在轨光学目标检测模型轻量化研究

在轨光学目标检测模型轻量化研究 Research on Lightweight Model of On-orbit Optical Object Detection 1 first-author 吕晓宁（1994-），主要研究方向为遥感图像处理。E-mail：746166746@qq.com 吕晓宁（1994-），主要研究方向为遥感图像处理。E-mail：746166746@qq.com 746166746@qq.com 1 corresp 夏玉立（1982-），主要研究方向为遥感图像处理。E-mail： xiayuli@iscas.ac.cn 夏玉立（1982-），主要研究方向为遥感图像处理。E-mail： xiayuli@iscas.ac.cn xiayuli@iscas.ac.cn 1 2 1 中国科学院软件研究所 天基综合信息系统重点实验室, 北京 100190 中国科学院软件研究所 天基综合信息系统重点实验室, 北京 100190 Science & Technology on Integrated Information System Laboratory, Institute of Software Chinese Academy of Sciences ,Beijing 100190, China Science & Technology on Integrated Information System Laboratory, Institute of Software Chinese Academy of Sciences ,Beijing 100190, China 中国科学院大学,北京 100049 中国科学院大学,北京 100049 University of Chinese Academy of Sciences, Beijing 100049,China University of Chinese Academy of Sciences, Beijing 100049,China 目前应用广泛的神经网络模型结构复杂、参数量大，对星上有限的计算和存储资源占用较多。本文面向微 纳卫星在轨计算平台，提出一种深度可分离卷积神经网络模型，该模型结合反向残差结构与通道注意力的思路改 进在轨识别算法Yolov4网络模型结构，改进网络模型的局部模块结构，降低整体网络结构的深度与复杂度；同时 利用可分离卷积结构实现空间卷积，改进SPP模块与PANet模块，降低模型参数量；通过合并卷积层与Batch Normalization层，进一步加快前向推理速度；此外借鉴Focal损失函数的思想，改进目标检测网络的损失函数，减 缓前景与背景样本比例不均衡问题。通过与原Yolov4网络模型对比，在保证识别精度94.09%的前提下参数量降低 约7倍，FLOPs降低约30倍。同时与Yolo系列、SSD、MobileNet、CenterNet等前沿网络模型对比的实验结果再 一次验证了本文的算法性能，为实现在轨目标识别与过滤无用数据提供了理论支撑。 As an important transport carrier and military target, aircraft detection in remote sensing images is of great significance in aircraft rescue, early warning and other fields. At present, the widely used neural network model has a complex structure and a large amount of parameters, which occupies a lot of limited computing and storage resources on the aircraft detection satellite. Considering the efficiency and accuracy of satellite in-orbit detection, the lightweight operation of neural network can reduce the amount of computation and compress the overall framework of neural network by optimizing the computational structure.In this paper, based on deep separable convolution neural network, Based on deeply separable convolution, the SwishBlcok bottleneck module is established by referring to the construction idea of reverse residual structure, and the characteristics of the network are simultaneously expanded from three aspects. ResBlock_body is replaced as the overall design idea of the main framework of Yolov4. At the same time, the Channel Attention thought of SENet is used for reference and integrated into the network structure. Different weights are given to the extracted feature maps and information. On the premise of keeping channel separation, separable convolution structure is used to improve SPP structure and PANet structure, so that the amount of the model parameter and the memory dependence is reduced. Meanwhile, the convolution layer and the Batch Normalization layer are merged to further speed up forward reasoning. Drawing on the Focal loss function, the loss function of object detection is improved to solve the imbalance between foreground and background data samples.In order to verify the quality of algorithm restoration, objective evaluation indexes are used to measure the algorithm from multiple angles. The public dataset RSOD and self-made dataset are used to compare the high-performance network model for algorithm verification. Meanwhile, in order to verify the rationality of various improvements of the network model, the verification experiments are carried out in the form of steps to measure the quality and processing speed of the algorithm. Then, the trained model is deployed to an embedded platform to verify the detection speed of the improved Yolov4 algorithm model for on-orbit object recognition. Compared with the original method, the parameter amount is reduced by about 7 times, and FLOPs is reduced by about 30 times on the premise of ensuring the recognition accuracy 94.09%. Furthermore, the experimental results compared with the Yolo series, SSD, MobileNet, CenterNet and other cutting-edge network models once again prove the performance of the algorithm.An on-orbit object detection model is proposed to solve the limitation of computing resources and storage resources, which cannot support the high-precision complex model. Experimental results from ground platform and embedded platform prove that the on-orbit object detection algorithm proposed can effectively detect remote sensing targets by taking into account the detection performance. In future research, it is still necessary to expand the scale of remote sensing data sets and improve the universality of the model application scenarios comprehensively. 