Simple and fast spectrophotometric determination of H2O2 in

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一种新的高光谱遥感图像超像素分割方法

一种新的高光谱遥感图像超像素分割方法

一种新的高光谱遥感图像超像素分割方法
杨洋;刘思樊;童恒建
【期刊名称】《计算机技术与发展》
【年(卷),期】2024(34)5
【摘要】为了解决简单线性迭代聚类算法在高光谱遥感图像超像素分割任务中分割精度较低的问题,提出一种基于多级线性迭代聚类结合改进标签传播算法(LPA)的新的无监督高光谱遥感图像超像素分割方法。

首先,扩充简单线性迭代聚类(SLIC)的适用范围至多通道对高光谱图像进行超像素初分割;然后,对色彩标准差较大的超像素进行多级迭代细致分割,引入基于局部二进制模式的高光谱遥感图像纹理特征提取方法计算高光谱图像纹理特征并融合多段光谱特征计算超像素间相似度以构建带权图网络;最后,改进LPA社区发现方法进行超像素合并,将改进的标签传播算法运用于超像素合并可以得到更加稳定准确的超像素合并效果,提高超像素分割精度。

将该方法与多种方法进行比较,结果表明,该方法对高光谱遥感图像的超像素分割结果更准确,超像素边缘更贴合真实地物边界,能有效改善高光谱遥感图像超像素分割中精度较低的问题。

【总页数】7页(P37-43)
【作者】杨洋;刘思樊;童恒建
【作者单位】中国地质大学(武汉)计算机学院
【正文语种】中文
【中图分类】TP391.4;TN911.73
【相关文献】
1.一种新的图像超像素分割方法
2.一种基于超像素分割的遥感图像道路提取方法
3.一种超像素上Parzen窗密度估计的遥感图像分割方法
4.一种基于超像素分割的遥感图像道路提取方法
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偏最小二乘法中主成分数确定的新方法

偏最小二乘法中主成分数确定的新方法

1.1 分组方法
交互证实方法通常是建立模型的样本分成 g 组 , 每次用其中 (g -1)组的样本建立模型对未参加建
模的样本进行预测 , 用同样方法将所有样本进行预测 , 计算因变量矩阵的剩余残差平方和 PRESS (Predic-
tion Error Sum of Square)作为主成分数的判据 , 这种估计主成分数的方法对矩阵的随机误差的影响不够灵
摘要 :目的 :合理地确定偏最小二乘法中的主成分 数 。 方法 :基 于对应 加权原 理建立 了适用于 矩阵元 素缺损 数 据的 加权偏最小二乘算法 , 将此算法应用于按矩阵元 素分组的 交互证实 (Cross-validation), 根据最大 熵原理采 用 方差平方和 σ2 (自变量矩阵残差的平方和/ 自由度) 作为主成分数的判据 。 结果与结论 :通 过对 Monte-Carlo 法 产 生的多组分分光光度数据进行计算 , 与常规的偏最小 二乘法 相比更加 符合理 论值 , 表 明本算法 较好解 决了偏 最 小二乘法中主成分数的确定问题 。 关键词 :加权偏最小二乘法 ;缺损数据 ;最大熵原理 ;主成分数 中图法分类号 :O 241.5 文献标识码 :A 文章编号 :1001-4160 (2001) 03-237-240
1.2.1 取 k =0
∑ ∑ 1.2.2 计算 σ2 =
x2ij/(p -k), 自由度 f =p -k
n
∑(y0ij -y 0i )2
i =1
n -1
1.2.3 计算 σ2分组
1.2.3.1 按 1.1 方法分组 , 将其中一组元素视为缺损 , 用剩余的数据预测缺损一组元素并计算预示残差 。
采用元素缺损偏最小二乘法计算主成分数的步骤如下 :
首先 , 将数据标准化处理

fastestdet训练

fastestdet训练

fastestdet训练Fastestdet是一款现代化的目标检测框架,它使用轻量化卷积神经网络实现了目标检测的关键技术。

Fastestdet训练是理解和学习该框架的重要步骤,下面将分步骤介绍Fastestdet训练的过程。

1. 数据准备首先,我们需要先准备好数据集,通常是将图片数据和其对应的标注信息整理成训练集、验证集和测试集,要保证数据集的宽高比例一致,可以采用图像增强的方法来扩充数据量,同时还需要生成数据集的类别列表。

2. 预训练模型准备接下来需要准备好预训练模型,可选择在ImageNet等大规模数据集上训练好的模型权重作为基础。

Fastestdet支持多种轻量化的目标检测模型,通过引入特殊设计的骨干网络(如MobileNetV2、EfficientNet 等)来减小模型大小和计算复杂度,不断去除模型中的冗余参数,最终实现模型轻量化。

3. 网络定义与配置Fastestdet提供了丰富的配置选项,包括网络架构、网络结构超参数、训练器类型、学习率、优化器、正则化损失等。

用户可以根据自己的需求进行相应的调整,一般来说,可以采用较小的学习率和高的正则化系数来控制模型的过拟合,并使用优化器方式,如Adam等。

4. 模型训练运行Fastestdet的训练程序,可以通过命令行输入相关参数也可以在代码中指定,训练实施中需要慎重选择超参数,并通过观察训练指标、可视化损失函数等监测训练的质量和速度,训练时间长短视数据集大小和配置而定,一般数小时到数日不等。

5. 模型评估与测试训练完成后,需要对模型进行评估,使用验证集计算模型的性能指标,如准确率、召回率、AP 性能等,并进行模型测试,使用测试集计算模型的预测精度、精度和F值等指标,验证模型是否满足需求。

可以通过可视化的方式展示模型的检测效果。

总之,Fastestdet的训练过程需要保证数据集、预训练模型、网络架构和超参数的准备充分,同时训练过程需要调整合适的学习率、正则化系数和损失函数等参数,实时监测指标,并认真评估模型的性能和稳定性。

