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 noise. To address the shortcomings of generative models such as mode collapse, we augment our generative priors with classical image priors and report improved performance on complex image datasets. The deblurring performance depends on how well the range of the generator spans the image class. Interestingly, our experiments show that even an untrained structured (convolutional) generative networks acts as an image prior in the image deblurring context allowing us to extend our results to more diverse natural image datasets.
City University of Hong Kong（香港城市大学）；Dalian University of Technology（大连理工大学）；University of California Merced（加州大学默塞德分校）
In this paper, we propose a fully convolutional networks for iterative non-blind deconvolution We decompose the non-blind deconvolution problem into image denoising and image deconvolution. We train a FCNN to remove noises in the gradient domain and use the learned gradients to guide the image deconvolution step. In contrast to the existing deep neural network based methods, we iteratively deconvolve the blurred images in a multi-stage framework. The proposed method is able to learn an adaptive image prior, which keeps both local (details) and global (structures) information. Both quantitative…
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…
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）
Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise, quantization, as well as non-linear camera response function due to e.g., gamma correction. We show that accurately modeling a more realistic image acquisition pipeline leads to significant improvements, both in terms of image quality and PSNR. Furthermore, we show that incorporating the non-linear response in both the data and the regularization terms of the p…
Blind deconvolution is the problem of recovering a convolutional kernel $\boldsymbol a_0$ and an activation signal $\boldsymbol x_0$ from their convolution $\boldsymbol y = \boldsymbol a_0 \circledast \boldsymbol x_0$. This problem is ill-posed without further constraints or priors. This paper studies the situation where the nonzero entries in the activation signal are sparsely and randomly populated. We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. With this spherical constraint…
State-of-the-art atmospheric turbulence image restoration methods utilize standard image processing tools such as optical flow, lucky region and blind deconvolution to restore the images. While promising results have been reported over the past decade, many of the methods are agnostic to the physical model that generates the distortion. In this paper, we revisit the turbulence restoration problem by analyzing the reference frame generation and the blind deconvolution steps in a typical restoration pipeline. By leveraging tools in large deviation theory, we rigorously prove the minimum number o…
Leveraging Classic Deconvolution and Feature Extraction in Zero-Shot Image Restoration
Technical University of Munich（慕尼黑工业大学）；Helmholtz AI, Helmholtz Munich - German Research Center for Environmental Health（亥姆霍兹人工智能平台，亥姆霍兹慕尼黑中心——德国环境健康研究中心）；Georg-August-University Göttingen（哥廷根乔治-奥古斯特大学）；GEOMAR Helmholtz Centre for Ocean Research Kiel（基尔亥姆霍兹海洋研究中心）
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…
National Taiwan University（台湾大学）；Nanjing University of Science and Technology（南京理工大学）；Google Research（谷歌研究院）；University of California, Merced（加州大学默塞德分校）；Yonsei University（延世大学）
Most existing methods usually formulate the non-blind deconvolution problem into a maximum-a-posteriori framework and address it by manually designing kinds of regularization terms and data terms of the latent clear images. However, explicitly designing these two terms is quite challenging and usually leads to complex optimization problems which are difficult to solve. In this paper, we propose an effective non-blind deconvolution approach by learning discriminative shrinkage functions to implicitly model these terms. In contrast to most existing methods that use deep convolutional neural netw…
Tsinghua University（清华大学）；Beijing Institute of Technology（北京理工大学）
Under low-light environment, handheld photography suffers from severe camera shake under long exposure settings. Although existing deblurring algorithms have shown promising performance on well-exposed blurry images, they still cannot cope with low-light snapshots. Sophisticated noise and saturation regions are two dominating challenges in practical low-light deblurring. In this work, we propose a novel non-blind deblurring method dubbed image and feature space Wiener deconvolution network (INFWIDE) to tackle these problems systematically. In terms of algorithm design, INFWIDE proposes a two-b…
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…
Technical University of Munich（慕尼黑工业大学）；Helmholtz AI（亥姆霍兹人工智能中心）；GEOMAR Helmholtz Centre for Ocean Research Kiel（基尔亥姆霍兹海洋研究中心（GEOMAR））
We present a model for non-blind image deconvolution that incorporates the classic iterative method into a deep learning application. Instead of using large over-parameterised generative networks to create sharp picture representations, we build our network based on the iterative Landweber deconvolution algorithm, which is integrated with trainable convolutional layers to enhance the recovered image structures and details. Additional to the data fidelity term, we also add Hessian and sparse constraints as regularization terms to improve the image reconstruction quality. Our proposed model is \…
In this paper, we solve blind image deconvolution problem that is to remove blurs form a signal degraded image without any knowledge of the blur kernel. Since the problem is ill-posed, an image prior plays a significant role in accurate blind deconvolution. Traditional image prior assumes coefficients in filtered domains are sparse. However, it is assumed here that there exist additional structures over the sparse coefficients. Accordingly, we propose new problem formulation for the blind image deconvolution, which utilizes the structural information by coupling Student's-t image prior with ov…
We developed novel conditional expressions (CEs) for Lane and Bates' blind deconvolution. The CEs are given in term of the derivatives of the zero-values of the z-transform of given images. The CEs make it possible to automatically detect multiple blur convolved in the given images all at once without performing any analysis of the zero-sheets of the given images. We illustrate the multiple blur-detection by the CEs for a model image
We present conditional expression (CE) for finding blurs convolved in given images. The CE is given in terms of the zero-values of the blurs evaluated at multi-point. The CE can detect multiple blur all at once. We illustrate the multiple blur-detection by using a test image.