卷积神经网络 Yolov4 在轨目标检测 反向残差结构 Convolution Neural Network Yolov4 Optical Remote Object detection Reverse residual structure 1　引 言 1 光学遥感图像中的目标检测 （ Han等，2019 Han等，2019 ）是确定图像中是否包含一个或多个目标，进而确定每个目标的位置。遥感图像中的飞机作为重要的运输载体和军事目标，其检测在飞机救助、战争预警等领域具有重要意义 （ Dong等，2020 Dong等，2020 ； Ge等，2013 Ge等，2013 ）。因此，基于光学遥感图像中的飞机检测成为一个热点问题。 然而飞机探测平台多为卫星与机载平台，计算能力和存储能力有限（Hasan等，2010），无法支持高能耗的神经网络模型在轨目标检测，在轨检测准确率受限。目前，遥感目标检测主要由计算能力强大的地面处理器完成，但遥感图像在空间—地面传输链路带宽受限，从卫星载荷成像到飞机等目标检测过程中耗时较多，无法满足实际应用需求 （ Yu等，2016 Yu等，2016 ）。 近年来，深度学习在特征提取方面（ Chen等，2017 Chen等，2017 ）取得了较大成就，目标检测具有较强的鲁棒性，可以适应不同的情况。基于神经网络模型的目标检测主流算法分为Two-Stage和One-stage （ Tang等，2014 Tang等，2014 ）两种类型。Two-Stage具有代表性的算法有Fast R-CNN （ Girshick等，2015 Girshick等，2015 ），Faster R-CNN （ Ren等，2017 Ren等，2017 ）等，该算法第一阶段通过搜索遍历图像像素，提取预选的目标框，第二阶段基于当前目标框进一步特征提取，精细化目标特征，完成检测任务，这类算法检测精度虽高，但效率较低；One-Stage具有代表性的算法有SSD （ Liu等，2016 Liu等，2016 ），Yolov3 （Redmon等，2016），Yolov4 （BOCHKOVSKIY等，2020），Yolov5 （WANG等，2021），CornerNet （LAW等，2018），CenterNet （ Zhou等，2019 Zhou等，2019 ）等，相较于Two-Stage系列算法，One-Stage系列算法直接在图像中提取目标特征与目标区域，避免了区域候选阶段，同时兼顾检测速度与检测精度。而星上在轨检测飞机目标受计算能力、存储能力以及模型复杂度的限制导致实时检测效果不佳，为进一步提高检测速度并兼顾检测性能，需降低模型的参数与计算量。国内外研究者相继提出了MobileNet-SSD （Biswas等，2018）、Yolov3-Tiny、Yolov4-Tiny、Yolov5s等轻量级神经网络，通过优化计算结构来减少计算量。然而，上述网络模型大多针对数据量较低、目标较明显的可见光图像，例如VOC数据集等，而遥感图像数据量巨大，飞机目标尺寸相对于背景所占比例较小，模型对遥感目标的检测性能较低，无法满足在轨任务需求。考虑卫星在轨检测的效率与精度，本文借鉴反向残差结构结合SENet （ Roy等，2018 Roy等，2018 ）的通道注意力思想，改进在轨识别算法Yolov4网络模型的主干网络，并调整网络模块的层数，使用较少的参数来生成更多的特征，减少网络间特征冗余，压缩神经网络整体框架，基于深度可分离卷积结构实现空间卷积替换SPP结构与PANet结构的普通卷积，实现模型参数量减少，采用多尺度融合方式，有效检测遥感目标。 2　Yolov4算法原理 1 Yolov4算法主要包括三个部分：Backbone主干网络结构、Neck模块、Yolo Head预测模块。当输入的图像分辨率为608*608时，具体的网络框架如下 图1 图1 所示。Backbone网络结构主要使用CSPDarkNet53提取模型特征；Neck模块主要包括SPP结构和PANet结构，搭建图像目标特征金字塔结构，进一步加强特征提取网络；Yolo Head预测模块利用前面模块提取的特征完成目标检测任务。 CSPDarkNet53网络基于Mish激活函数与CSPNet结构对DarkNet53网络进行改进构建的，其中包含53个卷积层。输入图像分辨率为608*608时，首先经过一个3*3*32大小的滤波器，再经过5组ResBlock_body模块进行特征提取，其中5组ResBlock_body单元，每个单元由单个卷积层和一系列重复执行的卷积层组成，重复次数分别为1、2、8、8、4。 ResBlock_body模块为主干网络中重要组成模块，采用了CSPNet结构，主要提取图像的目标特征，同时降低计算瓶颈，构造残差边部分，避免模型出现梯度消失问题，具体内部Module架构如下 图2 图2 所示。 3　轻量化在轨目标识别模型 1 3.1　模型框架改进 2 神经网络模型构建过程中需满足三个原则（TAN等，2020）： 1）利用残差神经网络，搭建较深的神经网络实现特征提取，提升网络的深度； 2）改变每一层提取的特征层数，实现更多的特征提取，提升网络的宽度； 3）增大输入图片的分辨率，可使网络学习与表达的特征更加丰富，有利于提高精确度。 因此本次Yolov4的模型压缩中遵循上述特点，基于深度可分离卷积，借鉴反向残差结构的构建思路，建立SwishBlcok bottleneck模块，从三个方面同时拓充网络的特性，替换ResBlock_body以作为Yolov4的主框架总体设计思路，同时借鉴SENet的Channel Attention思想融入网络结构中，对提取的特征图赋予不同的权重，抽取更关键的特征信息，同时不会替模型的计算与存储增加开销。 本文构建的SwishBlcok bottleneck模块实际架构为倒置的残差结构，残差结构中间特征图通道数少而两边的特征图通道数多，反向残差结构中间特征图通道数多而两边的特征图通道数少，反向残差结构的架构设计被证实可以提高内存利用效率。 因此本文设计该模块在3*3可分离卷积结构前首先利用1*1卷积升维，增加提取特征图的维度，进一步提升图像的特征提取能力；后面紧接着3*3的可分离卷积、BatchNorm与Swish激活函数，高维度提取更多的图像纹理特征，同时兼具可分离卷积降低模型参数的特性；为了抽取更重要的特征信息，在3*3网络结构后增加了一个通道注意力机制结构，采用全局池化与Sigmoid激活函数训练每个通道的权重值，将权重值非线性映射至0-1区间，与图像特征图加权相乘；再利用1*1卷积降维处理，根据权重值保留更重要的特征向量；最后增加一个大残差边，避免网络发生梯度消失现象。具体的SwishBlcok bottleneck模块的架构设计如 图3 图3 所示。 本小节遵循Yolov4模块中的SPP与PANet基本体系结构的优势，利用SwishBlcok bottleneck替换Yolov4主框架中的ResBlock_body结构。利用SwishBlcok bottleneck结构构建神经网络模型，同时为了减少整体网络的参数量，调整原Yolov4的网络模型模块的数量，将原Yolov4模型的特征图维度由608*608*32、304*304*64、152*152*128、76*76*256、38*38*512、19*19*1024降低到304*304*16、152*152*24、76*76*48、38*38*88、38*38*120、19*19*208、19*19*352，大大减少参数量，达到压缩Yolov4网络模型的目的，改进后的网络结构如 图4 图4 所示。 3.2　SPP结构与PANet模块改进 2 Yolov4网络模型中的PANet结构与SPP结构起到加强特征提取网络。分析SPP结构与PANet的结构，发现网络结构内含大量的3*3卷积层与连续五次卷积的结构，大大增加了模型的计算量。 深度可分离卷积由深度卷积与1*1的点卷积构成，如图5（b）（c）所示。图（a）为常规卷积提取图像细节特征的过程，其中 <math id="M1"><mi mathvariant="bold-italic">M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611905&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611904&type= 3.04800010 2.62466669 为输入图像的维数， <math id="M2"><mi mathvariant="bold-italic">N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611926&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611925&type= 2.62466669 2.62466669 为卷积核滤波的通道数，卷积核大小为 <math id="M3"><mn mathvariant="normal">3</mn><mi mathvariant="normal">*</mi><mn mathvariant="normal">3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611934&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611933&type= 5.58799982 2.70933342 ，则常规卷积提取的特征层维度数为 <math id="M4"><mi mathvariant="bold-italic">N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611926&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611925&type= 2.62466669 2.62466669 ，则常规卷积的参数数量为 <math id="M5"><mi mathvariant="bold-italic">M</mi><mi mathvariant="normal">*</mi><mi mathvariant="bold-italic">N</mi><mi mathvariant="normal">*</mi><mn mathvariant="normal">3</mn><mi mathvariant="normal">*</mi><mn mathvariant="normal">3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611928&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611927&type= 14.90133286 2.70933342 。