稀疏距离扩展目标自适应检测及性能分析

稀疏距离扩展目标自适应检测及性能分析

第39卷第7期自动化学报Vol.39,No.7 2013年7月ACTA AUTOMATICA SINICA July,2013稀疏距离扩展目标自适应检测及性能分析魏广芬1苏峰2简涛2摘要在球不变随机向量杂波背景下,研究了稀疏距离扩展目标的自适应检测问题.基于有序检测理论,利用协方差矩阵估计方法,分析了自适应检测器(Adaptive detector,AD).其中,基于采样协方差矩阵(Sample covariance matrix,SCM)和归一化采样协方差矩阵(Normalized sample covariance matrix,NSCM),分别建立了AD-SCM和AD-NSCM检测器.从恒虚警率特性和检测性能综合来看,AD-NSCM的性能优于AD-SCM和已有的修正广义似然比检测器.最后,通过仿真实验验证了所提方法的有效性.关键词稀疏距离扩展目标,自适应检测,采样协方差矩阵,归一化采样协方差矩阵,有序统计量引用格式魏广芬,苏峰,简涛.稀疏距离扩展目标自适应检测及性能分析.自动化学报,2013,39(7):1126−1132DOI10.3724/SP.J.1004.2013.01126Sparsely Range-spread Target Detector and Performance AssessmentWEI Guang-Fen1SU Feng2JIAN Tao2Abstract In the background where the clutter is modeled as a spherically invariant random vector,the adaptive detection of sparsely range-spread targets is addressed.By exploiting the order statistics and the covariance matrix estimators,the adaptive detector(AD)is assessed.Herein,the detectors of AD-SCM and AD-NSCM are proposed based on the sample covariance matrix(SCM)and normalized sample covariance matrix(NSCM),respectively.In terms of constant false alarm rate properties and detection performance,the AD-NSCM outperforms the AD-SCM and the existing detector of modified generalized likelihood ratio.Finally,the performance assessment conducted by simulation confirms the effectiveness of the proposed detectors.Key words Sparsely range-spread target,adaptive detection(AD),sample covariance matrix(SCM),normalized sample covariance matrix(NSCM),order statisticsCitation Wei Guang-Fen,Su Feng,Jian Tao.Sparsely range-spread target detector and performance assessment.Acta Automatica Sinica,2013,39(7):1126−1132低分辨率雷达的目标尺寸小于距离分辨率,这种目标常称之为点目标[1].通过采用脉冲压缩技术,高分辨率雷达能够在空间上把一个目标分解成许多散射点[2−3],目标回波在雷达径向上的多个散射点分布在不同的距离分辨单元中,形成距离扩展目标[4].在许多情况下,距离扩展目标的散射点密度是稀疏的,可将这种目标简称为“稀疏距离扩展目标”.目前,高斯背景下的距离扩展目标检测已取得一定进收稿日期2011-12-28录用日期2012-08-27Manuscript received December28,2011;accepted August27, 2012国家自然科学基金(61174007,61102166),山东省优秀中青年科学家科研奖励基金(BS2010DX022)资助Supported by National Natural Science Foundation of China (61174007,61102166)and the Scientific Research Founda-tion for Outstanding Young Scientists of Shandong Province (BS2010DX022)本文责任编委韩崇昭Recommended by Associate Editor HAN Chong-Zhao1.山东工商学院信息与电子工程学院烟台2640052.海军航空工程学院信息融合技术研究所烟台2640011.School of Information and Electronics,Shandong Institute of Business and Technology,Yantai2640052.Research Insti-tute of Information Fusion,Naval Aeronautical and Astronauti-cal University,Yantai264001展,其中,针对估计参数空间过大的问题,文献[5]提出了一种无需辅助数据的检测器,简称为修正的广义似然比检验(Modified generalized likelihood ratio test,MGLRT)检测器,其在高斯背景下是有界恒虚警率(Constant false alarm rate,CFAR)的.但在高距离分辨率的条件下,背景杂波呈现出诸多的非高斯特性[1],高斯背景下获得的检测器已无法有效检测目标.在非高斯背景下,文献[6]研究了已知杂波协方差矩阵条件下的距离扩展目标检测;而通过利用不含目标信号的辅助数据,文献[7]和文献[8]分别针对距离扩展目标和距离–多普勒二维分布式目标展开了自适应检测研究.需要指出的是,以上自适应检测方法[7−8]都是基于辅助数据的.当无法获得满足条件的辅助数据时,实现非高斯背景下距离扩展目标的自适应检测具有重要意义.文献[9]基于迭代估计方法实现了自适应检测,但迭代估计计算量较大,如何在保证性能的同时减小计算量,也是值得探讨的问题.7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1127稀疏距离扩展目标的散射点只占据目标距离扩展范围的一部分,与含纯杂波的距离分辨单元幅值相比,含目标散射点的距离分辨单元幅值明显更高,这就为实现目标的自适应检测提供了条件.本文针对非高斯杂波中的稀疏距离扩展目标检测问题,在不需要辅助数据的条件下,首先,采用有序统计检测理论和协方差矩阵估计方法,粗略估计目标散射点单元集合;然后,进一步利用适当估计方法获得协方差矩阵的精确估计,设计了自适应检测器(Adaptivedetector,AD),并通过仿真实验验证了检测器的有效性.1问题观测数据来源于N个阵元的线性阵列天线,需跨过K个可能存在目标的距离分辨单元z t,t=1,···,K,判决一个距离扩展目标的存在与否.假设可能的目标完全包含在这些数据中,并且忽略目标距离走动的问题.在杂波背景下,待解决的检测问题可由以下二元假设检验公式来表达.H0:z t=c t,t=1,···,KH1:z t=αt p+c t,t=1,···,K(1)其中,p=(1,e jφ,e j2φ,···,e j(N−1)φ)T/√N表示已知单位导向矢量,即p H p=1,这里(·)H表示共轭转置,φ表示相移常量,(·)T表示转置,αt,t=1,···,K是反映目标幅度的未知参数.非高斯杂波可用球不变随机向量建模[10],由于中心极限定理在较小区域的杂波范围内仍是有效的,球不变随机向量可以表示为两个分量的乘积:一个是反映受照区域反射率的时空“慢变化”纹理分量,另一个是变化“较快”的“散斑”高斯过程.那么,距离分辨单元t的N维杂波向量c t为c t=√τt·ηt,t=1,···,K(2)其中,ηt=(ηt(1),ηt(2),···,ηt(N))T是零均值协方差矩阵为Σ的复高斯随机向量,非负的纹理分量τt与ηt相互独立,其用来描述杂波功率在不同距离分辨单元间的起伏,且服从未知分布fτ.另外,杂波协方差矩阵结构Σ可以表示为Σ=E{ηt ηHt}(3)距离扩展目标完全包含在K个距离分辨单元的滑窗中,假设一个等效散射点最多只占据一个距离分辨单元,即目标等效散射点数目与其所占据的距离分辨单元数目是相等的.通常目标散射点是稀疏分布的,与含纯杂波的距离分辨单元相比,有散射点的距离分辨单元幅值往往更高.含目标等效散射点的距离分辨单元数目用h0表示,而其所对应的距离分辨单元下标用集合Θh表示.为了简化分析,假设h0是已知的,若其未知,可利用模型阶数选择方法获得合适的估计值[11].如前所述,对距离扩展目标的检测只需在距离分辨单元Θh内进行,式(1)表示的假设检验问题可以进一步表示为H0:z t=c t,t∈ΘhH1:z t=αt p+c t,t∈Θh(4)在分布fτ未知的条件下,距离分辨单元t的杂波是条件高斯的,其相应的方差为τt.由于幅度αt 未知而向量p已知,针对不同假设,观测向量z t的联合概率密度可表示为t∈Θhf(z t|τt,H0)=t∈Θh1πNτN t det(Σ)×exp[−1τtz HtΣ−1z t](5)t∈Θhf(z t|αt,τt,H1)=t∈Θh1πNτN t det(Σ)×exp−1τt(z t−αt p)HΣ−1(z t−αt p)(6)其中,det(·)表示方阵的行列式.2检测器实现在未知集合Θh的条件下,为了获得估计的参数集合ˆΘh,这里先假设已知矩阵Σ.由于未知参数α={αt|t∈Θh}和τ={τt|t∈Θh},可利用广义似然比检验(GLRT)原理进行检测器设计[12].