Massachussetts Institute of Technology（麻省理工学院）；New York University（纽约大学）；Facebook Inc.（Facebook公司）
Blind deconvolution has made significant progress in the past decade. Most successful algorithms are classified either as Variational or Maximum a-Posteriori ($MAP$). In spite of the superior theoretical justification of variational techniques, carefully constructed $MAP$ algorithms have proven equally effective in practice. In this paper, we show that all successful $MAP$ and variational algorithms share a common framework, relying on the following key principles: sparsity promotion in the gradient domain, $l_2$ regularization for kernel estimation, and the use of convex (often quadratic) cos…
Due to image blurring image deconvolution is often used for studying biological structures in fluorescence microscopy. Fluorescence microscopy image volumes inherently suffer from intensity inhomogeneity, blur, and are corrupted by various types of noise which exacerbate image quality at deeper tissue depth. Therefore, quantitative analysis of fluorescence microscopy in deeper tissue still remains a challenge. This paper presents a three dimensional blind image deconvolution method for fluorescence microscopy using 3-way spatially constrained cycle-consistent adversarial networks. The restored…
Blind deconvolution is an ill-posed problem arising in various fields ranging from microscopy to astronomy. The ill-posed nature of the problem requires adequate priors to arrive to a desirable solution. Recently, it has been shown that deep learning architectures can serve as an image generation prior during unsupervised blind deconvolution optimization, however often exhibiting a performance fluctuation even on a single image. We propose to use Wiener-deconvolution to guide the image generator during optimization by providing it a sharpened version of the blurry image using an auxiliary kern…
Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should f…
Blind Deconvolution for Color Images Using Normalized Quaternion Kernels
School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University（数学科学学院、智能计算与应用重点实验室、同济大学）；Department of Mathematics, Hong Kong Baptist University（数学系、香港 Baptist 大学）；School of Mathematics and Statistics & RIIS, Jiangsu Normal University（数学与统计学学院及RIIS、江苏师范大学）
Beijing Normal University（北京师范大学）；Tianjin University（天津大学）
Most blind deconvolution methods usually pre-define a large kernel size to guarantee the support domain. Blur kernel estimation error is likely to be introduced, yielding severe artifacts in deblurring results. In this paper, we first theoretically and experimentally analyze the mechanism to estimation error in oversized kernel, and show that it holds even on blurry images without noises. Then to suppress this adverse effect, we propose a low rank-based regularization on blur kernel to exploit the structural information in degraded kernels, by which larger-kernel effect can be effectively supp…
In the previous blind deconvolution methods, de-blurred images can be obtained by using the edge or pixel information. However, the existing edge-based methods did not take advantage of edge information in ommi-directions, but only used horizontal and vertical edges when recovering the de-blurred images. This limitation lowers the quality of the recovered images. This paper proposes a method which utilizes edges in different directions to recover the true sharp image. We also provide a statistical table score to show how many directions are enough to recover a high quality true sharp image. In…
In this work, we propose a new approach for efficient edge-preserving image deconvolution. Our algorithm is based on a novel type of explicit image filter - guided filter. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter, but has better behaviors near edges. We propose an efficient iterative algorithm with the decouple of deblurring and denoising steps in the restoration process. In deblurring step, we proposed two cost function which could be computed with fast Fourier transform efficiently. The solution of the first one is used as the g…
Tianjin University（天津大学）；Harbin Institute of Technology（哈尔滨工业大学）
Blind deconvolution is a classical yet challenging low-level vision problem with many real-world applications. Traditional maximum a posterior (MAP) based methods rely heavily on fixed and handcrafted priors that certainly are insufficient in characterizing clean images and blur kernels, and usually adopt specially designed alternating minimization to avoid trivial solution. In contrast, existing deep motion deblurring networks learn from massive training images the mapping to clean image or blur kernel, but are limited in handling various complex and large size blur kernels. To connect MAP an…
In this article, two closed and convex sets for blind deconvolution problem are proposed. Most blurring functions in microscopy are symmetric with respect to the origin. Therefore, they do not modify the phase of the Fourier transform (FT) of the original image. As a result blurred image and the original image have the same FT phase. Therefore, the set of images with a prescribed FT phase can be used as a constraint set in blind deconvolution problems. Another convex set that can be used during the image reconstruction process is the epigraph set of Total Variation (TV) function. This set does…
Idiap Research Institute（伊迪亚普研究所）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
