基于稀疏表示和梯度先验的图像盲去模糊

针对目前基于稀疏表示的图像盲卷积算法细节恢复有限等问题,提出一种基于稀疏表示和梯度先验的图像盲卷积算法。虽然每个图像块可以通过字典稀疏表示,但是图像块重构出的图像常常出现“伪像”,本文将梯度先验知识和超拉普拉斯先验知识融入稀疏表示盲卷积模型中,采用迭代方法交替估计中间清晰图像和模糊核,一旦获得模糊核,采用超拉普拉斯非盲去卷积算法恢复出最终的清晰图像。实验结果表明,与其他去模糊算法相比,本文算法在抑制振铃方面效果显著。     

基于正则化方法的图像盲去模糊

针对标准化稀疏先验的正则化方法估计复杂模糊核时的不准确性, 引入图像的预处理, 提出了一种图像盲去模糊的新方法。该方法将图像盲去模糊分为三个步骤：利用双边滤波器和冲击滤波器对图像进行预处理, 使得图像的噪声降低、边缘突出, 有利于模糊核的估计; 对预处理后的图像, 利用基于标准化稀疏先验的正则化方法估计模糊核; 根据估计出的模糊核利用TV正则化方法对图像进行非盲去卷积。采用快速迭代收缩阈值算法和快速总变分图像复原算法分别求解模糊核估计模型和图像非盲去卷积模型。实验结果表明, 针对单幅模糊图像, 该方法可以估计出准确的模糊核, 对噪声具有鲁棒性, 并且提高了图像复原速度, 具有较好的图像恢复效果。     

Fast Bayesian blind deconvolution with Huber Super Gaussian priors

Expectation Maximization (EM) based inference has already proven to be a very powerful tool to solve blind image deconvolution (BID) problems. Unfortunately, three important problems still impede the application of EM in BID: the undesirable saddle points and local minima caused by highly nonconvex priors, the instability around zero of some of the most interesting sparsity promoting priors, and the intrinsic high computational cost of the corresponding BID algorithm. In this paper we first show how Super Gaussian priors can be made numerically tractable around zero by introducing the family of Huber Super Gaussian priors and then present a fast EM based blind deconvolution method formulated in the image space. In the proposed computational approach, image and kernel estimation are performed by using the Alternating Direction Method of Multipliers (ADMM), which allows to exploit the advantages of FFT computation. For highly nonconvex priors, we propose a Smooth ADMM (SADMM) approach to avoid poor BID estimates. Extensive experiments demonstrate that the proposed method significantly outperforms state-of-the-art BID methods in terms of quality of the reconstructions and speed.     

基于稀疏表示和结构自相似性的单幅图像盲解卷积算法

图像盲解卷积研究当模糊核未知时,如何从模糊图像复原出原始清晰图像.由于盲解卷积是一个欠定问题,现有的盲解卷积算法都直接或间接地利用各种先验知识.本文提出了一种结合稀疏表示与结构自相似性的单幅图像盲解卷积算法,该算法将图像的稀疏性先验和结构自相似性先验作为正则化约束加入到图像盲解卷积的目标函数中,并利用图像不同尺度间的结构自相似性,将观测模糊图像的降采样图像作为稀疏表示字典的训练样本,保证清晰图像在该字典下的稀疏性.最后利用交替求解的方式估计模糊核和清晰图像.模拟和真实数据上的实验表明本文算法能够准确估计模糊核,复原清晰的图像边缘,并具有很好的鲁棒性.     

处理异常值的相机抖动模糊图像复原

摘 要：目的：在曝光过程中由于相机抖动而导致的图像模糊,是一种常见的图像降质现象,并且模糊图像中存在的异常值会导致复原结果的振铃效应,为了解决这些问题,本文提出一种处理异常值的相机抖动模糊图像复原算法。方法：该算法以自然图像统计为先验模型,结合变分贝叶斯方法和KL散度构造易于优化的代价函数,进而求出模糊核。针对异常值造成的振铃效应,在解卷积的过程中采用期望-最大值算法估计并处理异常值以抑制振铃效应。结果：采用本文方法对大量模糊图片进行复原,实验结果表明该方法能有效地去除相机抖动产生的模糊,在保持图像边缘和细节的同时,可有效抑制振铃效应。结论：本文提出了一种通过处理异常值达到抑制振铃效应目的,进而提高复原效果的图像盲复原新方法。实验结果表明该方法切实有效,并且该方法引出了一种抑制振铃效应的新思路。     

