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多层局部块坐标下降法及其驱动的分类重构网络

王金甲 张玉珍 夏静 王凤嫔

王金甲, 张玉珍, 夏静, 王凤嫔. 多层局部块坐标下降法及其驱动的分类重构网络. 自动化学报, 2020, 46(12): 2647−2661 doi: 10.16383/j.aas.c190540
引用本文: 王金甲, 张玉珍, 夏静, 王凤嫔. 多层局部块坐标下降法及其驱动的分类重构网络. 自动化学报, 2020, 46(12): 2647−2661 doi: 10.16383/j.aas.c190540
Wang Jin-Jia, Zhang Yu-Zhen, Xia Jing, Wang Feng-Pin. Multi-layer local block coordinate descent algorithm and unfolding classification and reconstruction networks. Acta Automatica Sinica, 2020, 46(12): 2647−2661 doi: 10.16383/j.aas.c190540
Citation: Wang Jin-Jia, Zhang Yu-Zhen, Xia Jing, Wang Feng-Pin. Multi-layer local block coordinate descent algorithm and unfolding classification and reconstruction networks. Acta Automatica Sinica, 2020, 46(12): 2647−2661 doi: 10.16383/j.aas.c190540

多层局部块坐标下降法及其驱动的分类重构网络

doi: 10.16383/j.aas.c190540
基金项目: 国家自然科学基金(61473339), 首批“河北省青年拔尖人才” ([2013]17)资助项目, 京津冀基础研究合作专项 (F2019203583)
详细信息
    作者简介:

    王金甲:燕山大学信息科学与工程学院教授. 主要研究方向为信号处理和模式识别. 本文通信作者. E-mail: wjj@ysu.edu.cn

    张玉珍:燕山大学信息科学与工程学院硕士研究生. 主要研究方向为信号与信息处理. E-mail: 13091375387@163.com

    夏静:燕山大学信息科学与工程学院硕士研究生. 主要研究方向为信号处理. E-mail: xiajing_527@sina.com

    王凤嫔:燕山大学信息科学与工程学院博士研究生. 主要研究方向为模式识别. E-mail: landywang1105@163.com

Multi-layer Local Block Coordinate Descent Algorithm and Unfolding Classification and Reconstruction Networks

Funds: Supported by National Natural Science Foundation of China (61473339), The First Batch of “Top Young Talents in Hebei Province” ([2013]17), Basic Research Cooperation Projects of Beijing, Tianjin and Hebei (F2019203583)
  • 摘要: 卷积稀疏编码(Convolutional sparse coding, CSC)已广泛应用于信号或图像处理、重构和分类等任务中, 基于深度学习思想的多层卷积稀疏编码(Multi-layer convolutional sparse coding, ML-CSC)模型的多层基追踪(Multi-layer basic pursuit, ML-BP)问题和多层字典学习问题成为研究热点. 但基于傅里叶域的交替方向乘子法(Alternating direction multiplier method, ADMM)求解器和基于图像块(Patch)空间域思想的传统基追踪算法不能容易地扩展到多层情况. 在切片(Slice)局部处理思想的基础上, 本文提出了一种新的多层基追踪算法: 多层局部块坐标下降(Multi-layer local block coordinatedescent, ML-LoBCoD)算法. 在多层迭代软阈值算法(Multi-layer iterative soft threshold algorithm, ML-ISTA)和对应的迭代展开网络ML-ISTA-Net 的启发下, 提出了对应的迭代展开网络ML-LoBCoD-Net. ML-LoBCoD-Net实现信号的表征学习功能, 输出的最深层卷积稀疏编码用于分类. 此外, 为了获得更好的信号重构, 本文提出了一种新的多层切片卷积重构网络(Multi-layer slice convolutional reconstruction network, ML-SCRN), ML-SCRN实现从信号稀疏编码到信号重构. 我们对这两个网络分别进行实验验证. 然后将ML-LoBCoD-Net和ML-SCRN 进行级联得到ML-LoBCoD-SCRN合并网, 同时实现图像的分类和重构. 与传统基于全连接层对图像进行重建的方法相比, 本文提出的ML-LoBCoD-SCRN合并网所需参数少, 收敛速度快, 重构精度高. 本文将ML-ISTA和多层快速迭代软阈值算法(Multi-layer fast iterative soft threshold algorithm, ML-FISTA) 构建为ML-ISTA-SCRN和ML-FISTA-SCRN进行对比实验, 初步证明了所提出的ML-LoBCoD-SCRN分类重构网在MNIST、CIFAR10和CIFAR100数据集上是有效的, 分类准确率、损失函数和信号重构结果都优于ML-ISTA-SCRN和ML-FISTA-SCRN.
  • 图  1  优化算法三次迭代展开的ML-LoBCoD-Net

    Fig.  1  The unfolding ML-LoBCoD-Net based on three iterations of the optimization algorithm

    图  2  ML-LoBCoD 算法第 j 层一次迭代流程图

    Fig.  2  The flowchart of one iteration of the jth-layer of the ML-LoBCoD algorithm.