而深度可分离卷积采用逐通道卷积的策略，提取的特征图采用逐点卷积的形式同样得到维度数为 <math id="M6"><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611930&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611929&type= 2.53999996 2.62466669 的特征图，如图5（b）（c）所示，输入图像的维数为 <math id="M7"><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611932&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611931&type= 2.87866688 2.62466669 ，可分离卷积核大小为 <math id="M8"><mn mathvariant="normal">3</mn><mi mathvariant="normal">*</mi><mn mathvariant="normal">3</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611934&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611933&type= 5.58799982 2.70933342 。因此可分离卷积操作的参数数量为 <math id="M9"><mi mathvariant="bold-italic">M</mi><mi mathvariant="normal">*</mi><mn mathvariant="normal">3</mn><mi mathvariant="normal">*</mi><mn mathvariant="normal">3</mn><mo>+</mo><mn mathvariant="normal">1</mn><mi mathvariant="normal">*</mi><mn mathvariant="normal">1</mn><mi mathvariant="normal">*</mi><mi mathvariant="bold-italic">M</mi><mi mathvariant="normal">*</mi><mi mathvariant="bold-italic">N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611910&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611935&type= 29.88733101 2.70933342 。 1,2;3; 相较于常规卷积操作，采用可分离卷积提取图像的纹理特征，参数量减少如下 式（1） 式（1） 所示： <math display="block" id="M10"><mfrac><mrow><mi 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http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611936&type= 46.14333344 7.45066643 PANet结构与SPP结构含有连续五次卷积与连续三次卷积加强图像特征提取的过程， 式（1） 式（1） 分析采用可分离卷积操作相较于常规卷积操作大大减少参数量。为了进一步压缩网络模型，本文在保持通道分离的前提下，基于可分离卷积结构实现空间卷积，替换SPP结构与PANet结构的普通卷积，实现模型参数量减少，内存依赖减少，具体替换如下 图6 图6 所示 3.3　模型推理速度提升 2 第3.2小节中的SwishBlcok bottleneck 模块采用卷积层加Batch Normalization层的形式进行前向计算。Batch Normalization层能够加速网络的收敛，并且能够控制网络的过拟合，虽然训练时起到积极的作用，但在网络前向推理时增加了前向运算，占用更多的显存空间，影响处理速度。因此本节将SwishBlcok bottleneck模块中的Batch Normalization层中的参数与卷积层进行合并，以提升模型前向推理速度。 原Batch Normalization层 ［21］ 的表示方式为： <math display="block" id="M11"><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>←</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>m</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611941&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611940&type= 20.48933220 8.29733276 <math display="block" id="M12"><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>←</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>m</mi></mrow></munderover></mstyle><mrow><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611953&type= 33.02000046 8.29733276 <math display="block" id="M13"><mover><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow><mrow><mo>∧</mo></mrow></mover><mo>←</mo><mfrac><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>-</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow><mrow><mroot><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mi>ε</mi></mrow><mrow/></mroot></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611943&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611955&type= 23.45266724 10.24466610 <math display="block" id="M14"><msub><mrow><mi mathvariant="bold-italic">y</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>←</mo><mi>γ</mi><mover><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow><mrow><mo>∧</mo></mrow></mover><mo>+</mo><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611945&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611944&type= 20.74333191 5.84200001 其中 <math id="M15"><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611947&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611946&type= 3.38666677 4.48733330 为数据集batch的均值， <math id="M16"><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611957&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611956&type= 3.80999994 4.06400013 为数据集batch的方差， <math id="M17"><mover><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow><mrow><mo>∧</mo></mrow></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611959&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611958&type= 2.96333337 5.84200001 为数据集batch的归一化， <math id="M18"><msub><mrow><mi mathvariant="bold-italic">y</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611949&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611948&type= 2.62466669 4.57200003 为经过Batch Normalization层平移与缩放的输出结果。 