We present a semi-blind, spatially-variant deconvolution technique aimed at optical microscopy that combines a local estimation step of the point spread function (PSF) and deconvolution using a spatially variant, regularized Richardson-Lucy algorithm. To find the local PSF map in a computationally tractable way, we train a convolutional neural network to perform regression of an optical parametric model on synthetically blurred image patches. We deconvolved both synthetic and experimentally-acquired data, and achieved an improvement of image SNR of 1.00 dB on average, compared to other deconvo…
InnoVinn Inc.（因诺文恩公司）；Vinnitsa National Technical University（文尼察国立技术大学）
We have shown that the left side null space of the autoregression (AR) matrix operator is the lexicographical presentation of the point spread function (PSF) on condition the AR parameters are common for original and blurred images. The method of inverse PSF evaluation with regularization functional as the function of surface area is offered. The inverse PSF was used for primary image estimation. Two methods of original image estimate optimization were designed basing on maximum entropy generalization of sought and blurred images conditional probability density and regularization. The first me…
Seoul National University College of Medicine（首尔大学医学院）；KAIST（韩国科学技术院）
Deconvolution microscopy has been extensively used to improve the resolution of the widefield fluorescent microscopy. Conventional approaches, which usually require the point spread function (PSF) measurement or blind estimation, are however computationally expensive. Recently, CNN based approaches have been explored as a fast and high performance alternative. In this paper, we present a novel unsupervised deep neural network for blind deconvolution based on cycle consistency and PSF modeling layers. In contrast to the recent CNN approaches for similar problem, the explicit PSF modeling layers…
Images from positron emission tomography (PET) provide metabolic information about the human body. They present, however, a spatial resolution that is limited by physical and instrumental factors often modeled by a blurring function. Since this function is typically unknown, blind deconvolution (BD) techniques are needed in order to produce a useful restored PET image. In this work, we propose a general BD technique that restores a low resolution blurry image using information from data acquired with a high resolution modality (e.g., CT-based delineation of regions with uniform activity in PET…
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Washington University in St. Louis（圣路易斯华盛顿大学）
A common problem that arises in radar imaging systems, especially those mounted on mobile platforms, is antenna position ambiguity. Approaches to resolve this ambiguity and correct position errors are generally known as radar autofocus. Common techniques that attempt to resolve the antenna ambiguity generally assume an unknown gain and phase error afflicting the radar measurements. However, ensuring identifiability and tractability of the unknown error imposes strict restrictions on the allowable antenna perturbations. Furthermore, these techniques are often not applicable in near-field imagin…
This paper addresses the problem of high-resolution Doppler blood flow estimation from an ultrafast sequence of ultrasound images. Formulating the separation of clutter and blood components as an inverse problem has been shown in the literature to be a good alternative to spatio-temporal singular value decomposition (SVD)-based clutter filtering. In particular, a deconvolution step has recently been embedded in such a problem to mitigate the influence of the experimentally measured point spread function (PSF) of the imaging system. Deconvolution was shown in this context to improve the accurac…
The lack of interpretability in current deep learning models causes serious concerns as they are extensively used for various life-critical applications. Hence, it is of paramount importance to develop interpretable deep learning models. In this paper, we consider the problem of blind deconvolution and propose a novel model-aware deep architecture that allows for the recovery of both the blur kernel and the sharp image from the blurred image. In particular, we propose the Deep Unfolded Richardson-Lucy (Deep-URL) framework -- an interpretable deep-learning architecture that can be seen as an am…
Blind Deconvolution of Binary and Pattern Images with Pixel Intensity Constraints and Sparse Gradient Prior
Beijing Normal University（北京师范大学）；Anhui University（安徽大学）；University of Electronic Science and Technology of China（电子科技大学）；Northeast Normal University（东北师范大学）
In this paper, we introduce a variational Bayesian algorithm (VBA) for image blind deconvolution. Our generic framework incorporates smoothness priors on the unknown blur/image and possible affine constraints (e.g., sum to one) on the blur kernel. One of our main contributions is the integration of VBA within a neural network paradigm, following an unrolling methodology. The proposed architecture is trained in a supervised fashion, which allows us to optimally set two key hyperparameters of the VBA model and lead to further improvements in terms of resulting visual quality. Various experiments…
InnoVinn Inc.（InnoVinn公司）；Vinnitsa National Technical University（文尼察国立技术大学）
We have shown that the vector of the point spread function (PSF) lexicographical presentation belongs to the left side conjugated null space (NS) of the autoregression (AR) matrix operator on condition the AR parameters are common for original and blurred images. The method of the PSF and inverse PSF (IPSF) evaluation in the basis of the NS eigenfunctions is offered. The optimization of the PSF and IPSF shape with the aim of fluctuation elimination is considered in NS spectral domain and image space domain. The function of surface area was used as the regularization functional. Two methods of …
