As an integral component of blind image deblurring, non-blind deconvolution removes image blur with a given blur kernel, which is essential but difficult due to the ill-posed nature of the inverse problem. The predominant approach is based on optimization subject to regularization functions that are either manually designed, or learned from examples. Existing learning based methods have shown superior restoration quality but are not practical enough due to their restricted and static model design. They solely focus on learning a prior and require to know the noise level for deconvolution. We address the gap between the optimization-based and learning-based approaches by learning a universal gradient descent optimizer. We propose a Recurrent Gradient Descent Network (RGDN) by systematically incorporating deep neural networks into a fully parameterized gradient descent scheme. A hyper-parameter-free update unit shared across steps is used to generate updates from the current estimates, based on a convolutional neural network. By training on diverse examples, the Recurrent Gradient Descent Network learns an implicit image prior and a universal update rule through recursive supervision. The learned optimizer can be repeatedly used to improve the quality of diverse degenerated observations. The proposed method possesses strong interpretability and high generalization. Extensive experiments on synthetic benchmarks and challenging real-world images demonstrate that the proposed deep optimization method is effective and robust to produce favorable results as well as practical for real-world image deblurring applications.
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…
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…
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…
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；University of British Columbia（不列颠哥伦比亚大学）
Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a {\em faster gradient descent method}. For unconstrained convex quadratic optimization these methods can converge much faster than steepest descent. But the context of interest here is application to certain ill-posed inverse problems, where the steepest descent method is known to have a smoothing, regularizing effect, and where a strict optimization solution is not necessary.…
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）
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…
Northwestern Polytechnical University（西北工业大学）；South China University of Technology（华南理工大学）；The University of Adelaide（阿德莱德大学）
Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges. Existing TV-based methods, however, often suffer from the over-smoothing issue and solution bias caused by the homogeneous penalization. In this paper, we consider addressing these issues by applying inhomogeneous regularization on different image components. We formulate the inhomogeneous TV minimization problem as a convex quadratic constrained linear programming problem. Relying on this new model, we propose a matching pursuit based total var…
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…
In blind image deconvolution, priors are often leveraged to constrain the solution space, so as to alleviate the under-determinacy. Priors which are trained separately from the task of deconvolution tend to be instable, or ineffective. We propose the Golf Optimizer, a novel but simple form of network that learns deep priors from data with better propagation behavior. Like playing golf, our method first estimates an aggressive propagation towards optimum using one network, and recurrently applies a residual CNN to learn the gradient of prior for delicate correction on restoration. Experiments s…
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…
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…
An open question in the Deep Learning community is why neural networks trained with Gradient Descent generalize well on real datasets even though they are capable of fitting random data. We propose an approach to answering this question based on a hypothesis about the dynamics of gradient descent that we call Coherent Gradients: Gradients from similar examples are similar and so the overall gradient is stronger in certain directions where these reinforce each other. Thus changes to the network parameters during training are biased towards those that (locally) simultaneously benefit many exampl…
With the vigorous development of artificial intelligence technology, various engineering technology applications have been implemented one after another. The gradient descent method plays an important role in solving various optimization problems, due to its simple structure, good stability and easy implementation. In multi-node machine learning system, the gradients usually need to be shared. Shared gradients are generally unsafe. Attackers can obtain training data simply by knowing the gradient information. In this paper, to prevent gradient leakage while keeping the accuracy of model, we pr…
Carnegie Mellon University（卡内基梅隆大学）；University of Southern California（南加州大学）；Peking University（北京大学）；Beijing Institute of Big Data Research（北京大数据研究院）；Massachusetts Institute of Technology（麻省理工学院）
Gradient descent finds a global minimum in training deep neural networks despite the objective function being non-convex. The current paper proves gradient descent achieves zero training loss in polynomial time for a deep over-parameterized neural network with residual connections (ResNet). Our analysis relies on the particular structure of the Gram matrix induced by the neural network architecture. This structure allows us to show the Gram matrix is stable throughout the training process and this stability implies the global optimality of the gradient descent algorithm. We further extend our …
