基于生成对抗网络的低秩图像生成方法

低秩纹理结构是图像处理领域中具有重要几何意义的结构,通过提取低秩纹理可以对受到各种变换干扰的图像进行有效校正.针对受到各种变换干扰的低秩图像校正问题,利用生成式框架来缓解图像中不具明显低秩特性区域的校正结果不理想的问题,提出了一种非监督式的由图像生成图像的低秩纹理生成对抗网络（Low-rank generative adversarial network,LR-GAN）算法.首先,该算法将传统的无监督学习的低秩纹理映射算法（Transform invariant low-rank textures,TILT）作为引导加入到网络中来辅助判别器,使网络整体达到无监督学习的效果,并且使低秩对抗对在生成网络和判别网络上都能够学习到结构化的低秩表示.其次,为了保证生成的图像既有较高的图像质量又有相对较低的秩,同时考虑到低秩约束条件下的优化问题不易解决（NP难问题）,在经过一定阶段TILT的引导后,设计并加入了低秩梯度滤波层来逼近网络的低秩最优解.通过在MNIST,SVHN和FG-NET这三个数据集上的实验,并使用分类算法评估生成的低秩图像质量,结果表明,本文提出的LR-GAN算法均取得了较好的生成质量与识别效果.     

High quality 3D reconstruction based on fusion of polarization imaging and binocular stereo vision

Polarization imaging can retrieve inaccurate objects’ 3D shapes with fine textures, whereas coarse but accurate depths can be provided by binocular stereo vision. To take full advantage of these two complementary techniques, we investigate a novel 3D reconstruction method based on the fusion of polarization imaging and binocular stereo vision for high quality 3D reconstruction. We first generate the polarization surface by correcting the azimuth angle errors on the basis of registered binocular depth, to solve the azimuthal ambiguity in the polarization imaging. Then we propose a joint 3D reconstruction model for depth fusion, including a data fitting term and a robust low-rank matrix factorization constraint. The former is to transfer textures from the polarization surface to the fused depth by assuming their relationship linear, whereas the latter is to utilize the low-frequency part of binocular depth to improve the accuracy of the fused depth considering the influences of missing-entries and outliers. To solve the optimization problem in the proposed model, we adopt an efficient solution based on the alternating direction method of multipliers. Extensive experiments have been conducted to demonstrate the efficiency of the proposed method in comparison with state-of-the-art methods and to exhibit its wide application prospects in 3D reconstruction.     

低秩分块矩阵的核近似

为了探讨结构受限下的矩阵分解问题,通过最小化块外对角线来增强类与类之间数据表示的不相关性,从而实现分块约束,即数据来源于不同的聚类结构,是一种局部结构的约束;同时通过增强样本的自表达属性并缩小样本之间的差距来增强类内数据表示的相关性,从而实现低秩约束,即数据行出现冗余,是一种全局结构的约束。随后设计了一个低秩分块矩阵的核近似算法,通过交替方向乘子法迭代求解。最后将该方法分别在人脸识别和字符识别上进行测试。实验结果表明,所提出的低秩分块矩阵分解算法在收敛速度和近似精度上都具有一定的优势。     

Texture Repairing by Unified Low Rank Optimization

In this paper, we show how to harness both low-rank and sparse structures in regular or near-regular textures for image completion. Our method is based on a unified formulation for both random and contiguous corruption. In addition to the low rank property of texture, the algorithm also uses the sparse assumption of the natural image: because the natural image is piecewise smooth, it is sparse in certain transformed domain (such as Fourier or wavelet transform). We combine low-rank and sparsity properties of the texture image together in the proposed algorithm. Our algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. This algorithm integrates texture rectification and repairing into one optimization problem. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Our method demonstrates significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.     

基于模板校正与低秩分解的纺织品瑕疵检测方法

针对周期性纺织品存在的拉伸变形问题,提出结合模板校正与低秩分解的纺织品瑕疵检测方法.首先对原图像进行模板校正,减少图像拉伸变形对检测结果的影响.然后提出低秩校正分解模型,包含低秩项、稀疏项和校正项,通过交替方向法优化求解,生成低秩矩阵和稀疏矩阵.最后利用最优阈值分割算法,分割由稀疏矩阵产生的显著图,完成瑕疵检测.在标准数据库上的实验表明,文中方法的查全率有所提高.     

An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.     

基于低秩约束的熵加权多视角模糊聚类算法EI北大核心CSCD

如何有效挖掘多视角数据内部的一致性以及差异性是构建多视角模糊聚类算法的两个重要问题.本文在Co-FKM算法框架上,提出了基于低秩约束的熵加权多视角模糊聚类算法(Entropy-weighting multi-view fuzzy C-means with low rank constraint,LR-MVEWFCM).一方面,从视角之间的一致性出发,引入核范数对多个视角之间的模糊隶属度矩阵进行低秩约束;另一方面,基于香农熵理论引入视角权重自适应调整策略,使算法根据各视角的重要程度来处理视角间的差异性.本文使用交替方向乘子法(Alternating direction method of multipliers,ADMM)进行目标函数的优化.最后,人工模拟数据集和UCI(University of California Irvine)数据集上进行的实验结果验证了该方法的有效性.     

