DOA estimation of high-dimensional signals based on Krylov subspace and weighted l_(1)-norm

With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.

l_(1)-norm Based GWLP for Robust Frequency Estimation

In this work,we address the frequency estimation problem of a complex single-tone embedded in the heavy-tailed noise.With the use of the linear prediction(LP)property and l_(1)-norm minimization,a robust frequency estimator is developed.Since the proposed method employs the weighted l_(1)-norm on the LP errors,it can be regarded as an extension of the l_(1)-generalized weighted linear predictor.Computer simulations are conducted in the environment of α-stable noise,indicating the superiority of the proposed algorithm,in terms of its robust to outliers and nearly optimal estimation performance.

L_(2,1)-norm robust regularized extreme learning machine for regression using CCCP method

As a way of training a single hidden layer feedforward network(SLFN),extreme learning machine(ELM)is rapidly becoming popular due to its efficiency.However,ELM tends to overfitting,which makes the model sensitive to noise and outliers.To solve this problem,L_(2,1)-norm is introduced to ELM and an L_(2,1)-norm robust regularized ELM(L_(2,1)-RRELM)was proposed.L_(2,1)-RRELM gives constant penalties to outliers to reduce their adverse effects by replacing least square loss function with a non-convex loss function.In light of the non-convex feature of L_(2,1)-RRELM,the concave-convex procedure(CCCP)is applied to solve its model.The convergence of L_(2,1)-RRELM is also given to show its robustness.In order to further verify the effectiveness of L_(2,1)-RRELM,it is compared with the three popular extreme learning algorithms based on the artificial dataset and University of California Irvine(UCI)datasets.And each algorithm in different noise environments is tested with two evaluation criterions root mean square error(RMSE)and fitness.The results of the simulation indicate that L_(2,1)-RRELM has smaller RMSE and greater fitness under different noise settings.Numerical analysis shows that L_(2,1)-RRELM has better generalization performance,stronger robustness,and higher anti-noise ability and fitness.

一种用于目标跟踪边界框回归的光滑IoU损失

边界框回归分支是深度目标跟踪器的关键模块,其性能直接影响跟踪器的精度.评价精度的指标之一是交并比(Intersection over union,IoU).基于IoU的损失函数取代了l_(n)-norm损失成为目前主流的边界框回归损失函数,然而IoU损失函数存在2个固有缺陷:1)当预测框与真值框不相交时IoU为常量0,无法梯度下降更新边界框的参数;2)在IoU取得最优值时其梯度不存在,边界框很难收敛到IoU最优处.揭示了在回归过程中IoU最优的边界框各参数之间蕴含的定量关系,指出在边界框中心处于特定位置时存在多种尺寸不同的边界框使IoU损失最优的情况,这增加了边界框尺寸回归的不确定性.从优化两个统计分布之间散度的视角看待边界框回归问题,提出了光滑IoU(Smooth-IoU,SIoU)损失,即构造了在全局上光滑(即连续可微)且极值唯一的损失函数,该损失函数自然蕴含边界框各参数之间特定的最优关系,其唯一取极值的边界框可使IoU达到最优.光滑性确保了在全局上梯度存在使得边界框更容易回归到极值处,而极值唯一确保了在全局上可梯度下降更新参数,从而避开了IoU损失的固有缺陷.提出的光滑损失可以很容易取代IoU损失集成到现有的深度目标跟踪器上训练边界框回归,在LaSOT、GOT-10k、TrackingNet、OTB2015和VOT2018测试基准上所取得的结果,验证了光滑IoU损失的易用性和有效性.