在矩阵Σ已知的条件下,根据GLRT原理,对于似然比中的未知参数,可用最大似然(Maximum likelihood,ML)估计进行替换,即考虑如下二元判决:maxτmaxαt∈Θhf(z t|αt,τt,H1)maxτt∈Θhf(z t|τt,H0)H1><H0T0(7)在H1假设下求得αt的ML估计为[13]ˆαt=p HΣ−1z tp HΣ−1p(8)将ˆαt代入式(7)后,可进一步在不同假设条件下求得τt的ML估计:H0:ˆτt=1Nz HtΣ−1z t(9) H1:ˆτt=1N(z t−ˆαt p)HΣ−1(z t−ˆαt p)(10)1128自动化学报39卷将式(8)∼(10)代入式(7)中,可得自然对数形式的GLRT判决为λ1=−Nt∈Θh0ln1−|p HΣ−1z t|2(z H tΣ−1z t)(p HΣ−1p)H1><H0T1(11)令w t=|p HΣ−1z t|2(z H tΣ−1z t)(p HΣ−1p)(12)值得注意的是,w t的结构类似于一个归一化匹配滤波器(权向量为Σ−1p)[14].可以看出,式(12)的分子部分p HΣ−1z t等效于给定距离分辨单元观测z t经过匹配滤波后的结果[14].而分母部分的两项z HtΣ−1z t和p HΣ−1p起到了归一化处理的作用,因此,w t是距离单元观测z t经过匹配滤波后模平方的归一化,可以看作是距离单元观测经归一化匹配滤波后的能量.由于目标完全包含在K个单元的距离滑窗中,且距离扩展目标等效散射点所占据的距离分辨单元幅值往往大于纯杂波的距离分辨单元幅值,因此,可通过归一化能量w t,t=1,···,K中最大的h0个值来确定未知集合ˆΘh.实际应用中协方差矩阵结构Σ往往是未知的,为了确定集合ˆΘh,需先对协方差矩阵结构进行估计.如前所述,纹理分量τt的分布fτ是未知的,因此,协方差矩阵结构Σ的ML估计不能通过期望最大化得到[13].本文考虑两种协方差矩阵估计方法.一种是高斯背景下的经典采样协方差矩阵(Sample covariance matrix,SCM),其可以表示为ˆΣSCM =1RRr=1y r y Hr(13)其中,y r,r=1,···,R表示可用于估计的R个数据.当R≥N时,SCM是以概率为1非奇异的,同时也是正定Hermitian矩阵[12].另外,在非高斯背景下,也常常利用辅助数据获得归一化采样协方差矩阵(Normalized sample covariance matrix, NSCM),可以表示为ˆΣNSCM =1RRr=1Ny Hry ry r y Hr(14)与文献[9]类似,针对稀疏距离扩展目标的自适应检测,AD检测器的实现分为如下三个步骤.步骤1.基于SCM或NSCM方法,利用K个待检测单元的观测数据获得初步估计矩阵ˆΣ1,进一步将估计矩阵ˆΣ1代入式(12)中,可得到初步估计ˆw(1)t.对ˆw(1)t,t=1,···,K按升序排列,可得如下有序序列:0≤ˆw(1)(1)≤···≤ˆw(1)(t)≤···≤ˆw(1)(K)≤1(15)步骤2.考虑有序序列的K−h0个最小值(即ˆw(1)(t),t=1,···,K−h0),并用Ωh表示相应距离分辨单元下标的集合.为了获得可逆的估计矩阵,需满足K−h0≥N.根据之前的分析,集合Ωh中的距离分辨单元极可能只包含纯杂波,故可以利用Ωh0对应的距离分辨单元观测值,精确估计矩阵Σ,并采用与初步估计中相同的估计方法(SCM或NSCM),进一步获得较为精确的协方差矩阵结构估计ˆΣ2.利用ˆΣ2代替式(12)中的未知矩阵Σ,得到w t的精确估计值用ˆw(2)(t)表示.对ˆw(2)(t),t=1,···,K按升序排列,可得如下有序序列:0≤ˆw(2)(1)≤···≤ˆw(2)(t)≤···≤ˆw(2)(K)≤1(16)考虑有序序列的h0个最大值(即ˆw(2)(t),t=K−h0+1,···,K),并用ˆΘh表示相应距离分辨单元下标的集合.步骤3.将距离分辨单元下标的集合ˆΘh和协方差矩阵的精确估计ˆΣ2代入式(11)中,获得自适应检测器AD的检测统计量可以表示为λ2=−NKt=K−h0+1ln(1−ˆw(2)(t))=−Nt∈ˆΘhln[1−|p HˆΣ−12z t|2(z H tˆΣ−12z t)(p HˆΣ−12p)]H1><H0T2(17)需要说明的是,在存在目标散射点的情况下,步骤1的初步估计矩阵不可避免地引入了估计误差,虽然这种误差在步骤2中得到了一定的抑制,但它仍将影响后续精确估计矩阵的精度.在存在辅助数据的前提下,为了获得良好的检测性能,一般要求辅助数据个数不小于阵元数N的两倍[15].在待检测单元数K不变的情况下,可利用的纯杂波单元数(K−h0)将随着散射点个数的增加而减小,因此,此处需等价满足(K−h0)≥2N.进一步考虑到步骤1中散射点单元所引起的估计误差,实际应用中可能需要更大的(K−h0)/N值以弥补步骤1中导致的性能损失,具体取值将在接下来的性能评估中给出.由于采用不同的估计方法会获得不同的自适应检测器,在这里,我们分别将采用SCM和NSCM估计方法获得的相应检测器简称为AD-SCM和AD-NSCM.由于本文的自适应检测器中ˆΘh和ˆΣ2均受到协方差矩阵估计方法的影响,因此,有必要评估自适应距离扩展目标检测器的CFAR特性,这将在接下来的性能分析中进行.7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1129 3性能评估本节对稀疏距离扩展目标自适应检测器AD-SCM和AD-NSCM进行了CFAR特性和检测性能评估,并与无需辅助数据的MGLRT检测器[5]进行了比较分析.利用Toeplitz矩阵对Σ进行建模,具体采用指数相关结构,在杂波一阶相关系数为γ的条件下,第m行第n列的矩阵元素为[Σ]m,n=γ|m−n|,1≤m,n≤N(18)利用Γ分布对纹理分量的分布fτ进行建模:fτ(x)=LbLΓ(L)x L−1e−(L b)x,x≥0(19)其中,Γ(·)是Gamma函数,均值b代表了平均杂波功率;参数L表示分布fτ的非高斯拖尾特征,具体来说,随着L的减小,函数fτ的拖尾将增大,而杂波的非高斯尖峰程度将增大.采用蒙特卡罗方法计算相应的检测概率P d和虚警概率P fa.根据前面的假设,在所有距离分辨单元均存在杂波的条件下,目标等效散射点只存在于h0个距离分辨单元中,且一个等效散射点最多只占据一个距离分辨单元.在所有K个距离分辨单元上,每个单元的目标或杂波的平均功率分别用σ2s 或σ2c表示.对于存在目标散射点的距离分辨单元(t∈Θh),用零均值独立复高斯变量对等效散射点建模,即目标散射点幅度在不同距离分辨单元间瑞利起伏;相应的方差表示为E{|αt|2}=εtσ2sK(εt表示单个散射点占目标总能量的比率).由|αt|2,t=1,···,K的独立性可知,检测性能与散射点在待检测单元中的位置无关.几种典型的散射点分布模型如表1所示.其中,Model 1中的目标能量等量分布在h0个距离分辨单元范围内;Model2∼4中某个距离分辨单元具有大部分能量,而剩下的能量在其余距离分辨单元中等量分布.Model5相当于点目标,是Model2∼4的极端特例.输入信杂比(Signal to clutter ratio,SCR)定义为K个距离分辨单元内的平均信杂比,即SCR=σ2sσ2cp HΣ−1p(20)为了便于CFAR特性评估,需针对杂波功率水平(对应于b)、尖峰程度(对应于L)和协方差矩阵结构(对应于γ)的不同情况,分析检测器的检测阈值与虚警概率间的关系.相关研究表明[9],在非高斯杂波下MGLRT是非CFAR的,即高斯背景下获得的MGLRT检测器不适用于非高斯背景.为了便于比较,在K=15,h0=3,N=2,L=0.1,1,γ=0,0.5,0.9和b=1,10条件下,图1和图2分别给出了AD-SCM和AD-NSCM的检测阈值(De-tection threshold)与虚警概率(False alarm prob-ability)的关系曲线.图1表明,AD-SCM检测器对杂波协方差矩阵结构和功率水平具有自适应性,但对杂波尖峰不具有适应能力.而图2说明,AD-NSCM对杂波尖峰和杂波功率水平具有CFAR特性,但其检测阈值仍受协方差矩阵结构的轻微影响.综合来看,AD-NSCM的检测阈值在不同杂波条件下的鲁棒性更好.图1K=15,N=2,L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3时,AD-SCM的CFAR特性曲线Fig.1CFAR curves of AD-SCM for K=15,N=2, L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3表1不同散射点分布模型的εt值Table1Values ofεt for typical scatters models目标距离分辨单元12···h0Model11h01h01h01h0Model20.50.5h0−10.5h0−10.5h0−1Model30.90.1h0−10.1h0−10.1h0−1Model40.990.01h0−10.01h0−10.01h0−1Model510001130自动化学报39卷图2K=15,N=2,L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3时,AD-NSCM的CFAR特性曲线Fig.2CFAR curves of AD-NSCM for K=15,N=2, L=0.1,1,γ=0,0.5,0.9,b=1,10,h0=3接下来分析AD检测器的检测性能.图3给出了MGLRT、AD-SCM和AD-NSCM的性能曲线.可以看出,AD-NSCM的检测性能最优,MGLRT 其次,而AD-SCM的检测性能最差.从以上分析综合来看,与MGLRT和AD-SCM相比,AD-NSCM 在CFAR特性和检测性能方面均具有一定的优势.下文将重点对AD-NSCM的检测性能展开分析.图3K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4, Model1时,MGLRT,AD-SCM和AD-NSCM的检测性能曲线Fig.3Detectability curves of MGLRT,AD-SCM and AD-NSCM for K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4,Model1首先,针对表1中5种不同模型,图4评估了散射点能量分布对AD-NSCM检测性能的影响.