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Coherence and entanglement dynamics in Shor’s algorithm 认领 引用
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作者 Linlin Ye Zhaoqi Wu Shao-Ming Fei 《Communications in Theoretical Physics》 SCIE CAS CSCD 2026年第1期61-70,共10页
Shor’s algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor’s algorithm, showing that the coherence i... Shor’s algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor’s algorithm, showing that the coherence in each step relies on the dimension of register or the order, and discuss the relations between geometric coherence and geometric entanglement. We investigate how unitary operators induce variations in coherence and entanglement, and analyze the variations of coherence and entanglement within the entire algorithm, demonstrating that the overall effect of Shor’s algorithm tends to deplete coherence and produce entanglement. Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms. 展开更多
关键词 Shor's algorithm Tsallis relativeαentropy of coherence l1 p norm of coherence geometric coherence geometric entanglement
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Efficient Concurrent L1-Minimization Solvers on GPUs 认领 引用 被引量：1
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作者 Xinyue Chu Jiaquan Gao Bo Sheng 《Computer Systems Science & Engineering》 SCIE EI 2021年第9期305-320,共16页
Given that the concurrent L1-minimization(L1-min)problem is often required in some real applications,we investigate how to solve it in parallel on GPUs in this paper.First,we propose a novel self-adaptive warp impleme... Given that the concurrent L1-minimization(L1-min)problem is often required in some real applications,we investigate how to solve it in parallel on GPUs in this paper.First,we propose a novel self-adaptive warp implementation of the matrix-vector multiplication(Ax)and a novel self-adaptive thread implementation of the matrix-vector multiplication(ATx),respectively,on the GPU.The vector-operation and inner-product decision trees are adopted to choose the optimal vector-operation and inner-product kernels for vectors of any size.Second,based on the above proposed kernels,the iterative shrinkage-thresholding algorithm is utilized to present two concurrent L1-min solvers from the perspective of the streams and the thread blocks on a GPU,and optimize their performance by using the new features of GPU such as the shuffle instruction and the read-only data cache.Finally,we design a concurrent L1-min solver on multiple GPUs.The experimental results have validated the high effectiveness and good performance of our proposed methods. 展开更多
关键词 Concurrent L1-minimization problem dense matrix-vector multiplication fast iterative shrinkage-thresholding algorithm CUDA GPUs
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A Semi-Supervised WLAN Indoor Localization Method Based on l1-Graph Algorithm 认领 引用 被引量：1
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作者 Liye Zhang Lin Ma Yubin Xu 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2015年第4期55-61,共7页
For indoor location estimation based on received signal strength( RSS) in wireless local area networks( WLAN),in order to reduce the influence of noise on the positioning accuracy,a large number of RSS should be colle... For indoor location estimation based on received signal strength( RSS) in wireless local area networks( WLAN),in order to reduce the influence of noise on the positioning accuracy,a large number of RSS should be collected in offline phase. Therefore,collecting training data with positioning information is time consuming which becomes the bottleneck of WLAN indoor localization. In this paper,the traditional semisupervised learning method based on k-NN and ε-NN graph for reducing collection workload of offline phase are analyzed,and the result shows that the k-NN or ε-NN graph are sensitive to data noise,which limit the performance of semi-supervised learning WLAN indoor localization system. Aiming at the above problem,it proposes a l1-graph-algorithm-based semi-supervised learning( LG-SSL) indoor localization method in which the graph is built by l1-norm algorithm. In our system,it firstly labels the unlabeled data using LG-SSL and labeled data to build the Radio Map in offline training phase,and then uses LG-SSL to estimate user's location in online phase. Extensive experimental results show that,benefit from the robustness to noise and sparsity ofl1-graph,LG-SSL exhibits superior performance by effectively reducing the collection workload in offline phase and improving localization accuracy in online phase. 展开更多