In this paper, we present an algorithm for identifying a parametrically described destructive unknown system based on a non-gaussianity measure. It is known that under certain conditions the output of a linear system is more gaussian than the input. Hence, an inverse filter is searched, such that its output is minimally gaussian. We use the kurtosis as a measure of the non-gaussianity of the signal. A maximum of the kurtosis as a function of the deconvolving filter coefficients is searched. The search is done iteratively using the gradient ascent algorithm, and the coefficients at the maximum …
Don Mariano Marcos Memorial State University（唐马里亚诺马科斯纪念州立大学）；Ateneo de Manila University（马尼拉雅典耀大学）
Text detection in natural scenes has been a significant and active research subject in computer vision and document analysis because of its wide range of applications as evidenced by the emergence of the Robust Reading Competition. One of the algorithms which has good text detection performance in the said competition is the Character Region Awareness for Text Detection (CRAFT). Employing the ICDAR 2013 dataset, this study investigates the impact of automatic image classification and blind deconvolution as image pre-processing steps to further enhance the text detection performance of CRAFT. T…
Instituto de Astrofísica de Canarias（加那利群岛天体物理研究所）；Universidad de La Laguna（拉古纳大学）；Max Planck Institute for Solar System Research（马克斯·普朗克太阳系研究所）
Observations from ground based telescopes are affected by the presence of the Earth atmosphere, which severely perturbs them. The use of adaptive optics techniques has allowed us to partly beat this limitation. However, image selection or post-facto image reconstruction methods applied to bursts of short-exposure images are routinely needed to reach the diffraction limit. Deep learning has been recently proposed as an efficient way to accelerate these image reconstructions. Currently, these deep neural networks are trained with supervision, so that either standard deconvolution algorithms need…
Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
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 glo…
Beijing University of Technology（北京工业大学）；Tsinghua University（清华大学）
Blind image deconvolution is the problem of recovering the latent image from the only observed blurry image when the blur kernel is unknown. In this paper, we propose an edge-based blur kernel estimation method for blind motion deconvolution. In our previous work, we incorporate both sparse representation and self-similarity of image patches as priors into our blind deconvolution model to regularize the recovery of the latent image. Since almost any natural image has properties of sparsity and multi-scale self-similarity, we construct a sparsity regularizer and a cross-scale non-local regulari…
Multi-Frame Blind Manifold Deconvolution for Rotating Synthetic Aperture Imaging
School of Mathematics, Statistics and Actuarial Science, University of Kent（肯特大学数学、统计与精算科学学院）；Department of Computer Science, University College London（伦敦大学学院计算机科学系）
Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Université catholique de Louvain (UCL)（鲁汶天主教大学信息与通信技术、电子与应用数学研究所（ICTEAM））；Royal Observatory of Belgium（比利时皇家天文台）
Context: Characterization of instrumental effects in astronomical imaging is important in order to extract accurate physical information from the observations. The measured image in a real optical instrument is usually represented by the convolution of an ideal image with a Point Spread Function (PSF). Additionally, the image acquisition process is also contaminated by other sources of noise (read-out, photon-counting). The problem of estimating both the PSF and a denoised image is called blind deconvolution and is ill-posed. Aims: We propose a blind deconvolution scheme that relies on image r…
University of Chinese Academy of Sciences（中国科学院大学）；The Institute of Microelectronics, Tsinghua University（清华大学微电子研究所）；Chinese Academy of Sciences Artificial Intelligence Research（中国科学院人工智能研究院）
This paper proposes a novel model for video generation and especially makes the attempt to deal with the problem of video generation from text descriptions, i.e., synthesizing realistic videos conditioned on given texts. Existing video generation methods cannot be easily adapted to handle this task well, due to the frame discontinuity issue and their text-free generation schemes. To address these problems, we propose a recurrent deconvolutional generative adversarial network (RD-GAN), which includes a recurrent deconvolutional network (RDN) as the generator and a 3D convolutional neural networ…
In this work, we study the problem of non-blind image deconvolution and propose a novel recurrent network architecture that leads to very competitive restoration results of high image quality. Motivated by the computational efficiency and robustness of existing large scale linear solvers, we manage to express the solution to this problem as the solution of a series of adaptive non-negative least-squares problems. This gives rise to our proposed Recurrent Least Squares Deconvolution Network (RLSDN) architecture, which consists of an implicit layer that imposes a linear constraint between its in…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
We describe a learning-based approach to blind image deconvolution. It uses a deep layered architecture, parts of which are borrowed from recent work on neural network learning, and parts of which incorporate computations that are specific to image deconvolution. The system is trained end-to-end on a set of artificially generated training examples, enabling competitive performance in blind deconvolution, both with respect to quality and runtime.