双重字典学习与自适应PCNN相结合的医学图像融合

目的 针对基于稀疏编码的医学图像融合方法存在的细节保存能力不足的问题,提出了一种基于卷积稀疏表示双重字典学习与自适应脉冲耦合神经网络（PCNN）的多模态医学图像融合方法。方法 首先通过已配准的训练图像去学习卷积稀疏与卷积低秩子字典,在两个字典下使用交替方向乘子法（ADMM）求得其卷积稀疏表示系数与卷积低秩表示系数,通过与对应的字典重构得到卷积稀疏与卷积低秩分量;然后利用改进的的拉普拉斯能量和（NSML）以及空间频率和（NMSF）去激励PCNN分别对卷积稀疏与卷积低秩分量进行融合;最后将融合后的卷积稀疏与卷积低秩分量进行组合得到最终的融合图像。结果 对灰度图像与彩色图像进行实验仿真并与其他融合方法进行比较,实验结果表明,所提出的融合方法在客观评估和视觉质量方面明显优于对比的6种方法,在4种指标上都有最优的表现;与6种多模态图像融合方法相比,3组实验平均标准差分别提高了7%、10%、5.2%;平均互信息分别提高了33.4%、10.9%、11.3%;平均空间频率分别提高了8.2%、9.6%、5.6%;平均边缘评价因子分别提高了16.9%、20.7%、21.6%。结论 与其他稀疏表示方法相比,有效提高了多模态医学图像融合的质量,更好地保留了源图像的细节信息,使融合图像的信息更加丰富,符合人眼的视觉特性,有效地辅助医生进行疾病诊断。     

Learning low-rank and discriminative dictionary for image classification

Dictionary learning plays a crucial role in sparse representation based image classification. In this paper, we propose a novel approach to learn a discriminative dictionary with low-rank regularization on the dictionary. Specifically, we apply Fisher discriminant function to the coding coefficients to make the dictionary more discerning, that is, a small ratio of the within-class scatter to between-class scatter. In practice, noisy information in the training samples will undermine the discriminative ability of the dictionary. Inspired by the recent advances in low-rank matrix recovery theory, we apply low-rank regularization on the dictionary to tackle this problem. The iterative projection method (IPM) and inexact augmented Lagrange multiplier (ALM) algorithm are adopted to solve our objective function. The proposed discriminative dictionary learning with low-rank regularization (D²L²R²) approach is evaluated on four face and digit image datasets in comparison with existing representative dictionary learning and classification algorithms. The experimental results demonstrate the superiority of our approach.     

An augmented Lagrangian relaxation for analytical target cascading using the alternating direction method of multipliers

Analytical target cascading is a method for design optimization of hierarchical, multilevel systems. A quadratic penalty relaxation of the system consistency constraints is used to ensure subproblem feasibility. A typical nested solution strategy consists of inner and outer loops. In the inner loop, the coupled subproblems are solved iteratively with fixed penalty weights. After convergence of the inner loop, the outer loop updates the penalty weights. The article presents an augmented Lagrangian relaxation that reduces the computational cost associated with ill-conditioning of subproblems in the inner loop. The alternating direction method of multipliers is used to update penalty parameters after a single inner loop iteration, so that subproblems need to be solved only once. Experiments with four examples show that computational costs are decreased by orders of magnitude ranging between 10 and 1000.     

A robust DOA estimator based on the correntropy in alpha-stable noise environments

By introducing correntropy as the robust statistics, a novel direction of arrival estimator for α-stable noise is proposed. In this method, the signal subspace is estimated by solving the correntropy based optimization problem under the maximum correntropy criterion. An optimal step size based iterative algorithm is developed and the convergence of it is proved. Comprehensive simulation results demonstrate that the proposed method is superior to several existing algorithms in terms of the probability of resolution and the estimation accuracy, especially in the highly impulsive noise environments.     

隐式低秩稀疏表示的多视角子空间聚类

针对多视角子空间聚类问题,提出基于隐式低秩稀疏表示的多视角子空间聚类算法(LLSMSC).算法构建多个视角共享的隐式结构,挖掘多视角之间的互补性信息.通过对隐式子空间的表示施加低秩约束和稀疏约束,捕获数据的局部结构和稀疏结构,使聚类结果更准确.同时,使用基于增广拉格朗日乘子交替方向最小化算法高效求解优化问题.在6个不同数据集上的实验验证LLSMSC的有效性和优越性.     

Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in Frick et al. (Electron. J. Stat. 6:231–268, 2012). It constitutes a variational regularization technique that uses an ? _∞-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra’s projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy.     