关键词 indoor location estimation l1-graph algorithm semi-supervised learning wireless local area networks(WLAN)
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Numerical Studies of the Generalized l1Greedy Algorithm for Sparse Signals 认领 引用
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作者 Fangjun Arroyo Edward Arroyo +2 位作者 Xiezhang Li Jiehua Zhu Jiehua Zhu 《Advances in Computed Tomography》 2013年第4期132-139,共8页
The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results ... The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l1 greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l1 greedy algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in the successful recovery of randomly generated Gaussian sparse signals from data generated by Gaussian random matrices. In particular, the generalized l1 greedy algorithm performs extraordinarily well in recovering random sparse signals with nonzero small entries. The stability of the generalized l1 greedy algorithm with respect to its parameters and the impact of noise on the recovery of Gaussian sparse signals are also studied. 展开更多
关键词 Compressed Sensing Gaussian Sparse Signals l1-Minimization Reweighted l1-Minimization l1 Greedy Algorithm Generalized l1 Greedy Algorithm
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AN ADAPTIVE ALGORITHM FOR L1-FIDELITY COLOR IMAGE RESTORATION 认领 引用
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作者 Wei Wang Chengyun Yang Qifan Song 《Journal of Computational Mathematics》 SCIE CSCD 2026年第3期779-793,共15页
In this paper,we propose an adaptive algorithm for L1-fidelity color image restoration by using saturation-value total variation.The main contribution of this paper is to employ the generalized cross validation method... In this paper,we propose an adaptive algorithm for L1-fidelity color image restoration by using saturation-value total variation.The main contribution of this paper is to employ the generalized cross validation method efficiently and automatically to estimate the regularization parameter in a saturation-value total variation plus L1-fidelity color image restoration model.We consider Poisson noise and mixed noise in this paper,and the experimental results show that the visual quality and the SSIM/PSNR/SAM values of the restored images by using the proposed algorithm are competitive with other tested existing methods,which makes the proposed algorithm to be comparable both quantitatively and qualitatively. 展开更多
关键词 Adaptive algorithm Saturation-value total variation L1-fideLity Cross validation Poisson noise
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Guidance and Control for UAV Aerial Refueling Docking Based on Dynamic Inversion with L_1 Adaptive Augmentation 认领 引用 被引量：3
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作者 袁锁中 甄子洋 江驹 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2015年第1期35-41,共7页
The guidance and control for UAV aerial refueling docking based on dynamic inversion with L1 adaptive augmentation is studied.In order to improve the tracking performance of UAV aerial refueling docking,aguidance algo... The guidance and control for UAV aerial refueling docking based on dynamic inversion with L1 adaptive augmentation is studied.In order to improve the tracking performance of UAV aerial refueling docking,aguidance algorithm is developed to satisfy the tracking requirement of position and velocity,and it generates the UAV flight control loop commands.In flight control loop,based on the 6-DOF nonlinear model,the angular rate loop and the attitude loop are separated based on time-scale principle and the control law is designed using dynamic inversion.The throttle control is also derived from dynamic inversion method.Moreover,an L1 adaptive augmentation is developed to compensate for the undesirable effects of modeling uncertainty and disturbance.Nonlinear digital simulations are carried out.The results show that the guidance and control system has good tracking performance and robustness in achieving accurate aerial refueling docking. 展开更多
关键词 aerial refueling dynamic inversion guidance algorithm L1adaptive augmentation
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组稀疏表示的双重l1范数优化图像去噪算法 认领 引用 被引量：6
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作者 骆骏 刘辉 尚振宏 《四川大学学报（自然科学版）》 CAS CSCD 北大核心 2019年第6期1065-1072,共8页
由于图像受噪声的影响,无法从降质信号中获得准确的稀疏系数.针对此问题,对一种组稀疏表示的双重l1范数优化图像去噪算法进行研究,该算法同时采用非局部相似图像块组稀疏表示的l1范数和稀疏残差作为正则项对组稀疏系数进行约束,并利用... 由于图像受噪声的影响,无法从降质信号中获得准确的稀疏系数.针对此问题,对一种组稀疏表示的双重l1范数优化图像去噪算法进行研究,该算法同时采用非局部相似图像块组稀疏表示的l1范数和稀疏残差作为正则项对组稀疏系数进行约束,并利用一种有效的迭代收缩算法实现对模型的优化求解,以获取更鲁棒的稀疏系数,另外,为了进一步提高去噪性能,采用贝叶斯公式推导出自适应调整两个正则化参数的方法.实验结果表明,与现有的许多算法相比,新算法能够在去除噪声的同时抑制伪影,保护图像的细节信息,峰值信噪比相对经典的BM3D算法而言,最多可提高1.24 dB. 展开更多
