结合总变差和组稀疏性的压缩感知重构方法

为了提高图像重建的质量,基于压缩感知理论,提出了一种基于总变差和组稀疏性的图像重建方法,同时考虑图像像素灰度值的梯度稀疏性和重叠图像块的非局部相似性两种先验知识。为了准确挖掘先验知识,本文选择非凸lp范数描述,并利用交替方向乘子法求解产生的重构模型。实验结果表明,与当前主流的重建算法相比,所提算法能够获得更高的图像重构结果。

基于重叠组稀疏超拉普拉斯正则化的高光谱图像恢复

高光谱图像混合噪声去除是遥感领域的一个基本问题,也是一个重要的预处理步骤。本研究针对高光谱图像去噪问题,为有效地对高光谱图像进行恢复,提出了一种基于重叠组稀疏性超拉普拉斯正则化(OGS-HL)的新型去噪方法。该方法可以有效捕捉图像的局部相关性和方向性结构,同时减少传统全变分正则化中的阶梯伪影。通过乘子交替方向法求解非凸优化问题,显著提高了去噪效率。在多个遥感图像数据集上的仿真实验表明,所提方法在峰值信噪比(PSNR)和结构相似度(SSIM)等评价指标上优于现有技术,展现了在复杂噪声环境下的优越去噪性能和广泛的应用潜力。The removal of mixed noise from hyperspectral images is a fundamental issue in the field of remote sensing and an important preprocessing step. This study focuses on the denoising problem of hyperspectral images. To effectively restore hyperspectral images, a new denoising method based on Overlap Group Sparse Hyper Laplacian Regularization (OGS-HL) is proposed. This method can effectively capture the local correlation and directional structure of images, while reducing the step artifacts in traditional total variation regularization. By using the alternating direction method of multipliers to solve non-convex optimization problems, the denoising efficiency has been significantly improved. Simulation experiments on multiple remote sensing image datasets have shown that the proposed method outperforms existing technologies in evaluation metrics such as peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), demonstrating superior denoising performance and broad application potential in complex noisy environments.

组稀疏模型及其算法综述

稀疏性与组稀疏性在统计学、信号处理和机器学习等领域中具有重要的应用.本文总结和分析了不同组稀疏模型之间的区别与联系,比较了不同组稀疏模型的变量选择能力、变量组选择能力、变量选择一致性和变量组选择一致性,总结了组稀疏模型的各类求解算法并指出了各算法的优点和不足.最后,本文对组稀疏模型未来的研究方向进行了探讨.

基于Adaptive Group LASSO的CVaR高维组合投资模型

传统的CVaR条件风险价值组合投资模型能够很好的度量市场风险，但是容易在决策的过程中产生极端的投资权重，对CVaR模型增加一般范数约束后可以解决极端投资权重的问题，但却忽略了金融市场上常见的板块联动效应。基于上述原因，文章在传统的CVaR模型的基础上，施加Adaptive Group LASSO惩罚，构建了一种基于Adaptive Group LASSO的CVaR高维组合投资模型，通过Adaptive Group LASSO分位数回归求解算法，实现了在消除极端投资头寸的同时达到金融资产组水平上变量稀疏化的目的。最后，蒙特卡洛模拟与实证研究均发现，与传统的CVaR组合投资模型以及带有LAS—SO约束的CVaR组合投资模型相比，基于Adaptive Group LASSO的CVaR模型能够更好的考虑板块联动效应，并在行业组水平上选择相应的金融资产。

基于OGS-HL的遥感图像混合噪声去除算法

遥感图像在成像过程中容易受到混合噪声污染,包括高斯噪声、条纹噪声和脉冲噪声等。这些混合噪声降低了遥感图像的质量,限制了其后续应用。为了解决这一问题,首先,通过对遥感图像的梯度值进行统计分析,发现遥感图像的空间梯度值是符合重尾分布,因此,设计了关于遥感图像空间梯度值的OGS-HL正则项来去除混合噪声模型,该正则项不仅可以减少全变分带来的阶梯效应,而且还可以对图像的梯度值进行合理的稀疏表示;其次,针对条纹噪声,考虑其具有低秩性且使用核范数来约束,而稀疏噪声则具有全局稀疏分布,并且采用L1范数来约束;最后,采用交替方向乘子法和Majorization-Minimization算法来求解所提出的模型。通过与现有的算法进行比较,结果表明我们提出的算法在去除高水平混合噪声方面具有良好的效果。

一种基于组稀疏结构的高分辨调制谱重构方法

螺旋桨节拍对水声目标宽带辐射噪声具有明显的幅度调制,其调制频率与螺旋桨的转速紧密相关,因而调制谱特征对水声目标分类和识别具有重要意义.本文针对传统的基于Fourier变换调制谱存在的缺点,提出一种基于子频带组稀疏结构的高分辨调制谱重构新方法.一方面,利用调制谱稀疏性特点,将稀疏调制谱的估计问题转化成逆Fourier基上的频率系数求解问题;另一方面,利用在分频技术中不同子频带间其稀疏调制线谱成组出现的特点,给出了组稀疏结构的调制谱重构方法.与传统的基于Fourier变换的调制谱不同,该稀疏调制谱会自动学习出线谱特征信息,有效地避免了在传统调制谱检测中的门限参数设计问题以及特征提取中人为因素.另外,本文提出的调制谱重构方法是非参数化的,可以自动学习出调制谱的稀疏度.

The Pre-processing Parallel Algorithm of A Sparse Linear Equation Group

The solution of linear equation group can be applied to the oil exploration, the structure vibration analysis, the computational fluid dynamics, and other fields. When we make the in-depth analysis of some large or very large complicated structures, we must use the parallel algorithm with the aid of high-performance computers to solve complex problems. This paper introduces the implementation process having the parallel with sparse linear equations from the perspective of sparse linear equation group.

Updating preconditioner for iterative method in time domain simulation of power systems

The numerical solution of the differential-algebraic equations(DAEs) involved in time domain simulation(TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems.The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems.The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS.As an improvement of dishonest preconditioner(DP) strategy,updating preconditioner strategy(UP) is introduced to the field of TDS for the first time.The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices.In order to make the linear system sequence in TDS suitable for UP strategy,a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating.The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China.Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%-61% the iteration count of the GMRES when compared with the DP method in all test cases.Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.

Implementation of the moving particle semi-implicit method on GPU

The Moving Particle Semi-implicit (MPS) method performs well in simulating violent free surface flow and hence becomes popular in the area of fluid flow simulation. However, the implementations of searching neighbouring particles and solving the large sparse matrix equations (Poisson-type equation) are very time-consuming. In order to utilize the tremendous power of parallel computation of Graphics Processing Units (GPU), this study has developed a GPU-based MPS model employing the Compute Unified Device Architecture (CUDA) on NVIDIA GTX 280. The efficient neighbourhood particle searching is done through an indirect method and the Poisson-type pressure equation is solved by the Bi-Conjugate Gradient (BiCG) method. Four different optimization levels for the present general parallel GPU-based MPS model are demonstrated. In addition, the elaborate optimization of GPU code is also discussed. A benchmark problem of dam-breaking flow is simulated using both codes of the present GPU-based MPS and the original CPU-based MPS. The comparisons between them show that the GPU-based MPS model outperforms 26 times the traditional CPU model.

Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.