Noncausal fractional directional differentiator and blind deconvoluation: motion blur estimation

The problem of blind estimation of motion blur parameters from a single image is addressed. The blur direction and extent of motion-blurred image, which are introduced by relative motion between a camera and its object scene, are needed in the methods of image restoration, such as blind deconvolution. As an extension to the fractional-order derivative, a noncausal fractional-order directional derivative operator is devised, which is robust to noise. Based on this new operator, a novel method identifying blur parameters is developed in this work. The performance comparison between the proposed method and the state-of-the-art method is also presented, demonstrating that the former provides better immunity to noise and capacity to identify motion blur extent, especially for large blur length.     

Blind Deblurring Based on L0Norm from Salient Edges简

Motion deblurring is a basic problem in the field of image processing and analysis. This paper proposes a new method of single image blind deblurring which can be significant to kernel estimation and non-blind deconvolution. Experiments show that the details of the image destroy the structure of the kernel, especially when the blur kernel is large. So we extract the image structure with salient edges by the method based on RTV. In addition, the traditional method for motion blur kernel estimation based on sparse priors is conducive to gain a sparse blur kernel. But these priors do not ensure the continuity of blur kernel and sometimes induce noisy estimated results. Therefore we propose the kernel refinement method based on L0 to overcome the above shortcomings. In terms of non-blind deconvolution we adopt the L1/L2 regularization term. Compared with the traditional method, the method based on L1/L2 norm has better adaptability to image structure, and the constructed energy functional can better describe the sharp image. For this model, an effective algorithm is presented based on alternating minimization algorithm.     

基于稀疏特性的盲二值图像去模糊

通过分析二值图像发现其像素值具有稀疏特性,因此采用L₀梯度反卷积算法结合二值图像的组合特性来处理盲二值图像的复原问题。常见的图像复原方法均将二值图像看作灰度值图像来处理,当其考虑到二值图像的特殊性质时,将会针对这种特定类型的图像得到更好的复原效果。提出的盲复原算法基于一阶梯度空间L₀最小化问题的框架,利用L₀梯度图像平滑方法来获得明显的图像边缘以估计模糊核,并将二值图像的特有属性作为正则项加入目标函数。在图像的复原过程中,通过二值图像先验来强制复原结果趋于二值图像。根据提出的模型,给出了基于稀疏特性的盲二值图像复原算法。通过实验将该算法与传统的盲反卷积复原算法进行比较,结果表明所提算法具有良好的性能,对二值图像进行复原是有效的。     

混合高阶全变差正则化的运动模糊图像盲复原

针对运动模糊图像的盲复原,提出一种基于混合高阶全变差正则化的盲复原方法。该方法首先采用shock滤波器从模糊图像中预测出清晰的图像边缘,并用多尺度策略实现对模糊核由粗到细的准确估计。然后根据自然图像边缘的稀疏特性,将全变差模型的保护边缘特性结合高阶全变差克服平滑区域阶梯效应的优势,对图像进行正则化约束,提出新的混合高阶全变差正则化模型。最后,利用分裂布雷格曼迭代策略对提出模型进行最优化求解。实验结果表明,提出的方法能够很好地保护图像边缘细节,同时有效地抑制平滑区域内振铃和阶梯效应的产生,获得高质量的复原图像。与近几年图像盲复原算法相比,不仅改进了复原图像的主观视觉效果,而且客观上提高了峰值信噪比。     

A variational Bayesian strategy for solving the DOA estimation problem in sparse array

This paper reformulates the problem of direction-of-arrival (DOA) estimation for sparse array from a variational Bayesian perspective. In this context, we propose a hierarchical prior for the signal coefficients that amounts marginally to a sparsity-inducing penalty in maximum a posterior (MAP) estimation. Further, the specific hierarchy gives rise to a variational inference technique which operates in latent variable space iteratively. Our hierarchical formulation of the prior allow users to model the sparsity of the unknown signal with a high degree, and the corresponding Bayesian algorithm leads to sparse estimators reflecting posterior information beyond the mode. We provide experimental results with synthetic signals and compare with state-of-the-art DOA estimation algorithm, in order to demonstrate the superior performance of the proposed approach.     