卷积层的计算为： <math display="block" id="M19"><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">u</mi><mi mathvariant="bold-italic">t</mi><mo>=</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>k</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>+</mo><mi>b</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611951&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611950&type= 25.90800095 8.29733276 BN层经过卷积层的输出为： <math display="block" id="M20"><mi mathvariant="bold-italic">B</mi><mi mathvariant="bold-italic">N</mi><mo>=</mo><mfrac><mrow><mi>γ</mi><mi mathvariant="normal">*</mi><mo stretchy="false">(</mo><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">u</mi><mi mathvariant="bold-italic">t</mi><mo>-</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mroot><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mi>ε</mi></mrow><mrow/></mroot></mrow></mfrac><mo>+</mo><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611961&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611960&type= 36.40666580 10.41399956 将 式（6） 式（6） 代入到 式（7） 式（7） 中，将式进行展开，以计算卷积层新的权重与偏置项。 <math display="block" id="M21"><mi mathvariant="bold-italic">B</mi><mi mathvariant="bold-italic">N</mi><mo>=</mo><mfrac><mrow><mi>γ</mi><mi mathvariant="normal">*</mi><mo stretchy="false">(</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>k</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>+</mo><mi>b</mi></mrow><mo>-</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mroot><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mi>ε</mi></mrow><mrow/></mroot></mrow></mfrac><mo>+</mo><mi>β</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mfrac><mrow><mi>γ</mi><mi mathvariant="normal">*</mi><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>k</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>+</mo><mi>γ</mi><mi mathvariant="normal">*</mi><mo stretchy="false">(</mo><mi>b</mi></mrow><mo>-</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mroot><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mi>ε</mi></mrow><mrow/></mroot></mrow></mfrac><mo>+</mo><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611963&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611962&type= 95.50399780 14.81666565 这样新的权重与偏置为 <math display="block" id="M22"><msub><mrow><mi>w</mi></mrow><mrow><mi>n</mi><mi>e</mi><mi>w</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>γ</mi><mi mathvariant="normal">*</mi><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>k</mi></mrow></munderover></mstyle><mrow><msub><mrow><mi mathvariant="bold-italic">w</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow></mrow><mrow><mroot><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mi>ε</mi></mrow><mrow/></mroot></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611952&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611964&type= 24.21466637 14.81666565 <math display="block" id="M23"><msub><mrow><mi>b</mi></mrow><mrow><mi>n</mi><mi>e</mi><mi>w</mi></mrow></msub><mo>=</mo><mfrac><mrow><mi>γ</mi><mi mathvariant="normal">*</mi><mo stretchy="false">(</mo><mi>b</mi><mo>-</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mroot><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msubsup><mo>+</mo><mi>ε</mi></mrow><mrow/></mroot></mrow></mfrac><mo>+</mo><mi>β</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611967&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611966&type= 32.85066605 10.41399956 使用上述新的权重与偏置项来执行SwishBlcok bottleneck模块的卷积层计算，得到与原始卷积层加Batch Normalization层相同结果的同时减少模型前向推理速度。 3.4　损失函数的改进 2 Yolov4网络训练时的损失函数由边界框回归损失 <math id="M24"><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>i</mi><mi>o</mi><mi>u</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611969&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611968&type= 5.24933338 3.72533321 、置信度损失 <math id="M25"><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>f</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611971&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611970&type= 5.24933338 3.72533321 、分类损失 <math id="M26"><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611973&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611972&type= 5.67266655 3.72533321 等3部分组成。 <math display="block" id="M27"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>f</mi></mrow></msub><mo>=</mo><mo>-</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></munderover></mstyle><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>j</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><mi>B</mi></mrow></munderover></mstyle><mrow><msubsup><mrow><mi mathvariant="bold-italic">I</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>,</mo><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">[</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></mrow></mtd></mtr><mtr><mtd><mtext>          </mtext><mo>-</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi><mi>o</mi><mi>o</mi><mi>b</mi><mi>j</mi></mrow></msub><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></munderover></mstyle><mrow><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>j</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><mi>B</mi></mrow></munderover></mstyle><mrow><msubsup><mrow><mi mathvariant="bold-italic">I</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>,</mo><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">n</mi><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">[</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></mrow></mtd></mtr><mtr><mtd><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi></mrow></msub><mo>=</mo><mo>-</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></munderover></mstyle><mrow><msubsup><mrow><mi mathvariant="bold-italic">I</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>,</mo><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">j</mi></mrow></msubsup><munder><mo movablelimits="false">∑</mo><mrow><mi>c</mi><mo>∈</mo><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>e</mi><mi>s</mi></mrow></munder><mrow><mo stretchy="false">[</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></mrow></mtd></mtr><mtr><mtd><mi>L</mi><mi>o</mi><mi>s</mi><mi>s</mi><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>i</mi><mi>o</mi><mi>u</mi></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>f</mi></mrow></msub><mo>+</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi></mrow></msub></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611975&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611974&type= 88.56133270 36.83000183 其中， <math id="M28"><msup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mi mathvariant="normal">、</mi><mi>B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611977&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611976&type= 7.36600018 3.30200005 为特征图尺度与先验框， <math id="M29"><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi><mi>o</mi><mi>o</mi><mi>b</mi><mi>j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611979&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611978&type= 6.43466663 3.72533321 为权重系数， <math id="M30"><msubsup><mrow><mi mathvariant="bold-italic">I</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>,</mo><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">j</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611981&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611980&type= 4.23333359 4.06400013 与 <math id="M31"><msubsup><mrow><mi mathvariant="bold-italic">I</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>,</mo><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">n</mi><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">j</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611983&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611982&type= 6.26533365 4.06400013 为第 <math id="M32"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611985&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611984&type= 1.10066664 2.62466669 网格的第 <math id="M33"><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611987&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611986&type= 0.84666669 3.47133350 先验框处有目标与没有目标， <math