基于深度学习的单幅图像超分辨率重建方法研究

为了解决基于单幅图像自适应稠密连接超分辨率(ADCSR)算法中的残差单元的融合问题,本文提出了一种基于行稀疏约束l_(0,2)-范数和soft-max运算的新策略.根据ADCSR算法,本文算法分为两部分:BODY和SKIP,前者专注图像的高频特征学习,后者专注低频特征学习.BODY部分中所有自适应密集残差单元(ADRU)的输出,作为初始特征图,可用特征数目l_(0,2)-范数作为活动水平度量,然后利用基于块的平均算子计算最终活动水平图,最后利用soft-max得到融合后特征映射,改进了原ADCSR算法中卷积融合粗糙的缺点,保留了更多的结构信息和特征.此外特征数目l_(0,2)-范数作为字典原子更加精确地获取更高的权重,获得了更优的峰值信噪比PSNR、结构相似性SSIM和视觉效果,计算机实验证明了本文算法的有效性.

L_1-Norm Estimation and Random Weighting Method in a Semiparametric Model

In this paper, the L_1-norm estimators and the random weighted statistic fora semiparametric regression model are constructed, the strong convergence rates of estimators areobtain under certain conditions, the strong efficiency of the random weighting method is shown. Asimulation study is conducted to compare the L_1-norm estimator with the least square estimator interm of approximate accuracy, and simulation results are given for comparison between the randomweighting method and normal approximation method.

KNOT PLACEMENT FOR B-SPLINE CURVE APPROXIMATION VIA l_(∞,1)-NORM AND DIFFERENTIAL EVOLUTION ALGORITHM

In this paper,we consider the knot placement problem in B-spline curve approximation.A novel two-stage framework is proposed for addressing this problem.In the first step,the l_(∞,1)-norm model is introduced for the sparse selection of candidate knots from an initial knot vector.By this step,the knot number is determined.In the second step,knot positions are formulated into a nonlinear optimization problem and optimized by a global optimization algorithm—the differential evolution algorithm(DE).The candidate knots selected in the first step are served for initial values of the DE algorithm.Since the candidate knots provide a good guess of knot positions,the DE algorithm can quickly converge.One advantage of the proposed algorithm is that the knot number and knot positions are determined automatically.Compared with the current existing algorithms,the proposed algorithm finds approximations with smaller fitting error when the knot number is fixed in advance.Furthermore,the proposed algorithm is robust to noisy data and can handle with few data points.We illustrate with some examples and applications.

Multiple access interference suppression for CDMA systems via l_(∞)-minimization

A key problem in code-division multiple access(CDMA)system is to mitigate the multiple access interference(MAI)from other users while detecting the desired user.The performance of the conventional minimum output energy(MOE)multiuser detector for CDMA system significantly degrades in the presence of signature waveform distortions induced by multipath propagation or timing asynchronism.In this paper,a robust linear programming(ROLP)algorithm for blind multiuser detection is proposed.Different from the existing MOE-based multiuser detection techniques,the proposed ROLP minimizes the l_∞-norm of the output to exploit the non-Gaussianity of the communication signals.To achieve robustness against signature waveform mismatch,the proposed method constrains the magnitude response of any signature vector within a specified uncertainty set to exceed unity.The uncertainty set is modeled as a rhombus,which differs from the spherical uncertainty region widely taken in the existing robust multiuser detectors.The resulting optimization problem is reformulated into a linear programming program and hence can be solved efficiently.The proposed ROLP is computationally simpler than its robust counterparts that requires solving a second-order cone programming.Simulation results demonstrate the superiority of the ROLP over several robust detectors,which indicate that its performance approaches the optimal performance bound.

Simultaneous Approximation of Sobolev Classes by Piecewise Cubic Hermite Interpolation

For the approximation in L_(p)-norm,we determine the weakly asymptotic orders for the simultaneous approximation errors of Sobolev classes by piecewise cubic Hermite interpolation with equidistant knots.For p=1,∞,we obtain its values.By these results we know that for the Sobolev classes,the approximation errors by piecewise cubic Hermite interpolation are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.At the same time,the approximation errors of derivatives are weakly equivalent to the corresponding infinite-dimensional Kolmogorov widths.