关键词 图像去噪 组稀疏表示 l1范数 稀疏残差 迭代收缩算法
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约束非线性l_1问题的调节熵函数法 认领 引用 被引量：5
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作者 王若鹏 邢志栋 《系统工程与电子技术》 EI 北大核心 2005年第2期260-261,319,共2页
针对约束非线性l1问题不可微的特点,提出了一种光滑函数的近似逼近方法。该方法利用调节熵函数和罚函数技术将约束非线性l1问题转化为无约束可微优化问题,因而可利用光滑优化的经典算法求出原问题的近似最优解。给出了基于光滑优化问题... 针对约束非线性l1问题不可微的特点,提出了一种光滑函数的近似逼近方法。该方法利用调节熵函数和罚函数技术将约束非线性l1问题转化为无约束可微优化问题,因而可利用光滑优化的经典算法求出原问题的近似最优解。给出了基于光滑优化问题的BFGS迭代,并介绍了约束非线性l1问题的调节熵函数的有关性质、算法的迭代步骤及其收敛性分析。最后通过数值实例表明了该算法的有效性。 展开更多
关键词 非线性l1问题 调节熵函数 全局收敛性 算法
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An Efficient CSP-PDW Approach for ECG Signal Compression and Reconstruction for IoT-Based Healthcare 认领 引用
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作者 Hari Mohan Rai Chandra Mukherjee +3 位作者 Joon Yoo Hanaa AAbdallah Saurabh Agarwal Wooguil Pak 《Computers, Materials & Continua》 SCIE EI 2025年第12期5723-5745,共23页
A hybrid Compressed Sensing and Primal-Dual Wavelet(CSP-PDW)technique is proposed for the compression and reconstruction of ECG signals.The compression and reconstruction algorithms are implemented using four key conc... A hybrid Compressed Sensing and Primal-Dual Wavelet(CSP-PDW)technique is proposed for the compression and reconstruction of ECG signals.The compression and reconstruction algorithms are implemented using four key concepts:Sparsifying Basis,Restricted Isometry Principle,Gaussian Random Matrix,and Convex Minimization.In addition to the conventional compression sensing reconstruction approach,wavelet-based processing is employed to enhance reconstruction efficiency.A mathematical model of the proposed algorithm is derived analytically to obtain the essential parameters of compression sensing,including the sparsifying basis,measurement matrix size,and number of iterations required for reconstructing the original signal and determining the type and level of wavelet processing.The low time complexity of the proposed algorithm makes it an ideal candidate for ECG monitoring systems in IoT-based e-healthcare applications.A feature extraction algorithm is also developed to show that the important ECG peaks remain unaltered after reconstruction.The clinical relevance of the reconstructed signal and the efficiency of the developed algorithm are evaluated using four validation parameters at three different compression ratios. 展开更多
关键词 CSP-PDW compression sensing greedy iterative algorithm wavelet transform L1 minimization restricted isometry property
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求解极小l_1模问题的修正Bland规则 认领 引用
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作者 颜世建 尤兴华 《南京师大学报（自然科学版）》 CAS 2001年第2期1-6,共6页
改进了Bland规则 ,给出了一个解极小l1模问题的有效算法 .
关键词 极小l1模解 单纯形方法 Bland规则
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Some Numerical Extrapolation Methods for the Fractional Sub-diffusion Equation and Fractional Wave Equation Based on the L1 Formula 认领 引用 被引量：1
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作者 Ren-jun Qi Zhi-zhong Sun 《Communications on Applied Mathematics and Computation》 2022年第4期1313-1350,共38页
With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.T... With the help of the asymptotic expansion for the classic Li formula and based on the L1-type compact difference scheme,we propose a temporal Richardson extrapolation method for the fractional sub-diffusion equation.Three extrapolation formulas are presented,whose temporal convergence orders in L∞-norm are proved to be 2,3-α,and 4-2α,respectively,where 0<α<1.Similarly,by the method of order reduction,an extrapola-tion method is constructed for the fractional wave equation including two extrapolation formulas,which achieve temporal 4-γ and 6-2γ order in L∞-norm,respectively,where1<γ<2.Combining the derived extrapolation methods with the fast algorithm for Caputo fractional derivative based on the sum-of-exponential approximation,the fast extrapolation methods are obtained which reduce the computational complexity significantly while keep-ing the accuracy.Several numerical experiments confirm the theoretical results. 展开更多
关键词 L1 formula Asymptotic expansion Fractional sub-diffusion equation Fractional wave equation Richardson extrapolation Fast algorithm
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一类最大度为3的图的L(2,1)-边标号的有效算法 认领 引用 被引量：1
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作者 叶林 郭健红 《绍兴文理学院学报》 2016年第9期33-35,共3页
主要研究了一类其线图最大度为3的图的L(2,1)-边标号,给出了一个有效算法在线性时间之内可以找到该类图的9-L(2,1)-边标号,同时验证了Griggs和Yeh猜想对于该图类成立.