基于跨尺度低秩约束的图像盲解卷积算法EI北大核心CSCD

在模糊核未知的情况下对模糊图像进行复原称为盲解卷积问题,这是一个欠定逆问题,现有的大部分盲解卷积算法利用图像的各种先验知识约束问题的解空间.由于清晰图像的跨尺度自相似性强于模糊图像的跨尺度自相似性,且降采样模糊图像与清晰图像具有更强的相似性,本文提出了一种基于跨尺度低秩约束的单幅图像盲解卷积算法,利用图像跨尺度自相似性,在降采样图像中搜索相似图像块构成相似图像块组,从整体上对相似图像块组进行低秩约束,作为正则项加入到图像盲解卷积的目标函数中,迫使重建图像的边缘接近清晰图像的边缘.本文算法没有对噪声进行特殊处理,由于低秩约束更好地表示了数据的全局结构特性,因此避免了盲解卷积过程受噪声的干扰.在模糊图像和模糊有噪图像上的实验验证了本文的算法能够解决大尺寸模糊核的盲复原并对噪声具有良好的鲁棒性.     

可学习高阶微分方程的图像盲复原

目的 图像盲复原是图像处理中的常见的重要问题之一,具有巨大的研究价值和广泛的应用。通常情况下,相机抖动,聚焦不准,环境噪声等因素都会造成图像模糊。由于图像盲复原需要同时求解模糊核和清晰图像,导致该问题是病态的而难于求解。现有的盲复原方法可以分为两大类,一类是基于最大后验概率来同时估计潜在图像和模糊核的方法,但是这样耦合在一起的方法由于先验条件和初值设置不恰当,常常会导致最终求得的是问题的平凡解,以至于盲复原的效果并不理想。另一类是基于变分贝叶斯来估计模糊核,这种方法通常是采用最大化强边图像的边缘概率,由此估计的模糊核鲁棒性较强,但是对潜在图像的强边条件要求比较高,计算复杂度和实现难度都较大。鉴于以上方法的优缺点,提出基于高阶微分方程学习的方法来实现图像去模糊。方法 借鉴传统的迭代演化方法和网络学习方法各自的优势,将网络学习到的特征（引导图像,卷积滤波器,稀疏测度）融入到高阶微分方程的演化过程中区,提出可学习的基于高阶微分方程的演化来模拟图像的演化过程。具体地,先用范数约束得到一个粗略的强边引导图像,然后将学习到的卷积滤波器和稀疏函数一起作用在当前的潜在图像上,得到一个关于图像的更好的梯度下降方向,将此作为微分方程演化的一个步骤,得到一个更为精炼的强边图像。最后用精炼的强边图像来估计模糊核。该方法可以通过先验知识和训练数据来有效地控制模糊核的估计,进而得到较为清晰的盲复原结果。结果 在图像建模层面上,用非盲复原的方法验证了本文提出的微分方程演化过程是可行的。通过和其他盲复原方法做对比,在不同的基准图像数据库上的定量的实验中,本文方法在数据库上的峰值信噪比,结构相似度分别达到30.30,0.91,误差率低至1.24;比其他方法的结果都要好,在时间上,虽然我们的算法不是用时最少的,但是和性能相当的本文的方法相比,本文算法时间消耗远比该算法少。在各种不同类型的模糊图像去模糊结果也表明了本文方法是有效的。结论 本文可学习的高阶微分方程去模糊的方法,能够有效地估计模糊核,进而更好地恢复出清晰图像。实验结果表明本文方法在各种场景中具有较高的灵活性,都能自适应地对图像去模糊。     

Ultrasound image restoration based on a learned dictionary and a higher-order MRF

