This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the partic...This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.展开更多
It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian ...It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as d → 0. The constants C and c are very sensitive. A slight change of them will result in a huge change of the error bound. The number c can be calculated as shown in [9]. However, C cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.展开更多
This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels sub...This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.展开更多
从滤波理论出发,通过将ICGEM(International Centre for Global Earth Models)发布的DDK1-DDK8滤波处理的GRACE时变重力位系数去条带效果与高斯滤波效果进行对比分析,研究发现CSR机构的数据质量相比于其它两个机构信号的RMS更小,同时DDK...从滤波理论出发,通过将ICGEM(International Centre for Global Earth Models)发布的DDK1-DDK8滤波处理的GRACE时变重力位系数去条带效果与高斯滤波效果进行对比分析,研究发现CSR机构的数据质量相比于其它两个机构信号的RMS更小,同时DDK2滤波的效果与450 km高斯滤波效果相近,其信噪比相较于其它DDK滤波也具有较好水平。最后,对比分析了DDK2滤波与450 km高斯滤波处理的时变重力场反演分析了河南省的陆地水储量变化情况,结果表明其与高斯滤波反演的水储量变化趋势一致,且对信号保留效果更好,表明所选DDK2滤波方法较为合理。展开更多
A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularit...A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.展开更多
Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative ad...Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate （MSER） criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.展开更多
The Bjorck and Pereyra algorithms used for solving Vandermonde systemof equation are modified for the case where the points are symmetricly situated aroundzero. The working operation is saved about half. A forward err...The Bjorck and Pereyra algorithms used for solving Vandermonde systemof equation are modified for the case where the points are symmetricly situated aroundzero. The working operation is saved about half. A forward error analysis is presentedfor the modified algorithms, and it's shown that if the points are situated in some order,the error bound are as good as Higham's result in 1987.展开更多
Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for ...Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for sparse scatterer density, the detection of target scatterer in each range cell is derived, and then an M/K detector is proposed to detect the whole range-spread target. Se- condly, an integrating detector is devised to detect a range-spread target with dense scatterer density. Finally, to make the best of the advantages of M/K detector and integrating detector, a robust detector based on scatterer density （DBSD） is designed, which can reduce the probable collapsing loss or quantization error ef- fectively. Moreover, the density decision factor of DBSD is also determined. The formula of the false alarm probability is derived for DBSD. It is proved that the DBSD ensures a constant false alarm rate property. Furthermore, the computational results indi- cate that the DBSD is robust to different clutter one-lag correlations and target scatterer densities. It is also shown that the DBSD out- performs the existing scatterer-density-dependent detector.展开更多
The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( F...The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( FSER) performance. In this paper,a theoretical derivation of the FSER performance of pilotless frame synchronization for LDPC code is presented. The FSER performance by theoretical analysis coincides well with that by simulation in additive white Gaussian channel and Rician fading channel. So it is estimated the FSER performance of an LDPC code by theoretical analysis can be used instead of the simulations which are much more time-consuming.展开更多
基金This work has been(partially)supported by the Project EFI ANR-17-CE40-0030 of the French National Research Agency.
文摘This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.
文摘It＇s well-known that there is a very powerful error bound for Gaussians put forward by Madych and Nelson in 1992. It＇s of the form｜f（x） - s（x）｜≤（Cd）c/d｜｜f｜｜h where C, c are constants, h is the Gaussian function, s is the interpolating function, and d is called fill distance which, roughly speaking, measures the spacing of the points at which interpolation occurs. This error bound gets small very fast as d → 0. The constants C and c are very sensitive. A slight change of them will result in a huge change of the error bound. The number c can be calculated as shown in [9]. However, C cannot be calculated, or even approximated. This is a famous question in the theory of radial basis functions. The purpose of this paper is to answer this question.
基金the support of SNCS Research Center and the Deanship of Scientific Research at the University of Tabukfinancial and inkind support for the project no. S-1438-0161
文摘This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.
文摘从滤波理论出发,通过将ICGEM(International Centre for Global Earth Models)发布的DDK1-DDK8滤波处理的GRACE时变重力位系数去条带效果与高斯滤波效果进行对比分析,研究发现CSR机构的数据质量相比于其它两个机构信号的RMS更小,同时DDK2滤波的效果与450 km高斯滤波效果相近,其信噪比相较于其它DDK滤波也具有较好水平。最后,对比分析了DDK2滤波与450 km高斯滤波处理的时变重力场反演分析了河南省的陆地水储量变化情况,结果表明其与高斯滤波反演的水储量变化趋势一致,且对信号保留效果更好,表明所选DDK2滤波方法较为合理。
文摘目的逆渲染旨在从二维多视图图像中同时恢复场景几何、材质及光照。近期,三维高斯泼溅(3D Gaussian splatting,3DGS)因其高效渲染特性被引入该领域,然而,当前基于物理真实的逆渲染时面临两大核心挑战:其一,3DGS基元本身主要为新视角合成优化,其提取的网格难以满足物理渲染的精度需求;其二,准确解耦材质与光照依赖对复杂光照传输和高频材质细节的精确建模,但现有方法在估计具有复杂可见性的直接光照时常面临高方差与计算瓶颈,影响了材质恢复的保真度和训练效率。方法为此,提出一种两阶段快速物理逆渲染框架:首先,在几何恢复阶段,引入扁平高斯基元压缩与多视图双向重投影误差约束,实现精度与速度的平衡,生成可直接用于下游渲染引擎的高精度三角网格;其次,在材质与光照恢复阶段,在提取的网格上采用基于单样本加权池采样的高效直接光照估计,并基于多分辨率哈希网格的神经表示实现复杂高频材质细节的恢复,在大幅降低渲染方差的同时显著缩短训练时间。结果为全面验证本文方法的有效性,本研究在基准数据集上开展了系统实验。在几何恢复方面,本文方法在TensoIR(tensorial inverse rendering)数据集上的法线平均角误差相比次优方法降低了19.59%;在DTU(Technical University of Denmark)数据集上,生成的网格在倒角距离分数上与最优方法持平,但训练速度提升了一倍。在材质恢复和新视角合成任务上,本文方法同样表现出色:在TensoIR数据集中,材质恢复的峰值信噪比(peak signal-to-noise ratio,PSNR)值较次优方法提升了2.84%,新视角合成的PSNR值提高了0.08。结论本工作成功构建了从三维高斯泼溅表达到可物理渲染的网格与材质贴图的快速、端到端逆渲染流程,为逆渲染技术在实时交互与工业级场景中的应用提供了高效且鲁棒的新范式。
基金The project is supported by National Natural Science Foundation of China(No.59975025).