id="M34"><mi>c</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611989&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611988&type= 1.43933344 2.62466669 为预测框与实际框闭包区域的对角线距离， <math id="M35"><mi>b</mi><mi mathvariant="normal">、</mi><mi>w</mi><mi mathvariant="normal">、</mi><mi>h</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611998&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611990&type= 9.48266602 2.96333337 为预测框的中心坐标及宽高， <math id="M36"><msup><mrow><mi>b</mi></mrow><mrow><mi>g</mi><mi>t</mi></mrow></msup><mi mathvariant="normal">、</mi><msup><mrow><mi>w</mi></mrow><mrow><mi>g</mi><mi>t</mi></mrow></msup><mi mathvariant="normal">、</mi><msup><mrow><mi>h</mi></mrow><mrow><mi>g</mi><mi>t</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611999&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611991&type= 14.64733315 3.30200005 为实际框的中心坐标及宽高， <math id="M37"><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mi mathvariant="normal">、</mi><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">C</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611992&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612000&type= 9.05933285 5.50333309 为预测框与标注框的置信度、 <math id="M38"><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mi mathvariant="normal">、</mi><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612002&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612001&type= 9.14400005 5.50333309 为预测框与标注框的类别概率。 模型处理遥感影像在轨目标检测时，为减缓前景与背景数据样本比例不均衡的问题，本节借鉴RetinaNet网络 （Lin 等，2017） 的Focal Loss损失函数，给目标检测分类的交叉熵损失函数添加一个调制系数 <math id="M39"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611994&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611993&type= 2.20133328 2.62466669 ，变成 <math display="block" id="M40"><msub><mrow><mi>L</mi></mrow><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi></mrow></msub><mo>=</mo><mo>-</mo><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi><mo>=</mo><mn mathvariant="normal">0</mn></mrow><mrow><msup><mrow><mi>S</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></munderover></mstyle><mrow><msubsup><mrow><mi mathvariant="bold-italic">I</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>,</mo><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">o</mi><mi mathvariant="bold-italic">b</mi><mi mathvariant="bold-italic">j</mi></mrow></msubsup><munder><mo movablelimits="false">∑</mo><mrow><mi>c</mi><mo>∈</mo><mi>c</mi><mi>l</mi><mi>a</mi><mi>s</mi><mi>s</mi><mi>e</mi><mi>s</mi></mrow></munder><mrow><mo stretchy="false">[</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><msup><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mover><mrow><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup></mrow><mrow><mo>—</mo></mrow></mover><mo stretchy="false">)</mo></mrow><mrow><mi>α</mi></mrow></msup><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msubsup><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611996&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27611995&type= 85.51332855 8.63599968 4　实验结果与分析 1 4.1　客观评价指标 2 基于深度卷积神经网络的在轨目标识别方法采用客观评价指标定量衡量，可以多角度的获得衡量复原算法质量。目标检测性能公开的客观评价指标指标如 <math id="M41"><mi>I</mi><mi>O</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612018&type= 6.18066692 2.62466669 、准确率（ <math id="M42"><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612012&type= 13.12333298 2.62466669 ）、召回率（ <math id="M43"><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612050&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612049&type= 9.05933285 2.62466669 ）、 <math id="M44"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 。交并比（ <math id="M45"><mi>I</mi><mi>O</mi><mi>U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612018&type= 6.18066692 2.62466669 ）是模型所预测的边界框和真实边界框的交集和并集之比，同时被称作Jaccard指数。 