Degree of approximation of analytic functions by “near-best” polynomial approximants

We study the rate of approximation of a functionfA(K) in the interior of the compact setK by polynomials, that are close to best polynomial approximants on the whole setK. Lower and upper estimates of possible improvement of convergence (depending on the geometry ofK) are obtained.Communicated by Vilmos Totik.     

Necessary and sufficient conditions for mean convergence of orthogonal expansions for Freud weights

A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weightedL _p convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weightsW ²:=e ^–2Q , by first proving a bound for the difference of the orthonormal polynomials of degreen+1 andn–1 of the weightW ². Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least forp>1. Moreover, our necessary conditions apply whenQ(x)=|x|, >1 while our sufficient conditions apply at least for =2,4,6,....Communicated by Vilmos Totik.     

A counterexample to subexponential growth of orthogonal polynomials

We construct an example of polynomialsp _n orthonormal with respect to a measure such that the sequencep _n (x) has an exponential lower bound for a pointx in the support of .Communicated by Paul Nevai.     

On Lipschitz property of solutions of functional equations

In this work it is proved that under certain conditions the continuous vector-valued solutionsf of the functional equation

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :

Convex polynomial and spline approximation in C[−1, 1]

We prove that a convex functionf C[–1, 1] can be approximated by convex polynomialsp _n of degreen at the rate of ₃(f, 1/n). We show this by proving that the error in approximatingf by C² convex cubic splines withn knots is bounded by ₃(f, 1/n) and that such a spline approximant has anL third derivative which is bounded by n³₃(f, 1/n). Also we prove that iff C²[–1, 1], then it is approximable at the rate ofn ^–2 (f, 1/n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore.     

一种基于实例语义图的屏幕反窃照识别算法

目前防窃照技术手段主要依靠图像采集设备实时采集视频流,对拍照行为进行识别检测,但受复杂环境影响,现有识别方法存在精确度低、实时性差等问题。针对上述问题,提出了一种基于实例语义图的屏幕反窃照识别算法。该算法首先通过图像分割模型U²-Net提取原图像的显著视觉目标后生成实例语义图,然后通过微调单阶段的目标检测模型YOLO-v5实现对语义图中感兴趣对象的目标检测,最后通过设计的基于Inception-ResNet的拍照识别二分类模型实现对屏幕窃照行为的识别。实验结果表明,该算法在实际场景下的平均识别准确率达到95%以上。     

一种信号调制识别网络的轻量化设计

神经网络在信号调制识别领域得到了广泛关注和研究。针对现有调制识别算法为提高识别准确率,导致模型尺寸过大、计算时间过长的问题,提出了一种调制识别神经网络的轻量化设计方案。该方案由信号失真校正模块和分类模块两部分组成。其中,信号失真校正模块通过参数估计器提取相位偏移信息,再经参数转换器对相位偏移进行参数校正,保证信号识别精度;分类模块由一维卷积神经网络(One-Dimensional Convolutional Neural Network, 1D-CNN)、选通递归单元(Gated Recurrent Unit, GRU)和高斯衰减层构成,从时间和空间的角度有效提取信号特征,并减少冗余参数量以缩减模型大小。仿真结果表明,所提方案与同精度网络相比,平均识别准确率提升0.21%,计算时间缩减到1/3.4,模型尺寸缩减到1/7.77。     

引入自上向下特征融合的小目标检测算法

针对原始SSD(Single Shot Multibox Detector)算法未充分利用各特征层之间关系导致浅层特征层缺乏小目标语义信息的问题,为了提高对小目标的检测能力,提出了一种结合PANet多尺度特征融合网络和自上向下特征融合路径的TTB-SSD(Top to Bottom SSD)改进算法。首先,使用PANet多尺度特征融合网络对特征进行反复提取,从而获得丰富的多尺度语义信息;然后,使用一种深层特征融合模块将浅层特征层的空间信息传递到深层特征层,进而更准确地对小目标进行定位;最后,为了增强浅层特征层的语义信息,构造了自上向下的特征融合路径,从而强化浅层对小目标检测的准确率。实验结果表明,在PASCAL VOC2007测试集检测的mAP(Mean Average Precision)值达到80.5%,对目标的mAP较原始SSD提高了5.7%,证明了该算法对小目标检测的有效性。     

基于显著性检测的星载嵌入式跟踪系统

随着航天科技的不断发展,计算机视觉算法在卫星上的应用方兴未艾,为了实现更多的功能需求和应对可能的威胁,视觉目标跟踪作为其中基础但具有挑战性的任务更是至关重要。然而,目前已有的目标跟踪算法大多数算法只限于对图像序列进行跟踪。另一方面,受到硬件条件制约,很多优秀的算法因为复杂度较高很少被应用到星载嵌入式系统中。这些目标跟踪算法运行时,通常需要人为地给出目标的边界框。为了自动得到边界框,需要目标检测算法对输入图像进行运动目标检测。本文提出了一种基于显著性检测和相关滤波的单目标检测与跟踪一体化算法,并与嵌入式系统相结合,在搭载的TMS320C6678芯片上达到了2 048 pixel×2 048 pixel分辨率下24 fps的帧率。具体地,检测算法负责对图像进行预处理并获得边界框,然后目标跟踪算法给出目标在后续帧中的位置。为了验证算法在实际跟踪中的有效性,本研究搭建了一个由相机、DSP和云台组成的光学平台并进行了实验验证。在该系统中,DSP自动完成检测、跟踪、驱动云台和再检测任务,达到了很好的检测跟踪效果。