Weighted Nuclear Norm Minimization-Based Regularization Method for Image Restoration

Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.

Parameter Optimization of Regularization Variational Merging and Its Application in GNSS/MET Water Vapor

The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regularization parameter. Classical 3 D/4 D variational merging is based on the theory that error follows Gaussian distribution. It involves the solution of the objective functional gradient in minimization iteration,which requires the data to have continuity and differentiability. Classic 3 D/4 D-dimensional variational merging method was extended,and L1 norm was used as the constraint coupling to the classical variational merged model. Experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model,and parameter optimization of this method is discussed. Considering the strong temporal and spatial variation of water vapor,this method is further applied to the precipitable water vapor( PWV) merging by calculating reanalysis data and GNSS retrieval.Parameters were adjusted gradually to analyze the influence of background field on the merging result,and the experiment results show that the mathematical algorithm adopted in this paper is feasible.

Regularised Layerwise Weight Norm Based Skin Lesion Features Extraction and Classification

Melanoma is the most lethal malignant tumour,and its prevalence is increasing.Early detection and diagnosis of skin cancer can alert patients to manage precautions and dramatically improve the lives of people.Recently,deep learning has grown increasingly popular in the extraction and categorization of skin cancer features for effective prediction.A deep learning model learns and co-adapts representations and features from training data to the point where it fails to perform well on test data.As a result,overfitting and poor performance occur.To deal with this issue,we proposed a novel Consecutive Layerwise weight Con-straint MaxNorm model(CLCM-net)for constraining the norm of the weight vector that is scaled each time and bounding to a limit.This method uses deep convolutional neural networks and also custom layer-wise weight constraints that are set to the whole weight matrix directly to learn features efficiently.In this research,a detailed analysis of these weight norms is performed on two distinct datasets,International Skin Imaging Collaboration(ISIC)of 2018 and 2019,which are challenging for convolutional networks to handle.According to thefindings of this work,CLCM-net did a better job of raising the model’s performance by learning the features efficiently within the size limit of weights with appropriate weight constraint settings.The results proved that the proposed techniques achieved 94.42%accuracy on ISIC 2018,91.73%accuracy on ISIC 2019 datasets and 93%of accuracy on combined dataset.

THE PRODUCT OPERATOR BETWEEN BLOCH-TYPE SPACES OF SLICE REGULAR FUNCTIONS

There is little work concerning the properties of quaternionic operators acting on slice regular function spaces defined on quaternions.In this paper,we present an equivalent characterization for the boundedness of the product operator C_(φ)D^(m) acting on Bloch-type spaces of slice regular functions.After that,an equivalent estimation for its essential norm is established,which can imply several existing results on holomorphic spaces.

Two-dimensional NMR inversion based on fast norm smoothing method

Two-dimensional(2D)nuclear magnetic resonance(NMR)inversion operates with massive echo train data and is an ill-posed problem.It is very important to select a suitable inversion method for the 2D NMR data processing.In this study,we propose a fast,robust,and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters.Firstly,a method that combines window averaging(WA)and singular value decomposition(SVD)is used to compress the echo train data and obtain the singular values of the kernel matrix.Subsequently,an optimum regularization parameter in a fast manner using the signal-to-noise ratio(SNR)of the echo train data and the maximum singular value of the kernel matrix are determined.Finally,we use the Butler-Reeds-Dawson(BRD)method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion.The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.

一种求解低秩矩阵补全的修正加速近端梯度算法

设计适应大规模数据的快速算法是求解低秩矩阵补全的重点。文章改变了加速近端梯度算法的步长,对近似函数的近端最优点和上一迭代点增加了一个仿射组合。通过控制仿射系数,能够使得到的新迭代点有靠近原函数的趋势,进而能在保持算法精度的同时提高算法效率。最后通过相应的数值实验证明了算法的有效性和稳定性。

利用冗余扩展余弦字典的复杂动载荷识别研究

针对真实测量噪声影响下复杂动载荷识别精度低的问题,提出了一种基于冗余扩展余弦字典的L1范数正则化载荷识别方法。根据系统响应与外部动载荷的卷积关系,建立用于载荷识别的离散系统控制方程;选择与动载荷相适应的离散余弦基函数进行时延扩展,构造了扩展余弦字典与Db10小波字典相级联的冗余扩展字典,对复杂载荷进行稀疏表示;使用L1范数正则化方法求解稀疏表示系数,基于改进L曲线准则获取最优正则化参数,通过在GARTEUR飞机模型上试验得到的响应数据,实现不同噪声水平下对拍频载荷与连续冲击载荷时间历程的识别。试验研究结果表明:本文提出的冗余扩展余弦字典对拍频载荷与连续冲击载荷的表示稀疏性高,基于冗余扩展余弦字典的L1范数正则化载荷识别方法的识别精度高、抗噪性能好。

