well when the blurry images and the blur kernels during testing are very different from the ones used during training. This happens mainly because of the overfitting of the network parameters on the training data. In this work, we present a …
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Tübingen（蒂宾根大学）
As handheld video cameras are now commonplace and available in every smartphone, images and videos can be recorded almost everywhere at anytime. However, taking a quick shot frequently yields a blurry result due to unwanted camera shake during recording or moving objects in the scene. Removing these artifacts from the blurry recordings is a highly ill-posed problem as neither the sharp image nor the motion blur kernel is known. Propagating information between multiple consecutive blurry observations can help restore the desired sharp image or video. Solutions for blind deconvolution based on n…
Istituto Italiano di Tecnologia（意大利技术研究院）；Ca’Foscari University of Venice（威尼斯大学）
Most computer vision and machine learning-based approaches for historical document analysis are tailored to grayscale or RGB images and thus, mostly exploit their spatial information. Multispectral (MS) and hyperspectral (HS) images contain, next to the spatial information, much richer spectral information than RGB images (usually spreading beyond the visible spectral range) that can facilitate more effective feature extraction, more accurate classification and recognition, and thus, improved analysis. Although utilization of rich spectral information can improve historical document analysis t…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Tübingen（图宾根大学）
We present a neural network model approach for multi-frame blind deconvolution. The discriminative approach adopts and combines two recent techniques for image deblurring into a single neural network architecture. Our proposed hybrid-architecture combines the explicit prediction of a deconvolution filter and non-trivial averaging of Fourier coefficients in the frequency domain. In order to make full use of the information contained in all images in one burst, the proposed network embeds smaller networks, which explicitly allow the model to transfer information between images in early layers. O…
Blind image deblurring is an important yet very challenging problem in low-level vision. Traditional optimization based methods generally formulate this task as a maximum-a-posteriori estimation or variational inference problem, whose performance highly relies on the handcraft priors for both the latent image and the blur kernel. In contrast, recent deep learning methods generally learn, from a large collection of training images, deep neural networks (DNNs) directly mapping the blurry image to the clean one or to the blur kernel, paying less attention to the physical degradation process of th…
University of Electronic Science and Technology of China（电子科技大学）；The Chinese University of Hong Kong（香港中文大学）；Northeast Normal University（东北师范大学）
Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing the prior of the kernel (or induced) error. However, how to design a suitable prior for the kernel (or induced) error remains challenging. Hand-crafted prior, incorporating domain knowledge, generally performs well but may lead to poor performance when kernel (or induced) error is complex. Data-driven prior, which excessively depends on the diversity and abund…