可以看出,随着距离分辨单元间散射点能量分布的均匀性增加,检测性能逐渐改善.为了便于分析,下文中主要针对Model1模型.另外,在不同的散射点密度条件下,图5分析了AD-NSCM检测性能.由图5可知,当h0<7时,协方差矩阵结构的估计误差较小,其对检测性能的影响也较小,当散射点数目增加时,检测器可利用的目标能量增大,AD-NSCM的检测性能得到一定的改善.当h0≥7时,协方差矩阵结构的估计误差影响较大,当散射点数目增加时,进行矩阵估计所用的观测数据量减少,估计矩阵的误差加大,导致较为严重的检测损失,且损失量高于增加散射点数目所获得的性能增益,并引起总检测性能的退化.综合来看,当h0<K/2时,AD-NSCM 的检测性能较好.图4K=15,N=2,L=1,γ=0.9,h0=3,P fa=10−4, Model1∼5对应的AD-NSCM检测性能曲线Fig.4Detectability curves of AD-NSCM for K=15, N=2,L=1,γ=0.9,h0=3,P fa=10−4,Model1∼5图5K=15,N=2,L=1,γ=0.9,P fa=10−4,Model 1时,h0=2,4,6,7,8,10,12对应的AD-NSCM检测性能曲线Fig.5Detectability curves of AD-NSCM for K=15, N=2,L=1,γ=0.9,P fa=10−4,Model1,h0=2,4,6,7,8,10,12在不同杂波尖峰条件下,图6给出了AD-NSCM检测性能.由图6可知,随着L的减小,杂波尖峰程度增大,AD-NSCM的检测性能有所改善.图7给出了不同杂波相关性对应的检测性能曲线.可以看出,杂波一阶相关系数的变化对检测性能几乎没有影响,说明AD-NSCM对杂波相关性7期魏广芬等:稀疏距离扩展目标自适应检测及性能分析1131的变化具有良好适应性.图8进一步分析了阵元数变化(N =2,4,6,8)对AD-NSCM 检测性能的影响.可以看出,在阵元数N ≤4的条件下,当N 增加时,检测性能有所提高;而在N >4的条件下,当N 增加时,检测性能反而有所下降.可能的原因是,当进行矩阵估计所用的观测数据量不变时(R =K −h 0=12),N 的增加会导致协方差矩阵维数变大,待估参量的数目增加,估计精度下降,并直接引起检测性能的退化.综合来看,当K −h 0≥3N 时,AD-NSCM 的检测性能较好.图6K =15,N =2,γ=0.9,h 0=3,P fa =10−4,Model 1时,L =0.5,1,2,10对应的AD-NSCM 检测性能曲线Fig.6Detectability curves of AD-NSCM for K =15,N =2,γ=0.9,h 0=3,P fa =10−4,Model 1,L =0.5,1,2,10图7K =15,N =2,L =1,h 0=3,P fa =10−4,Model 1时,γ=0,0.5,0.9对应的AD-NSCM 检测性能曲线Fig.7Detectability curves of AD-NSCM for K =15,N =2,L =1,h 0=3,P fa =10−4,Model 1,γ=0,0.5,0.94结论本文研究了非高斯杂波中的稀疏距离扩展目标检测问题.在不需要辅助数据的条件下,基于SCM 和NSCM 估计器,分别建立了AD-SCM 和AD-NSCM 检测器.从CFAR 特性和检测性能综合来看,AD-NSCM 的性能优于AD-SCM 和MGLRT.对于典型的非高斯杂波环境,随着杂波尖峰程度的增大,AD-NSCM 的检测性能得到提高,且其对杂波相关性的变化也具有良好适应性.另外,对于h 0<K/2的稀疏距离扩展目标,在K −h 0≥3N 条件下,AD-NSCM 能获得满意的检测性能.需要说明的是,与文献[9]中的检测器相比,AD-NSCM 虽然减小了计算量,但也牺牲了部分CFAR 特性.如何减小检测器对散射点信息的依赖性,是下一步需要研究的问题.图8K =15,L =1,γ=0.9,h 0=3,P fa =10−4,Model 1时,N =2,4,6,8对应的AD-NSCM 检测性能曲线Fig.8Detectability curves of AD-NSCM for K =15,L =1,γ=0.9,h 0=3,P fa =10−4,Model 1,N =2,4,6,8References1Zhou Yu,Zhang Lin-Rang,Liu Xin,Liu Nan.Adap-tive detection based on Bayesian approach in heteroge-neous environments.Acta Automatica Sinica ,2011,37(10):1206−1212(周宇,张林让,刘昕,刘楠.非均匀杂波环境下基于贝叶斯方法的自适应检测.自动化学报,2011,37(10):1206−1212)2He Chu,Liu Ming,Feng Qian,Deng Xin-Ping.PolIn-SAR image classification based on compressed sensing and multi-scale pyramid.Acta Automatica Sinica ,2011,37(7):820−827(何楚,刘明,冯倩,邓新萍.基于多尺度压缩感知金字塔的极化干涉SAR 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distributed targets.IEEE Transac-tions on Aerospace and Electronic Systems,2008,44(2): 678−6969Jian Tao,Su Feng,He You,Li Bing-Rong,Gu Xue-Feng.Distributed target detection without secondary data.Acta Aeronautica et Astronautica Sinica,2011,32(8): 1542−1547(简涛,苏峰,何友,李炳荣,顾雪峰.无需辅助数据的分布式目标自适应检测器.航空学报,2011,32(8):1542−1547)10Jian T,He Y,Su F,Qu C W,Gu X F.Performance charac-terization of two adaptive range-spread target detectors for unwanted signal.In:Proceedings of the9th International Conference on Signal Processing.Beijing,China:IEEE, 2008.2326−232911Gini F,Bordoni F,Farina A.Multiple radar targets de-tection by exploiting induced amplitude modulation.IEEE Transactions on Signal Processing,2004,52(4):903−913 12Kay S M.Fundamentals of Statistical Signal Processing, vol.2:Detection Theory.New York:Prentice-Hall,1998.196−26013Kay S M.Fundamentals of Statistical Signal Processing, vol.1:Estimation Theory.New York:Prentice-Hall,1993.157−21814Kraut S,Scharf L L,McWhorter L T.Adaptive subspace detectors.IEEE Transactions on Signal Processing,2001, 49(1):1−1615Reed I S,Mallett J D,Brennan L E.Rapid convergence rate in adaptive arrays.IEEE Transactions on Aerospace and Electronic Systems,1974,10(6):853−863魏广芬博士,山东工商学院副教授.2005年获得大连理工大学机械电子工程专业工学博士学位.主要研究方向为传感器检测与信号处理理论及技术.本文通信作者.E-mail:*******************(WEI Guang-Fen Ph.D.,associateprofessor at Shandong Institute of Busi-ness and Technology.She received her Ph.D.degree from Dalian University of Technology in2005.Her research in-terest covers theory and technology of sensor detection and signal processing.Corresponding author of this paper.)苏峰博士,海军航空工程学院信息融合技术研究所讲师.主要研究方向为雷达信号检测与信号处理.E-mail:*****************(SU Feng Ph.D.,lecturer at NavalAeronautical and Astronautical Univer-sity.His research interest covers radarsignal detection and signal processing.)简涛博士,海军航空工程学院信息融合技术研究所讲师.主要研究方向为雷达信号检测与信号处理.E-mail:********************.cn(JIAN Tao Ph.D.,lecturer at NavalAeronautical and Astronautical Univer-sity.His research interest covers radarsignal detection and signal processing.)。