The restoration of images degraded by blur and multiplicative noise is a critical preprocessing step in medical ultrasound images which exhibit clinical diagnostic features of interest. This paper proposes a novel non-smooth non-convex variational model for ultrasound images denoising and deblurring motivated by the successes of sparse representation of images and FoE based approaches. Dictionaries are well adapted to textures and extended to arbitrary image sizes by defining a global image prior, while FoE image prior explicitly characterizes the statistics properties of natural image. Following these ideas, the new model is composed of the data-fidelity term, the sparse and redundant representations via learned dictionaries, and the FoE image prior model. The iPiano algorithm can efficiently deal with this optimization problem. The new proposed model is applied to several simulated images and real ultrasound images. The experimental results of denoising and deblurring show that proposed method gives a better visual effect by efficiently removing noise and preserving details well compared with two state-of-the-art methods.     

Nonlinear maximum likelihood estimation of electricity spot prices using recurrent neural networks

Electricity spot prices are complex processes characterized by nonlinearity and extreme volatility. Previous work on nonlinear modeling of electricity spot prices has shown encouraging results, and we build on this area by proposing an Expectation Maximization algorithm for maximum likelihood estimation of recurrent neural networks utilizing the Kalman filter and smoother. This involves inference of both parameters and hyper-parameters of the model which takes into account the model uncertainty and noise in the data. The Expectation Maximization algorithm uses a forward filtering and backward smoothing (Expectation) step, followed by a hyper-parameter estimation (Maximization) step. The model is validated across two data sets of different power exchanges. It is found that after learning a posteriori hyper-parameters, the proposed algorithm outperforms the real-time recurrent learning and the extended Kalman Filtering algorithm for recurrent networks, as well as other contemporary models that have been previously applied to the modeling of electricity spot prices.     

混合特性正则化约束的运动模糊盲复原

目的 为了提高运动模糊图像盲复原清晰度,提出一种混合特性正则化约束的运动模糊盲复原算法。方法 首先利用基于局部加权全变差的结构提取算法提取显著边缘,降低了噪声对边缘提取的影响。然后改进模糊核模型的平滑与保真正则项,在保证精确估计的同时,增强了模糊核的抗噪性能。最后改进梯度拟合策略,并加入保边正则项,使图像梯度更加符合重尾分布特性,且保证了边缘细节。结果 本文通过两组实验验证改进模型与所提算法的优越性。实验1以模拟运动模糊图像作为实验对象,通过对比分析5种组合步骤算法的复原效果,验证了本文改进模糊核模型与改进复原图像模型的鲁棒性较强。实验结果表明,本文改进模型复原图像的边缘细节更加清晰自然,评价指标明显提升。实验2以小型无人机真实运动模糊图像为实验对象,通过与传统算法进行对比,对比分析了所提算法的鲁棒性与实用性。实验结果表明,本文算法复原图像的标准差提升约11.4%,平均梯度提升约30.1%,信息熵提升约2.2%,且具有较好的主观视觉效果。结论 针对运动模糊图像盲复原,通过理论分析和实验验证,说明了本文改进模型的优越性,所提算法的复原效果较好。     

基于LMS自适应算法的图像去模糊研究

传统单幅图像去模糊方法需要稀疏先验约束,导致计算量较大。为此,在自适应最小均方误差(LMS)算法的基础上,提出一种点扩散函数(PSF)估计方法。利用模糊图像得到有效突出边缘,作为自适应滤波器的输入信号,并将模糊图像作为滤波器的期望信号,用以估计PSF。在非盲去卷积过程中,采用各项异性正规化方法对清晰图像进行约束,以减少恢复图像的振铃效应。实验结果表明,该方法不需要先验约束,对运动和非运动模糊图像均可适用,在保留图像细节的同时能抑制平滑区域的噪声。     

Improving probabilistic inference in graphical models with determinism and cycles