文摘A genetic algorithm(GA)-based new method is designed to evaluate thecircularity error of mechanical parts. The method uses the capability of nonlinear optimization ofGA to search for the optimal solution of circularity error. The finely-designed GA (FDGA)characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of thenonlinear problem is given. The implementation details in FDGA are described such as the crossoveror recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservationmethod; and the adaptive mutation which used the Gaussian probability distribution to determine thevalues of the offspring produced by mutation mechanism. The examples are provided to verify thedesigned FDGA. The computation results indicate that the FDGA works very well in the field of formerror evaluation such as circularity evaluation.
文摘Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate （MSER） criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.
基金Supported by National Natural Science Foundation of China,under Grant Number 60175008.and Natural Science Foundation of Fujian Province under Grant A0110004.
文摘The Bjorck and Pereyra algorithms used for solving Vandermonde systemof equation are modified for the case where the points are symmetricly situated aroundzero. The working operation is saved about half. A forward error analysis is presentedfor the modified algorithms, and it's shown that if the points are situated in some order,the error bound are as good as Higham's result in 1987.
基金supported by the National Natural Science Foundation of China (61102166)the Scientific Research Foundation of Naval Aeronautical and Astronautical University for Young Scholars (HY2012)
文摘Based on the target scatterer density, the range-spread target detection of high-resolution radar is addressed in additive non-Gaussian clutter, which is modeled as a spherically invariant random vector. Firstly, for sparse scatterer density, the detection of target scatterer in each range cell is derived, and then an M/K detector is proposed to detect the whole range-spread target. Se- condly, an integrating detector is devised to detect a range-spread target with dense scatterer density. Finally, to make the best of the advantages of M/K detector and integrating detector, a robust detector based on scatterer density （DBSD） is designed, which can reduce the probable collapsing loss or quantization error ef- fectively. Moreover, the density decision factor of DBSD is also determined. The formula of the false alarm probability is derived for DBSD. It is proved that the DBSD ensures a constant false alarm rate property. Furthermore, the computational results indi- cate that the DBSD is robust to different clutter one-lag correlations and target scatterer densities. It is also shown that the DBSD out- performs the existing scatterer-density-dependent detector.
基金Supported by the National Natural Science Foundation of China(No.61271230,61472190)the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University(No.2013D02)the Open Research Fund of National Key Laboratory of Electromagnetic Environment,China Research Institute of Radiowave Propagation(No.201500013)
文摘The pilotless frame synchronization approach and implementations of LDPC code are the crucial issue of LDPC decoder. The Maximum-A-Posteriori probability( MAP) decoder has a perfect frame synchronization error rate( FSER) performance. In this paper,a theoretical derivation of the FSER performance of pilotless frame synchronization for LDPC code is presented. The FSER performance by theoretical analysis coincides well with that by simulation in additive white Gaussian channel and Rician fading channel. So it is estimated the FSER performance of an LDPC code by theoretical analysis can be used instead of the simulations which are much more time-consuming.
文摘【目的】超宽带测距误差分布表明,在存在显著重尾的情况下,高斯混合模型比简单的高斯概率包络更接近经验分布。通过传统的超界分布(Overbounding Distribution)模型获得的保护水平过于保守,会降低系统可用性。【方法】为提高系统可用性,提出了基于高斯混合模型(GMM)的超界框架来处理基于TOA(Time of Arrival)定位的超宽带测距误差样本。首先,结合EM算法获得测距误差的双组分GMM概率密度函数,并修正边界参数,使左右边界均满足双边超界条件,以构建双组分GMM形式的距离域双边超界模型。随后,基于GMM双边超界模型推导出计算位置域保护级(PL)的方法,对距离域的概率密度函数进行卷积以获得位置概率密度函数,求逆运算出PL。【结果】最后,开展实验验证应用GMM双边超界模型收紧PL的效果,采集3~93 m范围内的样本数据用于误差模型的构建,真实测试的性能评估表明,基于GMM双边超界模型比传统高斯双边超界模型计算所得的PL减小了20%以上。【结论】GMM双边超界模型能够以较小的计算成本收紧PL,增强系统可用性。