fastestdet训练

fastestdet训练

fastestdet训练介绍fastestdet是一个用于物体检测任务的模型,其目标是在给定一张图像的情况下,准确地检测和定位图像中的物体。

fastestdet的目标是实现最快的检测速度,同时保持较高的检测准确率。

本文将探讨fastestdet训练的相关内容,包括其实现原理、训练过程和应用领域等。

实现原理fastestdet基于深度学习的目标检测方法,其中最常用的是基于卷积神经网络(Convolutional Neural Network,CNN)的方法。

CNN是一种用于图像处理任务的深度学习模型,通过多层卷积和池化层提取图像的特征,并通过全连接层进行分类或回归。

fastestdet使用了一种轻量级的CNN架构,以达到更快的检测速度。

其核心思想是通过减少模型的计算复杂度和参数量来提高速度。

为此,fastestdet采用了以下几种策略:1.剪枝:通过对已训练好的模型进行参数剪枝,将参数量减少到最小。

这样可以减少模型的计算量,并且降低了模型在推理阶段的内存消耗。

2.蒸馏:使用蒸馏技术将大型模型的知识传递给小型模型,从而提高小型模型的性能。

这样可以在保持速度的同时,不显著降低模型的准确率。

3.混合精度训练:使用混合精度训练技术,将模型的参数在训练过程中以低精度进行计算,并最终以高精度进行更新。

这样可以减少内存带宽和算力的需求,进一步提高训练速度。

训练过程fastestdet的训练过程主要包括数据准备、模型选择、超参数设置和模型训练等步骤。

1.数据准备:为了训练fastestdet模型,需要准备一组包含物体标注信息的图像数据集。

这些标注信息一般包括物体的类别和边界框的位置。

为了提高训练效果,可以使用数据增强技术对图像进行随机变换,如缩放、平移和翻转等操作。

2.模型选择:根据任务的需求和计算资源的限制,选择适合的fastestdet模型。

fastestdet提供了多种模型架构,可以根据需要选择对应的模型。

超快光学超快光谱

超快光学超快光谱

Chopper
Chopped excite pulse train
The excite pulse periodically changes the sample absorption seen by the probe pulse.
Probe pulse train
Lock-in detector
What’s going on in spectroscopy measurements
The excite pulse(s) excite(s) molecules into excited states, which changes the medium’s absorption coefficient and refractive index.
DT(t) / T0 Da0 exp(–t /tex) L
0
Delay, t
Modeling excite-probe measurements
(cont’d)
3
Excite transition
2 Probe transition
1
0
More complex decays occur if intermediate states are populated or if the motion is complex. Imagine probing an intermediate transition, whose states temporarily fill with molecules on their way back down to the ground state:
Ultrafast laser spectroscopy: Why
Most events that occur in atoms and molecules occur on fs and ps time scales because the length scales are very small.

等离子体发射光谱仪英文

等离子体发射光谱仪英文

等离子体发射光谱仪英文The plasma emission spectrometer is a pretty cool tool, you know? It's like a magic eye that can see what's happening inside a plasma. You just zap the plasma with some light, and it spits out a spectrum of colors that tell you what elements are there and how they're behaving.Imagine it like a party where everyone's wearing a different-colored shirt. The spectrometer is like the DJ who shines a spotlight on everyone and says, "Hey, you're wearing blue!" or "You're in green!" It's a way to identify who's who in the crowd.But it's not just about colors. This machine can also tell you how intense the colors are, like how loud someone's shouting at the party. That gives you a clue about how active or excited the elements are in the plasma.Sometimes, you might want to know if there's a specific person at the party, like your friend in a red shirt. Thespectrometer can help you look for that red color in the spectrum and see if it's there. If it's not, then you know your friend's not at the party – or in this case, that element isn't in the plasma.This tool is seriously handy for scientists studyingall sorts of things, like how stars make light or what happens in a lightning bolt. It's like having a superpower to see what's really going on behind the scenes of nature's coolest parties.。

【高中生物】华人学者开发更精细的肺癌成像法

【高中生物】华人学者开发更精细的肺癌成像法

【高中生物】华人学者开发更精细的肺癌成像法肺癌患者都知道,精确的医学成像可以帮助外科医生消除肿瘤,保留健康的组织。

目前的技术依靠压在病人胸部的扫描设备,胸部压缩可能产生不适感,并且产生的图像,处理起来是昂贵的,可能无法提供肿瘤部位的最准确的描述。

延伸阅读:pnas:抑制肺癌的“分子刹车”。

最近,德州大学阿灵顿分校(UTA)和华盛顿大学的研究人员正在努力开发一种解决方案。

他们开发了一种新的个性化呼吸运动系统,该系统使用数学模型捕捉患者肺部的图像,并提供受损肿瘤的更清晰、更准确的图像。

这项工作是由美国国家科学基金会一项为期三年、250000美元的基金资助支持的,有望带来改进的、更精确的放射疗法。

uta工业、制造与系统工程系的助理教授和数据分析专家王守毅(音译,shouyiwang),在该项目的首席研究员,王博士2021年毕业于哈尔滨工业大学获控制科学和工程学学士学位,2021年在荷兰delft科技大学获系统和控制工程硕士学位,在rutgersuniversity-newbrunswick获工业与系统工程博士学位。