平均精度 <math id="M46"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 是目标检测领域中用于评估算法精度的常用指标，以 <math id="M47"><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612050&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612049&type= 9.05933285 2.62466669 值为横轴， <math id="M48"><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612012&type= 13.12333298 2.62466669 值为纵轴，这样便可得到 <math id="M49"><mi>P</mi><mi>R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612036&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612011&type= 4.57200003 2.62466669 曲线，进而求取 <math id="M50"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 值，简单来说就是对 <math id="M51"><mi>P</mi><mi>R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612036&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612011&type= 4.57200003 2.62466669 曲线上的 <math id="M52"><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612012&type= 13.12333298 2.62466669 值求均值， <math id="M53"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 值 ［19］ 的定义为： <math display="block" id="M54"><mi>A</mi><mi>P</mi><mo>=</mo><msubsup><mo>∫</mo><mrow><mn mathvariant="normal">0</mn></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msubsup><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mi>d</mi><mi>r</mi></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612032&type= 21.84399986 7.53533268 其中 <math id="M55"><mi>p</mi><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612035&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612034&type= 6.26533365 3.64066648 为 <math id="M56"><mi>P</mi><mi>R</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612036&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612011&type= 4.57200003 2.62466669 曲线，而曲线的构建是通过准确率与召回率绘制得出，准确率（ <math id="M57"><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612012&type= 13.12333298 2.62466669 ）定义为： <math display="block" id="M58"><mi>P</mi><mi>r</mi><mi>e</mi><mi>c</mi><mi>i</mi><mi>s</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>P</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612044&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612043&type= 31.75000000 7.28133297 其中， <math id="M59"><mi>T</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612046&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612045&type= 4.31799984 2.62466669 为检测类别为正类预测成正类， <math id="M60"><mi>F</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612048&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612047&type= 4.57200003 2.62466669 为检测类别为负类预测成负类，预测正负类通过交并比（IOU）值超过阈值判断得到的。准确率即所有被预测为正类样本的识别正确个数。 召回率（ <math id="M61"><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612050&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612049&type= 9.05933285 2.62466669 ）定义为： <math display="block" id="M62"><mi>R</mi><mi>e</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>N</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi></mrow><mrow><mi>P</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612052&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612051&type= 37.42266846 7.36600018 其中 <math id="M63"><mi>F</mi><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612053&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612039&type= 4.74133301 2.62466669 为检测类别为正类预测成负类， <math id="M64"><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612054&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612040&type= 2.28600001 2.62466669 为测试数据集中正类样本个数，召回率反应模型的漏检率。精确率和召回率是相互独立的，若准确率很高意味误检率较低，误检率低的情况下会导致漏检率偏高。 4.2　测试用例 2 本节采用的公开的遥感数据集RSOD，RSOD 数据集在2015年公开，它是一个用于遥感图像目标检测的开放数据集，数据来源有 Tianditu 等平台，采用 PASCAL VOC的标注格式。数据集包括飞机、油箱、操场和立交桥四类对象，共有976张图像，每幅图像的大小约在512×512到1083×923像素之间，实例对象具体分布如下 表1 表1 所示。 Aircraft Playgroud Overpass Oiltank 图像数量 446 189 176 165 实例数量 4993 191 180 1586 RSOD数据集的飞机类别图像数量为446，数量较少，不能全面体现模型的检测性能与泛化能力，因此本节额外自制数据集进行神经网络模型的混合训练。自制数据集的图像来源于GoogleEarth，来自于多个城市，分辨率为2400*2400左右，飞机尺寸为30*30像素大小，目标所占背景比例大概为 <math id="M65"><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6400</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612057&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612056&type= 8.21266651 7.36600018 左右，采用PASCAL VOC的标注格式，因本节实际解决在轨检测飞机的需求，数据集只标注飞机的类别，一共有1863张，加上ROSD数据的飞机数量，一共2309张，飞机的实例数量大概为25623，采用中小目标为主，样本分布密集的构建原则。实际数据集的训练集、验证集与测试集划分数量如下 表2 表2 所示。 Aircraft 训练集 验证集 测试集 2 RSOD数据集 图像数量 446 268 60 118 实例数量 4993 2994 672 1327 2 自制数据集 图像数量 1863 1118 325 420 实例数量 20630 12522 3413 4695 图7 图7 为RSOD公开数据集的样本示例，看到图像分辨率尺度不一，数据集中民用客机也存在不同空间分辨率，分别为1-2m不等，由 图7 图7 仍可判断出飞机的轮廓与飞机的位置。 图8 图8 为自制数据集的样本示例，同样民用客机的空间分辨率也互有差异，分别为2-4m不等组成，从图像中隐约可判断飞机轮廓，目标极小且样本分布密集。 4.3　改进算法分模块的测试对比结果 2 为充分验证本文对Yolov4网络模型多方面改进的合理性，采用分步骤的形式开展验证实验，采用客观评价指标定性衡量复原算法质量与速度。目标检测性能公开的客观评价指标为 <math id="M66"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 、参数量、计算量FLOPs。测试数据集采用公开的RSOD数据集，测试平台为高性能GPU服务器。硬件条件为Intel I9-10900K、64G DDR4内存、NVIDIA GeForce RTX 2080 Super GPU，基于深度学习框架Pytorch 1.14。首先对模型分阶段的改进，具体的指标值如下 表3 表3 所示。 