Many important real-world applications of machine learning, statistical physics, constraint programming and information theory can be formulated using graphical models that involve determinism and cycles. Accurate and efficient inference and training of such graphical models remains a key challenge. Markov logic networks (MLNs) have recently emerged as a popular framework for expressing a number of problems which exhibit these properties. While loopy belief propagation (LBP) can be an effective solution in some cases; unfortunately, when both determinism and cycles are present, LBP frequently fails to converge or converges to inaccurate results. As such, sampling based algorithms have been found to be more effective and are more popular for general inference tasks in MLNs. In this paper, we introduce Generalized arc-consistency Expectation Maximization Message-Passing (GEM-MP), a novel message-passing approach to inference in an extended factor graph that combines constraint programming techniques with variational methods. We focus our experiments on Markov logic and Ising models but the method is applicable to graphical models in general. In contrast to LBP, GEM-MP formulates the message-passing structure as steps of variational expectation maximization. Moreover, in the algorithm we leverage the local structures in the factor graph by using generalized arc consistency when performing a variational mean-field approximation. Thus each such update increases a lower bound on the model evidence. Our experiments on Ising grids, entity resolution and link prediction problems demonstrate the accuracy and convergence of GEM-MP over existing state-of-the-art inference algorithms such as MC-SAT, LBP, and Gibbs sampling, as well as convergent message passing algorithms such as the concave–convex procedure, residual BP, and the L2-convex method.     

A Hybrid Motion Deblurring Strategy Using Patch Based Edge Restoration and Bilateral Filter

Motion blur is a common problem in digital photography. In the dim light, a long exposure time is needed to acquire a satisfactory photograph, and if the camera shakes during exposure, a motion blur is captured. Image deblurring has become a crucial image-processing challenge, because of the increased popularity of handheld cameras. Traditional motion deblurring methods assume that the blur degradation is shift-invariant; therefore, the deblurring problem can be reduced to a deconvolution problem. Edge-specific motion deblurring sharpened the strong edges of the image and then used them to estimate the blur kernel. However, this also enhanced noise and narrow edges, which cause ambiguity and ringing artifacts. We propose a hybrid-based single image motion deblurring algorithm to solve these problems. First, we separated the blurred image into strong edge parts and smooth parts. We applied the improved patch-based sharpening method to enhance the strong edge for kernel estimation, but for the smooth part, we used the bilateral filter to remove the narrow edge and the noise for avoiding the generation of ringing artifacts. Experimental results show that the proposed method is efficient at deblurring for a variety of images and can produce images of a quality comparable to other state-of-the-art techniques.     

Estimating time-varying densities using a stochastic learning automaton

The popular Expectation Maximization technique suffers a major drawback when used to approximate a density function using a mixture of Gaussian components; that is the number of components has to be a priori specified. Also, Expectation Maximization by itself cannot estimate time-varying density functions. In this paper, a novel stochastic technique is introduced to overcome these two limitations. Kernel density estimation is used to obtain a discrete estimate of the true density of the given data. A Stochastic Learning Automaton is then used to select the number of mixture components that minimizes the distance between the density function estimated using the Expectation Maximization and discrete estimate of the density. The validity of the proposed approach is verified using synthetic and real univariate and bivariate observation data.     

基于模糊核估计的图像盲超分辨率神经网络

模糊图像的超分辨率重建具有挑战性并且有重要的实用价值. 为此, 提出一种基于模糊核估计的图像盲超分辨率神经网络(Blurred image blind super-resolution network via kernel estimation, BESRNet). 该网络主要包括两个部分: 模糊核估计网络 (Blur kernel estimation network, BKENet)和模糊核自适应的图像重建网络(Kernel adaptive super-resolution network, SRNet). 给定任意低分辨率图像(Low-resolution image, LR), 首先利用模糊核估计子网络从输入图像估计出实际的模糊核, 然后根据估计到的模糊核, 利用模糊核自适应的图像重建子网络完成输入图像的超分辨率重建. 与其他图像盲超分辨率方法不同, 所提出的模糊核估计网络能够显式地从输入低分辨率图像中估计出完整的模糊核, 然后模糊核自适应的图像重建网络根据估计到的模糊核, 动态地调整网络各层的图像特征, 从而适应不同输入图像的模糊. 在多个基准数据集上进行了有效性实验, 定性和定量的结果都表明该网络优于同类的图像盲超分辨率神经网络.