曾先后在美国罗格斯大学、华盛顿大学担任研究助理、研究科学家,8月至今在德克萨斯大学阿灵顿分校担任助理教授。

这种由王博士开发的方法监控呼吸门控或患者一个接一个呼吸的操作,并使用收集的数据在胸部放松阶段将一束辐射集中在目标区域,这可以提供癌症部位的最佳图像。

王博士说:“我们将开发一种强大的新数学模型,考虑不同的因素,考虑到所有的主要变量,并预测性能和特定患者的最佳方法。

呼吸门控是一种现成的技术,但它一直没有得以被人们接受,用于放射治疗中管理呼吸运动。

我们提供证据表明,它可以更好地被利用,它可以更好地实施,并且是符合成本效益的。

”EVOS新显微镜细胞成像系统的详细信息和报价>>>王博士的研究有三个目标:1.创建一个数学模型,预测患者将如何从呼吸门控中受益。

该模型将使用华盛顿大学收集的数据,并将考虑到医生的经验和先验知识。

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Talanta66(2005)86–91Simple and fast spectrophotometric determination of H2O2inphoto-Fenton reactions using metavanadateRaquel F.Pupo Nogueira∗,Mirela C.Oliveira,Willian C.PaterliniUNESP–S˜a o Paulo State University,Institute of Chemistry of Araraquara,P.O.Box355,14801-970Araraquara,SP,BrazilReceived20May2004;received in revised form29September2004;accepted5October2004Available online23November2004AbstractThis work proposes a spectrophotometric method for the determination of hydrogen peroxide during photodegradation reactions.The method is based on the reaction of H2O2with amonium metavanadate in acidic medium,which results in the formation of a red-orange color peroxovanadium cation,with maximum absorbance at450nm.The method was optimized using the multivariate analysis providing the minimum concentration of vanadate(6.2mmol L−1)for the maximum absorbance signal.Under these conditions,the detection limit is 143␮mol L−1.The reaction product showed to be very stable for samples of peroxide concentrations up to3mmol L−1at room temperature during180h.For higher concentrations however,samples must be kept refrigerated(4◦C)or diluted.The method showed no interference of Cl−(0.2–1.3mmol L−1),NO3−(0.3–1.0mmol L−1),Fe3+(0.2–1.2mmol L−1)and2,4-dichlorophenol(DCP)(0.2–1.0mmol L−1).When compared to iodometric titration,the vanadate method showed a good agreament.The method was applied for the evaluation of peroxide consumption during photo-Fenton degradation of2,4-dichlorophenol using blacklight irradiation.©2004Elsevier B.V.All rights reserved.Keywords:Hydrogen peroxide;Vanadate;Photo-Fenton;2,4-Dichlorophenol;Spectrophotometry;Degradation1.IntroductionHydrogen peroxide is a versatile chemical and strong ox-idant,with a standard electrode potential of1.763V at pH0 (Eq.1)[1].H2O2+2H++2e–→2H2O,E◦=1.763V(1) While main industrial applications of H2O2are bleaching of textiles and paper,important environmental applications are the removal of inorganic and organic pollutants from wastewater.The use of H2O2as•OH generating agent in advanced oxidation processes(AOPs)such as ozona-tion(O3/H2O2/UV)[2],hydrogen peroxide photolysis (UV/H2O2)[3]and Fenton processes(Fe2+/H2O2)[4] improves its effectiveness,due to the higher oxidizing power of•OH species(E◦=2.730V for•OH,H+/H2O)[5].∗Corresponding author.Tel.:+551633016606;fax:+551633227932.E-mail address:nogueira@iq.unesp.br(R.F.P.Nogueira).In the last decades,the AOPs have been intensively studied for the application in the treatment of water and wastewaters, and remediation of contaminated soils.They are considered good alternatives to conventional treatment processes due to its ability to degrade a great variety of organic pollutants [6–8].Among AOPs,the Fenton and photo enhanced Fenton re-action(photo-Fenton process),have attracted great interest in the last years.Based on the decomposition of H2O2catalyzed by Fe2+(Eq.2),they are attractive for industrial application due to its high oxidation power,simplicity of operation and low costs especially when solar light is applied for regener-ation of Fe2+.In the established cycle additional hydroxyl radicals are generated(Eq.3)[9,10]:Fe2++H2O2→Fe3++•OH+OH–(2) FeOH2++h␯→Fe2++•OH(3) The destruction of organic contaminants using ferrioxalate as source of iron in photo-Fenton processes has been success-0039-9140/$–see front matter©2004Elsevier B.V.All rights reserved. doi:10.1016/j.talanta.2004.10.001R.F.P.Nogueira et al./Talanta66(2005)86–9187fully applied also under solar irradiation since it can absorbradiation up to550nm,employing considerable portion ofthe solar spectrum[11–14].The residual peroxide concentration during degradationof organic compounds in AOPs is a very important parame-ter to evaluate.In Fenton and photo-Fenton processes,whenH2O2is completely consumed,which can happen in a veryshort time depending on the organic matter concentration,thedegradation reaction practically stops making new additionsof the oxidant necessary[12].On the other hand,it can alsoact as•OH scavenger when high concentrations are present,hindering the photodegradation reaction due to the lower ox-idation power of the formed radical HO2•:H2O2+•OH→HO2•+H2O(4) Different methods have been used to measure H2O2inAOPs during degradation of organic compounds.Amongthem,the most commonly used in photo-Fenton processesis the iodometric titration[15–17].Spectrophotometricmethods employing titanium sulfate or oxalate and N,N-diethyl-p-phenylenediamine(DPD)are also often reportedin recent studies dealing with photo-Fenton degradation oforganic contaminants[18,19].While some methods suchas DPD use high cost reagents,the iodometric titrationis subjected to errors due to volatilization and hydrolysisof I2,and air oxidation of I−,besides of demandinglonger time than a spectrophotometric determination.Thepermanganate titration is considered a reliable methodfor determination of H2O2.However,it is not possibleto use the method in photo-Fenton reactions becauseFe2+reacts with permanganate interfering in the peroxidedetermination.The spectrophotometric determination ofI3−generated in the reaction of I−and H2O2has been alsoreported[20].However,the absorption maximum of I3−at λ=351nm limits its application in samples showing high absorbance in this region,frequently observed in the case ofwastewaters.Kosaka and co-workers[21]have compared differentmethods of H2O2determination for the evaluation of AOPand found that thefluorimetric method is the most sensitive.Although various methods can reach very low detectionlimits,in the range of0.77␮mol L−1(DPD method)to29␮mol L−1(titanium colorimetric method),what is impor-tant for determination of peroxide in natural waters,the de-tection limit should not be decisive for the choice of a methodfor H2O2measurement in AOP,since the concentrations usedin these processes are usually in the range of milimol per liter.A fast,simple and low cost method can be very advantageousfor the rapid determination of H2O2during photodegra-dation reactions,allowing the evaluation and optimizationof AOPs.The formation of a red-orange color peroxovanadiumcation in the reaction of H2O2with metavanadate has beenpreviously described in the application for the vanadium de-termination[22]:VO3–+4H++H2O2→VO23++3H2O(5) However,the use of this reaction for the determinationof peroxide in photo-Fenton degradation process wasfirst re-ported by Oliveira and co-workers[23],using aflow injectionspectrophotometric system.In the present work,the spectrophotometric determina-tion of hydrogen peroxide by the reaction with metavanadatein acidic medium(vanadate method)was studied.The op-timum concentrations of vanadate and sulfuric acid for theapplication in determination of H2O2in photo-Fenton pro-cesses were determined using the surface response multivari-ate analysis.The multivariate analysis has been extensivelyapplied for determination of the best conditions of analyticalmethods using mostly the central composite design,gener-ally a quadratic model in which the synergistic and antagonisteffects between the variables are taken into account[24–26].The interference of species such as chloride,nitrate,iron anda chlorophenol on the absorbance signal was evaluated.Af-ter optimization,the method was applied for H2O2deter-mination during the photodegradation of2,4-dichlorophenol(DCP).2.Experimental2.1.Reagents and solutionsAll the solutions were prepared with ultra pure(MilliporeMilli-Q)water.H2O230%(w/w)from Merck was dilutedto the required concentration.The concentration of the pur-chased solution was determined by titration with KMnO4(Merck)after appropriate dilution[27].Potassium iodide andthiosulfate used in iodometric titration were