基于有约束L_(1/2)范数稀疏正则化的声源识别方法

基于等效源法(equivalent source method,ESM)的近场声全息(near field acoustic holography,NAH)是一种有效的声源识别技术。然而,针对空间稀疏分布的声源识别问题,传统基于L_(2)范数以及基于L_(1)范数的ESM方法分别存在声源幅值被低估与算法稳定性差等问题。因此,提出了基于有约束L_(1/2)范数稀疏正则化的声源识别方法,该方法具有强稀疏性与强抗干扰的优势,可以解决传统方法的声源识别精度低的问题。通过数值模拟试验以及普通室内的实测实验,验证了方法的有效性。

光谱变化中基于Schatten-0范数正则化的高光谱和多光谱图像融合

高光谱和多光谱图像融合旨在获取同时具有高空间分辨率和高光谱分辨率的高质量图像。然而,针对光谱变化中的高光谱和多光谱图像融合问题,全变分正则化方法仅仅是在空间梯度域对图像局部特性信息进行建模,没有考虑高光谱图像光谱信息间的高阶相关性。针对上述问题,通过引入Schatten-0正则项,实现对光谱信息高阶相关性的建模,提出基于Schatten-0范数正则化的高光谱和多光谱图像融合方法。采用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解光谱变化中的融合问题。其中,Schatten-0正则项对应的子问题采用硬阈值迭代收缩算法求解。仿真实验验证了所提方法的可行性和有效性。可为更具有实际价值、更一般化的高光谱和多光谱图像融合应用提供理论与技术支撑。

基于联合仿真的飞机着陆机场跑道桥动载特性研究

为研究飞机着陆滑跑过程中冲击作用对机场桥梁动力响应的影响,以某拟供C类飞机使用的跑道桥为研究对象,以Boeing 737-800机型为例,首次基于有限元软件与多体动力学软件相结合的联合仿真技术建立了机-桥耦合模型,精细化模拟了飞机以不同的着陆姿态在桥梁上着陆滑跑的全过程。在验证机-桥耦合模型准确性的基础上,系统讨论了飞机着陆质量、下沉速度、俯仰角及滚转角等参数对桥梁动力响应的影响程度、影响规律,并明确了桥梁动力系数的分布范围。研究结果表明:飞机着陆冲击作用下,桥梁动力系数的主要分布区间为1.26~1.62;桥梁动力系数随着陆质量、下沉速度、滚转角增大而增大,随接地速度、俯仰角增大而减小;飞机下沉速度的影响最为显著,当下沉速度从1.00 m/s增大到3.05 m/s时,动力系数从0.98增大到1.87,增幅高达90%。跑道桥的设计需合理考虑飞机着陆滑跑过程的动载作用。

基于局部归一化互信息联合约束的三维头颈部CT/MR配准方法

针对头颈部图像的复杂解剖结构和不同模态图像的差异,提出一种改进的多模态配准方法。该方法采用局部归一化互信息作为相似性测度,以捕捉局部图像区域的相似性,并减少不同区域间的强度差异对配准结果的影响。此外,为解决MR图像易受到噪声和伪影的影响产生畸变的问题,引入F范数约束配准过程,抑制不必要的畸变。实验结果表明,所提方法在降低均方误差、提高配准精度和鲁棒性方面均有所提高。

基于正则化的胎心监护图智能分类算法研究

目的:基于凸优化理论探讨智能评估胎儿在子宫中健康状态的方法,快速准确评估胎儿在宫内的健康状态。方法:在详细描述胎心监护数据参数含义的基础上,阐述基于数据的核范数正则化评估方法;采用波尔图大学公开的真实数据集,在Matlab软件环境下实施算法流程,计算该方法用于胎儿健康状态分类的准确性。结果:基于正则化的胎心监护图智能分类算法优化了数据量过小所导致的过拟合问题,准确率最高达92.14%,高于逻辑回归模型、卷积神经网络方法、RF+GBDT+AdaBoost+XGBoost融合模型以及最小二乘支持向量机的算法准确率。结论:本算法可以辅助临床医师对胎儿状态进行智能评估,提高临床决策的准确性。

Fusion of Ground-Based and Spaceborne Radar Precipitation Based on Spatial Domain Regularization

High-quality and accurate precipitation estimations can be obtained by integrating precipitation information measures using ground-based and spaceborne radars in the same target area.Estimating the true precipitation state is a typical inverse problem for a given set of noisy radar precipitation observations.The regularization method can appropriately constrain the inverse problem to obtain a unique and stable solution.For different types of precipitation with different prior distributions,the L_(1) and L_(2) norms were more effective in constraining stratiform and convective precipitation,respectively.As a combination of L_(1) and L_(2) norms,the Huber norm is more suitable for mixed precipitation types.This study uses different regularization norms to combine precipitation data from the C-band dual-polarization ground radar(CDP)and dual-frequency precipitation radar(DPR)on the Global Precipitation Measurement(GPM)mission core satellite.Compared to single-source radar data,the fused figures contain more information and present a comprehensive precipitation structure encompassing the reflectivity and precipitation fields.In 27 precipitation cases,the fusion results utilizing the Huber norm achieved a structural similarity index measure(SSIM)and a peak signal-to-noise ratio(PSNR)of 0.8378 and 30.9322,respectively,compared with the CDP data.The fusion results showed that the Huber norm effectively amalgamate the features of convective and stratiform precipitation,with a reduction in the mean absolute error(MAE;16.1%and 22.6%,respectively)and root-mean-square error(RMSE;11.7%and 13.6%,respectively)compared to the 1-norm and 2-norm.Moreover,in contrast to the fusion results of scale recursive estimation(SRE),the Huber norm exhibits superior capability in capturing the localized precipitation intensity and reconstructing the detailed features of precipitation.