Low-rank image completion with entropy features

In this paper, we propose a novel method to complete the images or textures with the property of low rank. Our method leverages saliency detection with two entropy features to estimate initial corrupted regions. Then an iterative optimization model for low-rank and sparse errors recovery is designed to complete the corrupted images. Our iterative model can improve the initial corrupted regions and generate accurate and continuous corrupted regions via fully connected CRFs. By introducing a F-norm term in our model to absorb small noise, we can generate completed images which are more precise and have lower rank. Experiments indicate that our method introduces less local distortions than example-based methods for images with regular structures. It is also superior to the previous low-rank image completion method especially when the images contain low-rank corrupted regions. Furthermore, we show that the entropy features benefit the existing saliency detection methods too.     

A sharp augmented Lagrangian-based method in constrained non-convex optimization

In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.     

Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

An unconditionally stable alternating direction implicit (ADI) method of higher-order in space is proposed for solving two- and three-dimensional linear hyperbolic equations. The method is fourth-order in space and second-order in time. The solution procedure consists of a multiple use of one-dimensional matrix solver which produces a computational cost effective solver. Numerical experiments are conducted to compare the new scheme with the existing scheme based on second-order spatial discretization. The effectiveness of the new scheme is exhibited from the numerical results.     

基于超图正则化的域适应偏最小二乘多工况软测量模型

针对流程工业中, 因多工况导致数据分布变化引起传统软测量模型预测性能恶化问题, 本文提出一种基于 超图正则化的域适应多工况软测量回归模型框架. 首先, 采用非线性迭代偏最小二乘回归算法为基模型, 在潜变量 空间利用历史工况数据重构当前工况数据, 以增强工况间的相关性, 有效减小数据分布差异; 同时, 对重构系数施加 低秩稀疏约束, 保留了数据的局部和全局子空间结构; 其次, 通过超图拉普拉斯正则项对域适应潜变量求解过程进 行约束, 避免在寻找潜变量过程中破坏数据结构. 最后, 利用交替方向乘子法优化求解模型参数. 在多个数据集上 的实验表明, 本文方法在多工况环境下可有效提高软测量模型的预测精度和泛化性能.     

Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization

The matrix separation problem aims to separate a low-rank matrix and a sparse matrix from their sum. This problem has recently attracted considerable research attention due to its wide range of potential applications. Nuclear-norm minimization models have been proposed for matrix separation and proved to yield exact separations under suitable conditions. These models, however, typically require the calculation of a full or partial singular value decomposition at every iteration that can become increasingly costly as matrix dimensions and rank grow. To improve scalability, in this paper, we propose and investigate an alternative approach based on solving a non-convex, low-rank factorization model by an augmented Lagrangian alternating direction method. Numerical studies indicate that the effectiveness of the proposed model is limited to problems where the sparse matrix does not dominate the low-rank one in magnitude, though this limitation can be alleviated by certain data pre-processing techniques. On the other hand, extensive numerical results show that, within its applicability range, the proposed method in general has a much faster solution speed than nuclear-norm minimization algorithms and often provides better recoverability.     

基于交替方向乘子法的电力系统完全分布式动态经济调度方法

本文基于交替方向乘子法(alternating direction multiplier method,ADMM)提出了一种完全分布式的跨区域电力系统动态经济调度方法.其中的经济调度模型以整个系统的运行成本最小为目标,并满足各种系统运行约束.为了实现模型的分布式求解,本文利用交替方向乘子法将各区域之间的联系解耦,将整个系统的大型优化问题分解为各个区域内部的子优化问题,通过迭代求解每个区域的子问题即可得到整个系统的最优解.进一步地,本文算法取消了负责乘子更新的数据中心,实现了完全分布式的调度策略.同时,为了兼顾电力系统中时间断面之间的紧密联系,本文的经济调度模型采用了多时段优化方法.最后,本文对基于IEEE标准测试系统的3区域互联系统算例进行了分析,验证了本文的调度策略的有效性.     

基于局部和非局部正则化的图像压缩感知

基于低秩正则化的非局部低秩约束(Nonlocal low-rank regularization, NLR)算法利用相似块的结构稀疏性,获得了目前最好的重构结果。但是它仅仅利用了图像的非局部信息,忽略了图像像素间的局部信息,不能有 效地重建图像的边缘,同时Logdet函数不能很好地替代矩阵秩,因为它跟真实解之间存在着不可忽视的差距。因此,本文提出了一种基于局部和非局部正则化的压缩感知图像重建方法,同时考虑图像的非局部低秩性和图像像素的局部稀疏梯度性。选择利用Schatten-p 范数来替代矩阵秩,同时选择交替方向乘子算法求解产生的非凸优化问题。实验 结果表明,与传统的稀疏性先验重建算法和NLR算法相比,本文算法能够获得更高的图像重构质量。