purchased fromMerck.2,4-Dichlorophenol from Merck was used as modelcompound in photo-Fenton process.For the preparation ofvanadate solution,9mol L−1sulfuric acid(Mallinckrodt)was added slowly to ammonium metavanadate(NH4VO3from Vetec)under magnetic stirring and at50◦C until com-plete dissolution.After complete dissolution,the red colorsolution was cooled down and then diluted with deionizedwater to the desired concentration,resulting in a yellow color.Potassium ferrioxalate(K3Fe(C2O4)3)·3H2O)was preparedby mixing one volume of a1.5mol L−1Fe(NO3)3·9H2O so-lution(Mallinckrodt)with three volumes of a1.5mol L−1potassium oxalate(Merck).The green complex was recristal-ized three times for purification.All other reagents used wereanalytical grade.All the waste solutions containing vanadium were storedfor precipitation of vanadium by the addition of caustic soda(NaOH/Na2CO3)and proper disposal of the solid.88R.F.P.Nogueira et al./Talanta66(2005)86–912.2.Chemical analysisThe iodometric titration was applied in order to compare with the vanadate method for H2O2determination[27].Spec-trophotometric determinations were performed using a UV Mini1240spectrophotometer from SHIMADZU and1cm cells.Appropriate volume of a0.060mol L−1vanadate stock solution and of sample were diluted in a10mL volumetric flask.The blank solution was prepared in the same way but in absence of H2O2.Total organic carbon(TOC)concen-tration was determined using a TOC analyzer(TOC-5000A SHIMADZU)for the evaluation of the photodegradation pro-cess.The TOC concentration includes the carbon content of the target compound,and the intermediates generated during the experiment.All TOC determinations were performed im-mediately after samples withdrawal to avoid further reaction.2.3.Experimental designThe central composite design was applied to investigate the effect of vanadate and sulfuric acid concentrations in the absorbance signal,aiming the highest sensitivity with low-est possible concentrations.For this design,it was necessary to realize twelve experiments,in which the two variables were codified infive levels including four central points for statistical validity within the range−1.41to+1.41,which corresponds to the concentration range of vanadate between 1.6and9.6mmol L−1and sulfuric acid between0.058and 0.080mol L−1for the determination of a6.0mmol L−1H2O2 sample.These ranges were chosen based on previous results obtained inflow system[23]and on other preliminary tests in batch system.The equation used to quantitatively describe the method and draw the response surface was built based on the absorbance data obtained using STATISTICA software (SW7127999218G51).2.4.Photodegradation experimentsThe experiments of DCP photodegradation were realized using a15W blacklight lamp and an upflow photoreactor as described previously[12].The photoreactor was operated in a recirculation mode using a peristaltic pump(Master-flex L/S-7524-45)at aflow rate of40mL min−1.The aver-age irradiance of the lamp of25W m−2was measured us-ing a radiometer(Cole Parmer9811-50,365nm).The pH of DCP solution(500mL)was adjusted to2.8by addition of H2SO43mol L−1before starting the experiments,i.e.the op-timum pH value according to previous work[12].While DCP solution was magnetically stirred,the adequate volumes of Fe(NO3)3and H2O2stock solutions were added immediately before start of irradiation.3.Results and discussionIn order to evidence the formation of the peroxovanadium cation in the reaction of vanadate with H2O2and todetermine Fig.1.Absorbance spectra of peroxide,vanadate and peroxide in the pres-ence of vanadate solution.the wavelength of maximum absorption,UV–vis absorption spectra in the range of200–800nm were obtained for the mixture of H2O2/vanadate and compared to H2O2and vana-date solutions.The vanadate solution,of light yellow color, turns to red-orange in the presence of peroxide and a strong absorption band at450nm is observed,indicating the forma-tion of the peroxovanadium cation(Fig.1).All the subsequent absorption measurements were realized at450nm.3.1.Optimization of metavanadate and sulfuric acid concentration using multivariate analysisResults obtained in previous work showed that the con-centration of vanadate is an important parameter to consider for the best absorbance signal.The sulfuric acid is neces-sary once the reaction of vanadate and H2O2occurs in acidic medium.However,it can influence the absorbance signal, besides of being advantageous to minimize its concentration. An optimum concentration in this context is considered to be the minimum concentration of the reagents that results in the highest response.For the optimization of vanadate and sulfuric acid concentration,the multivariate analysis,in the form of surface methodology response was used.It permits to determine the importance of each variable and the opti-mum concentration range of the involved reagents.The ab-sorbance data werefirst analyzed in order to determine the second-order equation including term of interaction between the two variables.Eq.(6)was obtained based on the statistical analysis of the absorbance data(not shown).Z=98.76+6.61x1+0.13x2+0.49x1x2−5.92x21+1.61x22(6) In Eq.(6),Z represents the response factor corresponding to the absorbance percentage,variation relative to the maxi-mum absorbance measured.The variables x1and x2are the vanadate and sulfuric acid concentrations,respectively.The coefficients of the quadratic model were calculated by mul-tiple regression analysis and indicate the importance of each variable,which depends on their signs and values.PositiveR.F.P.Nogueira et al./Talanta66(2005)86–9189 coefficients indicate that the absorbance signal is increased inthe presence of high concentrations of the respective variablewithin the range studied,while negative coefficients indicatethat the absorbance signal is favored in the presence of lowconcentrations.Positive quadratic coefficients of x1x2vari-ables indicate a synergistic effect,while negative coefficients,an antagonistic effect between the variables.An analysis of Eq.(6)shows that linear coefficient ofx1has a high positive value(6.61)suggesting a strong ab-sorbance signal for high vanadate concentrations.On theother hand,the negative coefficient of x12(−5.92),indicatesthat very high values of vanadate concentration result in a de-crease of absorbance signal.The net effect can be observedin Fig.2,which shows the surface response with a maximumrelative absorbance percentage in positive codified range be-tween0.2and0.9.This corresponds to concentrations ofvanadate between6.2and8.3mmol L−1,decreasing above8.3mmol L−1.Considering the low values of the coefficentsof x2and x22,it can be concluded that the concentration of sul-furic acid plays a minor role on the absorbance signal.Basedon these results,the concentrations chosen for the determi-nation of H2O2were6.2mmol L−1vanadate,which is thelowest concentration within the optimum range determined,and0.058mol L−1H2SO4,which is the lowest concentrationof the tested range.The possibility to minimize reagents formaximum spectral response using multivariate analysis re-sults in lower costs and reduced generation of sulfuric acidand vanadate residues.In a next step,an analytical curve for peroxide in the range0.0250–6.00mmol L−1(concentrations in10mL volumetricflask)was obtained using the optimized concentrations ofvanadate and sulfuric acid(not shown).The obtained curveshowed good linearity(R=0.9997)up to the concentrationof5.00mmol L−1(absorbance=1.46),with a slight deviationfor5.50and6.00mmol L−1concentration.The linear datafit(n=8)resulted in the equation A450=283[H2O2],whereA450represents the difference of absorption between thesample and blank solution at450nm and[H2O2],the H2O2Fig.2.Response surface of quadratic model for vandate absorption as a function of sulfuric acid and vanadate concentration.concentration(mol L−1).The slope of the curve,giving the molar absorptiviyεis283±2mol L−1cm−1.The calculated detection limit(3×standard deviation of the curve/slope) is143␮mol L−1.The peroxide concentrations can be then calculated by the following