关键词 边-L(2,1)-标号 标号数 最大度 有效算法
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H_2/l_1混合优化问题的凸二次规划解法 认领 引用
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作者 孔亚广 吴俊 孙优贤 《控制与决策》 EI 北大核心 2001年第2期250-253,共4页
采用上逼近算法求解 H2 / l1 混合优化问题。首先将其转化为有限维的凸二次规划问题 ,并利用L emke互补转轴算法求解 ;然后逐次进行逼近。
关键词 H2/l1混合优化问题 凸二次规划 H∞优化控制 鲁棒性
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变异蝙蝠算法求解折扣{0-1}背包问题 认领 引用 被引量：19
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作者 吴聪聪 贺毅朝 +2 位作者 陈嶷瑛 刘雪静 才秀凤 《计算机应用》 CSCD 北大核心 2017年第5期1292-1299,共8页
针对确定性算法难于求解规模大、数据范围广的折扣{0-1}背包问题(D{0-1}KP),提出了基于蝙蝠算法的快速求解D{0-1}KP的变异蝙蝠算法(MDBBA)。首先,利用双重编码解决D{0-1}KP的编码问题;其次,将贪心修复与优化算法(GROA)应用于蝙蝠个体适... 针对确定性算法难于求解规模大、数据范围广的折扣{0-1}背包问题(D{0-1}KP),提出了基于蝙蝠算法的快速求解D{0-1}KP的变异蝙蝠算法(MDBBA)。首先,利用双重编码解决D{0-1}KP的编码问题;其次,将贪心修复与优化算法(GROA)应用于蝙蝠个体适应度计算中,使算法快速得到有效解;然后,选择使用差分演化(DE)的变异策略提高算法的全局寻优能力;最后,蝙蝠个体按一定概率进行Lévy飞行,增强算法探索能力和跳出局部极值的能力。对四类大规模实例的仿真计算表明:MDBBA非常适于求解大规模的D{0-1}KP,比第一遗传算法(FirEGA)和双重编码蝙蝠算法(DBBA)求得的最优值和平均值都更优,MDBBA收敛速度明显快于DBBA。 展开更多
关键词 折扣{0-1}背包问题 蝙蝠算法 差分演化 Lévy飞行 贪心策略 非正常编码
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Theory of Compressive Sensing via l1-Minimization:a Non-RIP Analysis and Extensions 认领 引用 被引量：16
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作者 Yin Zhang 《Journal of the Operations Research Society of China》 EI 2013年第1期79-105,共27页
Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the f... Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the former quantifies the central fact that a sparse signal of length n can be exactly recovered from far fewer than n measurements via l1-minimization or other recovery techniques,while the latter specifies the stability of a recovery technique in the presence of measurement errors and inexact sparsity.So far,most analyses in CS rely heavily on the Restricted Isometry Property(RIP)for matrices.In this paper,we present an alternative,non-RIP analysis for CS via l1-minimization.Our purpose is three-fold:(a)to introduce an elementary and RIP-free treatment of the basic CS theory;(b)to extend the current recoverability and stability results so that prior knowledge can be utilized to enhance recovery via l1-minimization;and(c)to substantiate a property called uniform recoverability of l1-minimization;that is,for almost all random measurement matrices recoverability is asymptotically identical.With the aid of two classic results,the non-RIP approach enables us to quickly derive from scratch all basic results for the extended theory. 展开更多
关键词 Compressive sensing l1-Minimization Non-RIP analysis Recoverability and stability Prior information Uniform recoverability
振荡型GM(1,1,k)幂模型的构建及其应用 认领 引用 被引量：4
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作者 白雪 任洪涛 +2 位作者 刘冬玉 刘盼 李晔 《系统工程》 CSSCI CSCD 北大核心 2023年第4期137-144,共8页
针对含有时间趋势性和振荡性的小样本序列的建模预测问题,提出了同时包含时间延迟参数、时间作用参数及多项式的振荡型GM(1,1,k)幂模型,采用遗传算法寻找模型中的最优非线性参数,提高了模型的预测精度。将该模型应用于我国季度风电产量... 针对含有时间趋势性和振荡性的小样本序列的建模预测问题,提出了同时包含时间延迟参数、时间作用参数及多项式的振荡型GM(1,1,k)幂模型,采用遗传算法寻找模型中的最优非线性参数,提高了模型的预测精度。将该模型应用于我国季度风电产量的预测,结果显示,振荡型GM(1,1,k)幂模型具有良好的预测性能,为含有时间趋势性的小样本振荡序列预测提供了一种有效的建模方法和预测手段。 展开更多
关键词 灰色预测 GM(1,1,k)幂模型 振荡序列 遗传算法