Idiap Research Institute（IDIAP研究所）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
Optical microscopy is an essential tool in biology and medicine. Imaging thin, yet non-flat objects in a single shot (without relying on more sophisticated sectioning setups) remains challenging as the shallow depth of field that comes with high-resolution microscopes leads to unsharp image regions and makes depth localization and quantitative image interpretation difficult. Here, we present a method that improves the resolution of light microscopy images of such objects by locally estimating image distortion while jointly estimating object distance to the focal plane. Specifically, we estimat…
One popular approach for blind deconvolution is to formulate a maximum a posteriori (MAP) problem with sparsity priors on the gradients of the latent image, and then alternatingly estimate the blur kernel and the latent image. While several successful MAP based methods have been proposed, there has been much controversy and confusion about their convergence, because sparsity priors have been shown to prefer blurry images to sharp natural images. In this paper, we revisit this problem and provide an analysis on the convergence of MAP based approaches. We first introduce a slight modification to…
We address for the first time the issue of motion blur in light field images captured from plenoptic cameras. We propose a solution to the estimation of a sharp high resolution scene radiance given a blurry light field image, when the motion blur point spread function is unknown, i.e., the so-called blind deconvolution problem. In a plenoptic camera, the spatial sampling in each view is not only decimated but also defocused. Consequently, current blind deconvolution approaches for traditional cameras are not applicable. Due to the complexity of the imaging model, we investigate first the case …
We present a self-supervised and self-calibrating multi-shot approach to imaging through atmospheric turbulence, called TurbuGAN. Our approach requires no paired training data, adapts itself to the distribution of the turbulence, leverages domain-specific data priors, and can generalize from tens to thousands of measurements. We achieve such functionality through an adversarial sensing framework adapted from CryoGAN, which uses a discriminator network to match the distributions of captured and simulated measurements. Our framework builds on CryoGAN by (1) generalizing the forward measurement m…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Coordinated Science Laboratory（协同科学实验室）；Department of Electrical and Computer Engineering（电气与计算机工程系）
Multichannel blind deconvolution is the problem of recovering an unknown signal $f$ and multiple unknown channels $x_i$ from their circular convolution $y_i=x_i \circledast f$ ($i=1,2,\dots,N$). We consider the case where the $x_i$'s are sparse, and convolution with $f$ is invertible. Our nonconvex optimization formulation solves for a filter $h$ on the unit sphere that produces sparse output $y_i\circledast h$. Under some technical assumptions, we show that all local minima of the objective function correspond to the inverse filter of $f$ up to an inherent sign and shift ambiguity, and all sa…
Microsoft Research（微软研究院）；Northwestern Polytechnical University（西北工业大学）
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the solution space. While this naturally leads to a standard MAP estimation framework, performance is compromised by unknown trade-off parameter settings, optimization heuristics, and convergence issues stemming from non-convexity and/or poor prior selections. To mitigate some of these problems, a number of authors have recently proposed substituting a variational…
In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier ptychography, X-ray crystallography, and in visible light communication. We propose to solve this inverse problem using alternating gradient descent algorithm under two pretrained deep generative networks as priors; one is trained on sharp images and the other on blur kernels. The proposed recovery algorithm strives to find a sharp image and a blur kernel in the range…