    图  3  j 层切片卷积层

    Fig.  3  The jth-layer of the slice convolution layer

    图  4  基于切片多层卷积重构神经网络(ML-SCRN)

    Fig.  4  The multi-layer slice convolutional reconstruction network (ML-SCRN)

    图  5  ML-LoBCoD-SCRN 分类重构网络

    Fig.  5  ML-LoBCoD-SCRN classification reconstruction network

    图  6  ML-LoBCoD-SCRN和LoBCoD-SCRN在MNIST数据集中的分类准确率

    Fig.  6  Classification accuracy of ML-LoBCoD-SCRN and LoBCoD-SCRN in the MNIST data

    图  7  ML-LoBCoD-SCRN和LoBCoD-SCRN在MNIST数据集中的损失函数值随迭代次数的变化

    Fig.  7  Loss function value of ML-LoBCoD-SCRN and LoBCoD-SCRN in the MNIST data with the number of iterations

    图  8  $\rho $在不同值时ML-LoBCoD-SCRN在MNIST数据集中的分类准确率

    Fig.  8  Classification accuracy of ML-LoBCoD-SCRN in the MNIST data at different values of $ \rho $

    图  9  $ \rho $在不同值时ML-LoBCoD-SCRN重构结果

    Fig.  9  Reconstruction results of ML-LoBCoD-SCRN at different values of $ \rho $

    图  10  $ \rho $在不同值时ML-LoBCoD-SCRN损失函数值随迭代次数的变化

    Fig.  10  Loss function value of ML-LoBCoD-SCRN with iterations at different values of $ \rho $

    图  11  $ \rho = 0 $时三种方法的分类准确率

    Fig.  11  Classification accuracy of the three methods at $ \rho = 0 $

    图  12  ML-SCRN网络的重构结果

    Fig.  12  Reconstruction results of ML-SCRN network

    图  13  逐层松弛模型的分类对比图

    Fig.  13  Classification comparison chart of layer-by-layer relaxation model

    图  14  逐层松弛模型重构损失函数对比图

    Fig.  14  Comparison chart of the reconstruction loss function value of the layer-by-layer relaxation model

    图  15  逐层松弛 ML-LoBCoD-SCRN 模型重构结果对比图

    Fig.  15  Comparison chart of the reconstruction images results of the layer-by-layer relaxation ML-LoBCoD-SCRN model

    图  16  两种分类重构网络在MNIST数据集的重构结果

    Fig.  16  Reconstruction results of two classification reconstruction networks in the MNIST data

    图  17  两种分类重构网在MNIST 数据集的损失函数

    Fig.  17  Loss function value of two classification reconstruction networks in the MNIST data

    图  18  三种网络在MNIST数据集下的重构结果

    Fig.  18  Reconstruction results of three networks of the MNIST data

    图  20  三种网络在CIFAR100数据集下的重构结果

    Fig.  20  Reconstruction results of three networks of the CIFAR100 data

    图  19  三种网络在CIFAR10数据集下的重构结果

    Fig.  19  Reconstruction results of three networks of the CIFAR10 data

    图  21  三种分类重构网在MNIST 数据集下的分类准确率

    Fig.  21  Classification accuracy of three classification reconstruction networks in the MNIST data

    图  22  三种分类重构网在CIFAR10数据集下的分类准确率

    Fig.  22  Classification accuracy of three classification reconstruction networks in the CIFAR10 data

    图  23  三种分类重构网在MNIST 数据集下的损失函数

    Fig.  23  Loss function value of three classification reconstruction networks in the MNIST data

    图  24  三种分类重构网在CIFAR10数据集下的损失函数

    Fig.  24  Loss function value of three classification reconstruction networks in the CIFAR10 data

    表  1  几种分类网络在迭代100次时的分类准确率 (%)

    Table  1  Classification accuracy of several classification networks at 100 iterations (%)

    模型 ACC (MNIST) ACC (CIFAR10)
    CNN 98.74 79.00
    ML-ISTA 99.11 82.93
    ML-FISTA 99.16 82.79
    ML-LISTA 98.80 82.68
    LBP 99.19 80.73
    ML-LoBCoD 99.15 85.53
    下载: 导出CSV

    表  2  两种分类重构网络在迭代100次对比

    Table  2  Comparison of two classification reconstruction networks over 100 iterations

    模型 ML-LoBCoD-SCRN ML-LoBCoD-FC
    分类准确率ρ=0 (%) 99.15 98.91
    重构误差 3.03×10−6 1.38×10−5
    平均峰值信噪比 (dB) 30.77 22.79
    时间 1 h 47 m 2 h 34 m
    下载: 导出CSV

    表  3  两种分类重构网络参数数量的比较

    Table  3  Comparison of the parameters of two classification reconstruction networks

    模型 ML-LoBCoD-SCRN ML-LoBCoD-FC
    1st layer 6×6×1×64+64 6×6×1×64+64
    2nd layer 6×6×64×128+128 6×6×64×128+128
    3rd layer 4×4×128×512+512 4×4×128×512+512
    4th layer 512×10+10 512×10+512×784+784
    Total 1 352 330 1 753 818
    下载: 导出CSV

    表  4  三种网络在MNIST、CIFAR10和CIFAR100数据集下迭代100次各参数对比

    Table  4  Comparison of the parameters of the three networks under the MNIST, CIFAR10 and CIFAR100 datasets 100 times

    模型 分类准确率 (%) 重构误差 ( × 10−6 ) 运行时间 平均峰值信噪比 (dB)
    MNIST CIFAR10 CINAR100 MNIST CIFAR10 CINAR100 MNIST CIFAR10 CINAR100 MNIST CIFAR10 CINAR100
    ML-LoBCoD-SCRN 98.90 84.40 83.41 3.03 1.44 3.14 1 h 47 m 1 h 12 m 0 h 57 m 30.77 32.46 29.97
    ML-ISTA-SCRN 98.65 82.62 81.26 3.87 5.28 6.75 1 h 54 m 1 h 20 m 1 h 00 m 26.51 28.21 27.00
    ML-FISTA-SCRN 98.41 83.48 80.34 3.42 6.52 8.95 1 h 56 m 1 h 25 m 1 h 05 m 29.75 27.63 25.14
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-07-19
  • 录用日期:  2019-12-23
  • 网络出版日期:  2020-01-17
  • 刊出日期:  2020-12-29

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