Method AP Parameters（M） FLOPs（GMacs） Yolov4 95.5 64.00 63.92 3.1小节改进 92.09 10.31 1.84 3.2小节改进 91.89 8.22 0.69 3.3小节改进 91.89 8.04 0.64 3.4小节改进 94.09 8.04 0.64 可看到3.1小节仅改进模型的主框架，相较于Yolov4网络模型， <math id="M67"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 指标为Yolov4模型的96.43%，模型参数量减少83.89%，算法的计算量减少97.12%。 3.2小节基于深度可分离卷积结构实现空间卷积替换SPP结构与PANet结构的普通卷积的操作后，模型的参数由10.31减少到8.22，计算量从1.84减少到0.69。 为提升模型前向推理速度，3.3小节执行合并卷积层与Batch Normalization层中的参数操作，采用每秒处理的帧数来考量前向推理速度的有效性，并对比原Yolov4网络模型的处理速度，具体的Frame/s的指标值如下 表5 表5 所示。 2 Method 2 Frame/s 416*416 608*608 Yolov4 32 22 3.2小节改进 59 51 3.3小节改进 62 54 注： 黑体为本文方法 Method Backbone AP Parameters（M） FLOPs（GMacs） Yolov4 CSPDarknet 89.89 64.00 63.92 SSD VGG-16 79.64 26.29 127.50 Yolov4-tiny CSPDarknet 54.22 5.90 4.31 Yolov5s CSPDarknet 67.32 7.30 17.00 Yolov5m CSPDarknet 76.58 21.40 51.30 MobileNet-SSD MobileNet-v1 69.28 8.85 12.40 Mobilev2-Yolov4 MobileNet-v2 71.82 12.13 8.25 GhostNet-Yolov4 GhostNet 78.98 11.07 7.07 CenterNet ResNet-50 82.35 32.67 35.79 Ours CSPDarknet 88.87 8.04 0.64 上表可看出，相较于原Yolov4网络模型，在不同尺寸下，改进的网络模型每秒处理的帧数均有一定的提高。而执行合并卷积层与Batch Normalization层中的参数操作后，在416*416的图像尺寸下处理速度由每秒59帧提升到每秒62帧，608*608图像尺寸下处理速度由每秒51帧提升到每秒54帧。 3.4小节为减缓前景与背景数据样本比例不均衡的问题，改进损失函数的具体 <math id="M68"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 、模型参数、计算量由 表3 表3 可看出，通过为模型的损失函数添加调制因子的操作，算法在测试数据集的 <math id="M69"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 指标由91.89提升到94.09。 同时由 表3 表3 可看出yolov4网络模型采用公开数据集RSOD压缩前的 <math id="M70"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 为95.5%，模型压缩后的 <math id="M71"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 值为94.09%，检测性能稍有下降。利用模型大小、计算量等评价指标对Yolov4模型压缩前后进行评测， Yolov4网络模型压缩后的图像检测性能 <math id="M72"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 为压缩前的98.52%，模型大小减少87.43%，算法的计算量减少98.99%。 4.4　前沿算法的测试对比结果 2 本文利用ROSD加自制数据集的形式进行训练测试，并与目标检测领域处于前沿水平的网络模型进行对比，并与前沿的轻量级神经网络进行对比，例如Yolov5、MobileNet-SSD、MobileNetv2-Yolov4、GhostNet-Yolov4对比的结果如 表5 表5 所示。 由 表5 表5 知，本文所提模型压缩算法在检测性能 <math id="M73"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 相较于高性能算法几乎没有损失，但模型大小与计算量大大减少。相较于速率较快的轻量级网络模型，模型大小指标几近相同，计算量FLOPs略有领先，但检测性能 <math id="M74"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 指标更优于经典轻量级网络模型。为了更直观对深度卷积神经网络的在轨目标识别方法的检测性能进行说明，本节从测试集挑选出一些飞机目标极小且样本分布密集的图像，取具有代表性的几个神经网络算法进行对比测试，检测结果如下 图9 图9 所示 由 图9 图9 可以看出，测试图像的飞机目标极小且分布密集，四张图像中飞机的分辨率由小到大递增。由四张图像可以看出，飞机像元尺寸较小（像元比例 <math id="M75"><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">6400</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612098&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612097&type= 8.21266651 7.36600018 ）的测试图像（如第一张第二张图像），Yolov4网络模型与本文压缩的网络模型检测效果几近相同，检测效果较好，而基于Mobilev2-Yolov4网络模型检测小目标效果较差；飞机像元尺寸较大（像元比例 <math id="M76"><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mn mathvariant="normal">144</mn></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612100&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612099&type= 6.34999990 7.28133297 ）的测试图像（如第三张第四张图像），三种神经网络模型的准确率较高，但Mobilev2-Yolov4网络模型对图像内像元较小的飞机目标仍未识别。由此证明该网络同时兼顾检测速度与检测精度，有效的检测出遥感小目标。 4.5　嵌入式平台实验结果 2 为验证本文改进Yolov4算法模型在轨目标识别的检测速度，将训练好的模型部署到Jetson Xavier NX嵌入式平台上进行验证处理，该处理器外形小巧、功耗较低、计算性能强，可作为卫星超算平台的计算节点之一。分别从 <math id="M77"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 与 <math id="M78"><mi>F</mi><mi>P</mi><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612104&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612103&type= 6.43466663 2.62466669 客观评价指标对比了Yolov4网络模型、Yolov4-tiny网络模型与本文改进模型的性能，如下 表6 表6 所示。 2 Method 2 AP 2 Frame/s 416*416 608*608 416*416 608*608 Yolov4 86.86 89.89 8 5 Yolov4-tiny 46.16 54.22 41 31 Our 85.03 88.87 32 26 由上表可知，面向Jetson Xavier NX嵌入式平台，输入图像尺寸为416*416与608*608时，Yolov4网络模型因模型结构复杂每秒处理的帧数为8帧与5帧，未能满足星上在轨实时检测的需求，而Yolov4-tiny网络模型与本文改进的模型每秒处理的帧数可达41、32与31、26帧，满足在轨实时检测，但Yolov4-tiny网络模型的 <math id="M79"><mi>A</mi><mi>P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=27612085&type= 4.31799984 2.62466669 指标为46.16，识别率较低，而本文改进的Yolov4网络模型较Yolov4-tiny网络模型精度高且处理速度快，满足在轨实时准确检测目标的需求。 4　结 论 1 本文基于深度卷积神经网络提出一种在轨目标检测模型，旨在解决星上计算资源和存储资源有限，无法支持高能耗的网络模型在轨检测目标的不足，结合反向残差结构与通道注意力思想改进在轨识别模型Yolov4网络模型的模块结构，加深加宽网络模型的模块结构；利用可分离卷积结构，改进SPP结构与PANet结构，实现空间卷积，减少模型参数量；为加快前向推理速度，同时合并卷积层与Batch Normalization层，重新计算卷积层参量；借鉴Focal损失函数改进目标检测分类的损失函数，解决前景与背景数据样本比例不均衡。实验从地面平台与嵌入式平台的结果证明：本文提出的在轨目标检测算法同时兼顾检测性能，能够有效检测遥感小目标。在未来研究中，仍需要扩展遥感数据集的规模，更全面提高模型应用场景的普适性。 参考文献（ References ） Han X , Jiang T , Zhao Z . 2019 . 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