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联合正交投影与CLEAN的测距仪脉冲干扰抑制方法 认领 引用 被引量：6
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作者 刘海涛 刘亚洲 张学军 《信号处理》 CSCD 北大核心 2015年第5期536-543,共8页
针对L频段数字航空通信系统1(L-DACS1)以内嵌方式部署在航空无线电导航频段而产生的高强度测距仪脉冲信号干扰正交频分复用(OFDM)接收机的问题,提出联合正交投影与CLEAN的测距仪脉冲干扰抑制方法。接收机首先通过将接收信号矢量投影到... 针对L频段数字航空通信系统1(L-DACS1)以内嵌方式部署在航空无线电导航频段而产生的高强度测距仪脉冲信号干扰正交频分复用(OFDM)接收机的问题,提出联合正交投影与CLEAN的测距仪脉冲干扰抑制方法。接收机首先通过将接收信号矢量投影到干扰信号正交补空间的方法消除高强度测距仪脉冲干扰,然后利用OFDM信号循环前缀的对称特性,采用CLEAN算法估计信号来向,然后通过常规波束成形提取OFDM直射径信号。计算机仿真表明:论文提出方法可有效克服测距仪脉冲及OFDM散射径信号的干扰,提高L频段数字航空通信系统1的链路传输的可靠性。 展开更多
关键词 L频段数字航空通信系统1 正交频分复用 CLEAN算法 测距仪脉冲干扰 阵列天线
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Sparse Solutions of Mixed Complementarity Problems 认领 引用 被引量：1
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作者 Peng Zhang Zhensheng Yu 《Journal of Applied Mathematics and Physics》 2020年第1期10-22,共13页
In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for t... In this paper, we consider an extragradient thresholding algorithm for finding the sparse solution of mixed complementarity problems (MCPs). We establish a relaxation l1 regularized projection minimization model for the original problem and design an extragradient thresholding algorithm (ETA) to solve the regularized model. Furthermore, we prove that any cluster point of the sequence generated by ETA is a solution of MCP. Finally, numerical experiments show that the ETA algorithm can effectively solve the l1 regularized projection minimization model and obtain the sparse solution of the mixed complementarity problem. 展开更多
关键词 Mixed Complementarity Problem Sparse Solution l1 Regularized Projection Minimization Model Extragradient Thresholding Algorithm
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Truncated L1 Regularized Linear Regression:Theory and Algorithm 认领 引用
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作者 Mingwei Dai Shuyang Dai +2 位作者 Junjun Huang Lican Kang Xiliang Lu 《Communications in Computational Physics》 SCIE 2021年第6期190-209,共20页
Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to ... Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse models.In this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery property.Moreover,a primal dual active set algorithm(PDAS)for variable estimation and selection is proposed.Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm(PDASC).Data-driven parameter selection rules such as cross validation,BIC or voting method can be applied to select a proper regularization parameter.The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA). 展开更多
关键词 High-dimensional linear regression sparsity truncated L1 regularization primal dual active set algorithm
1-Bit compressive sensing: Reformulation and RRSP-based sign recovery theory 认领 引用 被引量：5
20
作者 ZHAO YunBin XU ChunLei 《Science China Mathematics》 SCIE CSCD 2016年第10期2049-2074,共26页
Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or ... Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit. 展开更多
关键词 1-bit compressive sensing restricted range space property 1-bit basis pursuit linear program,l0-minimization sparse signal recovery
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