A fast and adaptive method for complex-valued SAR image denoising based on l_k norm regularization

This paper developed a fast and adaptive method for SAR complex image denoising based on lk norm regularization, as viewed from parameters estimation. We firstly establish the relationship between denoising model and ill-posed inverse problem via convex half-quadratic regularization, and compare the difference between the estimator variance obtained from the iterative formula and biased CramerRao bound, which proves the theoretic flaw of the existent methods of parameter selection. Then, the analytic expression of the model solution as the function with respect to the regularization parameter is obtained. On this basis, we study the method for selecting the regularization parameter through minimizing mean-square error of estimators and obtain the final analytic expression, which resulted in the direct calculation, high processing speed, and adaptability. Finally, the effect of regularization parameter selection on the resolution of point targets is analyzed. The experiment results of simulation and real complex-valued SAR images illustrate the validity of the proposed method.

基于正则化与范数归一化的概率损伤识别方法

提出基于正则化与范数归一化的概率损伤识别方法(Regularization and Norm Normalization Based Probabilistic Damage Identification Method,RNbPDI),对不适定性和不确定性条件下的结构损伤识别误差进行量化。以结构损伤前后的模态信息差为目标函数,引入正则化方法,建立结构损伤参数求解的目标函数。考虑到不同模态参数对损伤参数的灵敏度数值范围的差异,将不同模态参数的灵敏度矩阵和残差矩阵分别进行范数归一化处理,以提高损伤识别问题求解的数值稳定性。利用概率方法来量化损伤识别结果的不确定性,给出损伤参数的识别结果的名义值和方差求解公式。通过数值算例分析不同损伤工况、不同传感器测点方案、不同的测试噪声水平对损伤识别结果的影响,通过数值算例和一个四层剪切框架实验表明该方法具有识别精度高、鲁棒性强的特点。

用于人脸情感识别的低冗余稀疏性集成剪枝

为降低噪声和异常值对集成剪枝的影响,并鲁棒性地选择更稀疏的基分类器子集,从而提升人脸情感识别的性能,提出了一种具有依赖分数的鲁棒性稀疏低冗余集成剪枝方法用于人脸情感识别。首先,该方法将样本实例的预测结果视为基分类器特征,分别利用互信息和熵来评估成对基分类器之间的依赖性和它们之间的优先级。其次,将优先级依赖关系添加到基于回归的目标方程中实现冗余基分类器的修剪,此目标方程使用l_(2,1)范数来增加分类器子集的鲁棒性从而提升算法的泛化性能。然后,将内积正则化项引入到目标方程中,通过计算分类器特征系数向量内积的绝对值的和去选择稀疏和低冗余的基分类器。最后,使用大多数投票法对选择的基分类器子集进行集成从而得到最终的识别结果。结果表明:本文提出的方法在FER2013、JAFFE、CK+和KDEF 4个公共人脸情感数据集上的识别准确率,比所有基分类器进行集成得到的准确率分别高3.29%、10.39%、1.76%和4.89%,表明该方法可以选择出识别效果更好、冗余度更低的分类器子集,提高集成剪枝的泛化能力。

基于卷积神经网络的正则化方法

正则化方法是逆问题求解中经常使用的方法.准确的正则化模型在逆问题求解中具有重要作用.对于不同类型的图像和图像的不同区域,正则化方法的能量约束形式应当不同,但传统的L1,L2正则化方法均基于单一先验假设,对所有图像使用同一能量约束形式.针对传统正则化模型中单一先验假设的缺陷,提出了基于卷积神经网络的正则化方法,并将其应用于图像复原问题.该方法的创新之处在于将图像复原看作一个分类问题,利用卷积神经网络对图像子块的特征进行提取和分类,然后针对不同特征区域采用不同的先验形式进行正则化约束,使正则化方法不再局限于单一的先验假设.实验表明基于卷积神经网络的正则化方法的图像复原结果优于传统的单一先验假设模型.

基于l_k范数正则化方法的SAR图像超分辨

提高合成孔径雷达(SAR)图像的分辨率对自动目标识别等具有重要意义。为此改进了一种基于lk范数正则化方法,并用于SAR图像超分辨。该方法通过合理开发利用符合SAR成像工程背景的先验知识,构造附加约束,把图像超分辨问题规划为形式简单的带约束优化问题。仿真和实测数据计算结果证实了该方法的有效性。

线性最小二乘问题解法的理论分析

线性最小二乘问题的解法在数据拟合、测量平差、控制理论等方面均得到广泛的应用。针对复矩阵和酉空间这种最一般的情形,证明了线性最小二乘解的存在性,给出了线性最小二乘解的一般表示式和极小范数最小二乘解。另外还对正则化方程组的条件数进行了论证。许多结论与Euclid空间情况相近。