relation:A450=283[H2O2]V1V2(7) where V1is the volume of aliquot taken for analysis(mL) and V2is thefinal volume to which the aliquot V1is diluted (mL)before absorbance measurement.It is important to note that although the linear range of the calibration curve was up to5.00mmol L−1,higher peroxide concentrations can be determined after appropriate dilution of the sample,avoiding absorbance values above1.5.parison between vanadate and iodometric methodConsidering that the iodometric titration is one of the most used methods for the determination of H2O2in AOP [16,17],it was used for the comparison with the proposed method.Both methods were applied for the determination of H2O2in samples taken from DCP photo-Fenton degra-dation.A solution containing initially1.0mmol L−1DCP, 1.5mmol L−1ferrioxalate and15mmol L−1H2O2was ir-radiated and20.0mL samples were taken at0,5,10and 20min reaction,and used for H2O2determination by iodo-metric titration and by spectrophotometric vanadate method. The average result(n=3)obtained for each sample by both mehtods is shown in Table1.Although the results obtained by the vanadate method are something lower than that obtained by iodometric titration,there is a good agreement between the two methods.This fact shows clearly the applicability of the vanadate method in photo-Fenton reactions.3.3.Optical stability of the reaction products and possible interferencesThe optical stability of the VO23+formed in the reaction of peroxide and vanadate was evaluated using 4.00mL peroxide samples of concentrations between 1.00and 12.0mmol L−1,which were diluted to10.0mL after addi-tion of1.6mL of60mmol L−1vanadate solution.It can be Table1Concentration of hydrogen peroxide determined by iodometric titration and vanadate method in samples taken from1.0mmol L−1DCP photodegrada-tion in the presence of1.5mmol L−1FeOx and15mmol L−1H2O2(initial concentrations)Sample Reactiontime(min)Iodometric a(mmol L−1)Vanadate a(mmol L−1) 1015.3±0.0214.4±0.05 2510.1±0.029.63±0.06 315 3.63±0.01 3.78±0.04 4250.500±0.01<0.143a n=3.90R.F.P.Nogueira et al./Talanta66(2005)86–91Fig.3.Optical stability of vanadate/peroxide solution as a function of stor-age time at ambient temperature(solid symbols)and at4◦C(open symbols). observed in Fig.3that the reaction product is very stable since the measured absorbance of peroxide samples of1and 3mmol L−1remained unchanged during a period of180h at room temperature.However,as the peroxide concentration increases,the absorbance decreases gradually with storage time.While the absorbance of the reaction product of6 and9mmol L−1peroxide samples was stable up to35h,a decrease of17%after180h was observed for the sample containing12mmol L−1peroxide kept in the dark at room temperature.The appearance of yellow colour when excess peroxide is added was observed previously and attributed to the formation diperoxoorthovanadate(V)ions[28],what could explain the decrease of absorbance at450nm.On the other hand,all the solutions were very stable when kept at 4◦C.This stability permits to delay the peroxide determina-tion in favor of other analysis which,due to the difficulty in stopping the Fenton reaction,are more sensitive to reaction time such as TOC and determination of the target compound concentration.Some ions such as chloride and nitrate are usually present in wastewater samples,either from the acid used for pH ad-justment or as a product of photodegradation of organochlo-rine and nitro compounds.Fe3+added in the Fenton reaction is also present after photodegradation,due to the fast con-version of Fe2+to Fe3+.Therefore,the possible interference of these ions,including ferrioxalate,which is often used as source of iron,and DCP,was examined in order to evaluate the vanadate method.The following concentration ranges were tested:Cl−(0–1.3mmol L−1),NO3−(0–1.0mmol L−1), Fe3+(0–1.2mmol L−1),DCP(0–1.0mmol L−1)and ferriox-alate(0–1.2mmol L−1)in the presence of6.0mmol L−1 H2O2.The results shown in Fig.4indicate that no significant differences were observed in the absorbance signal obtained by the vanadate method in the presence of these species in the concentration ranges tested.The only exception is ferriox-alate at low concentrations of0.2and0.4mmol L−1,where a decrease of about9and7%in the absorbance values were ob-served,respectively.This decrease of the absorbance can be a consequence of the reduction of vanadium(V)tovanadium Fig.4.Influence of different species on the absorbance signal of vana-date/peroxide solution.(IV)[29].This small difference,however,causes only a small interference in the determination of H2O2in the present ap-plication,since the ferrioxalate concentration used in photo-Fenton treatment is usually much higher,above1mmol L−1 [12,14].3.4.Application:evaluation of peroxide consumption during photo-Fenton degradation of2,4-dichlorophenol The influence of DCP initial concentration(0.25and 2.50mmol L−1)on the peroxide consumption during pho-todegradation was evaluated using the proposed method for peroxide determination using optmized concentrations of vanadate(6mmol L−1)and H2SO4(0.058mol L−1).The ini-tial concentrations of H2O2and Fe3+used were11andFig. 5.Photodegradation of DCP.(A)Consumption of H2O2;(B) TOC removal.Initial concentrations:[H2O2]=11mmol L−1and[Fe3+]= 0.88mmol L−1.R.F.P.Nogueira et al./Talanta66(2005)86–91910.88mmol L−1,paring the consumption rates of peroxide for the two different DCP concentrations, similar rates were observed at the begining of the reaction. However,as the reaction proceeds,sharper decrease of per-oxide concentration is observed in the presence of the higher DCP concentration(Fig.5A),a consequence of the higher content of organic matter.In this case,after total consumption of peroxide in15min,a lower mineralization percentage and stagnation of TOC removal reaction are observed(Fig.5B). Similar behaviour was reported by Fallmann and co-workers (1999)[15]in the treatment of a mixture of herbicides,where higher consumption of H2O2occured when TOC started to decrease.On the other hand,multiple additions of H2O2dur-ing photodegradation reaction are reported to increase the processes efficiency[12].4.ConclusionsA simple,fast and reliable determination of hydrogen peroxide using a cheap reagent,amonium metavanadate,is proposed.The multivariate analysis provided the definition of the minimum concentration of vanadate for the maxi-mum absorbance signal,found to be6.2mmol L−1.Fur-thermore,it was also found that sulphuric acid concentra-tion plays minor role on the absorbance signal,therefore the lowest concentration tested was used(0.058mol L−1). Under these conditions,theεis283M−1cm−1and the de-tection limit is143␮mol L−1.The reaction showed to be very stable for samples of peroxide concentrations up to 3mmol L−1once no significant change in the absorbance at450nm was observed at room temperature until180h. However,for higher concentrations,absorbance starts to decrease after15min,what can be avoided keeping the solutions refrigerated at4◦C,or by dilution of the sam-ple.The method showed no significant interference of Cl−(0.2–1.3mmol L−1),NO3−(0.3–1.0mmol L−1),Fe3+ (0.2–1.2mmol L−1),FeOx0.2–1.2mmol L−1)and DCP (0.2–1.0mmol L−1).When compared to iodometric titration, the values determined by the vanadate method in a shorter time are in good agreament and opens the possibility of sam-ple storage for further analysis.The method was applied for the evaluation of peroxide consumption during photodegra-dation of DCP.The decrease of H2O2concentration until total consumption after15min irradiation limited the degradation reaction for2.50mmol L−1DCP.The demand for H2O2de-pends on the concentration and structure of the contaminants present on the wastewater and therefore will determine a con-siderable part of the treatment costs.In this regard,the pro-posed method can be very useful due to the fast and simple determination of H2O2.AcknowledgementsThe authors thank FAPESP for thefinancial support of this work(02/00737-9)and scholarship of W.C.Paterlini(proc. no.00/08870-4),and to CNPq for the scholarship of M.C. 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