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基于多尺度残差网络的压缩感知重构算法

练秋生 富利鹏 陈书贞 石保顺

练秋生, 富利鹏, 陈书贞, 石保顺. 基于多尺度残差网络的压缩感知重构算法. 自动化学报, 2019, 45(11): 2082-2091. doi: 10.16383/j.aas.c170546
引用本文: 练秋生, 富利鹏, 陈书贞, 石保顺. 基于多尺度残差网络的压缩感知重构算法. 自动化学报, 2019, 45(11): 2082-2091. doi: 10.16383/j.aas.c170546
LIAN Qiu-Sheng, FU Li-Peng, CHEN Shu-Zhen, SHI Bao-Shun. A Compressed Sensing Algorithm Based on Multi-scale Residual Reconstruction Network. ACTA AUTOMATICA SINICA, 2019, 45(11): 2082-2091. doi: 10.16383/j.aas.c170546
Citation: LIAN Qiu-Sheng, FU Li-Peng, CHEN Shu-Zhen, SHI Bao-Shun. A Compressed Sensing Algorithm Based on Multi-scale Residual Reconstruction Network. ACTA AUTOMATICA SINICA, 2019, 45(11): 2082-2091. doi: 10.16383/j.aas.c170546

基于多尺度残差网络的压缩感知重构算法

doi: 10.16383/j.aas.c170546
基金项目: 

国家自然科学基金 61471313

河北省自然科学基金 F2019203318

详细信息
    作者简介:

    富利鹏  燕山大学信息科学与工程学院硕士研究生.主要研究方向为图像压缩感知, 深度学习.E-mail:fulipeng87@gmail.com

    陈书贞  燕山大学信息科学与工程学院副教授.主要研究方向为图像处理, 压缩感知及生物识别.E-mail:chen_sz818@163.com

    石保顺  燕山大学信息科学与工程学院博士研究生.主要研究方向为图像处理, 压缩感知及深度学习.E-mail:shibaoshun@ysu.edu.cn

    通讯作者:

    练秋生  燕山大学信息科学与工程学院教授.主要研究方向为图像处理, 稀疏表示, 压缩感知及深度学习.本文通信作者.E-mail:lianqs@ysu.edu.cn

A Compressed Sensing Algorithm Based on Multi-scale Residual Reconstruction Network

Funds: 

National Natural Science Foundation of China 61471313

Natural Science Foundation of Hebei Province F2019203318

More Information
    Author Bio:

    Master student at the School of Information Science and Engineering, Yanshan University. His research interest covers image compressed sensing and deep learning

    Associate professor at the School of Information Science and Engineering, Yanshan University. Her research interest covers image processing, compressed sensing and biometrics recognition

    Ph. D. candidate at the School of Information Science and Engineering, Yanshan University. His research interest covers image processing, compressed sensing and deep learning

    Corresponding author: LIAN Qiu-Sheng Professor at the School of Information Science and Engineering, Yanshan University. His research interest covers image processing, sparse representation, compressed sensing and deep learning. Corresponding author of this paper
  • 摘要: 目前压缩感知系统利用少量测量值使用迭代优化算法重构图像.在重构过程中,迭代重构算法需要进行复杂的迭代运算和较长的重构时间.本文提出了多尺度残差网络结构,利用测量值通过网络重构出图像.网络中引入多尺度扩张卷积层用来提取图像中不同尺度的特征,利用这些特征信息重构高质量图像.最后,将网络的输出与测量值进行优化,使得重构图像在测量矩阵上的投影与测量值更加接近.实验结果表明,本文算法在重构质量和重构时间上均有明显优势.
    Recommended by Associate Editor HU Qing-Hua
    1)  本文责任编委  胡清华
  • 图  1  多尺度残差重构网络(MSRNet), s-Dconv表示扩张卷积, $s$ = 1, 2, 4

    Fig.  1  Mult-scale residuce recontruction network, s-Dconv denotes s-dilate convolution, here $s$ = 1, 2 and 4

    图  2  多尺度卷积层

    Fig.  2  Multi-scale convolution layer

    图  3  扩张卷积

    Fig.  3  Dilate convolution

    图  4  重构图像块修正前后误差的比较(Barbara图像)

    Fig.  4  The comparison of the error of the reconstructed image block before and after refined (Barbara)

    图  5  标准测试集图像

    Fig.  5  Standard test set images

    图  6  训练期间的损失

    Fig.  6  The network losses in training phase

    图  7  比较几种算法的重构性能(第1行到第3行采样率MR = 0.25, 0.10, 0.04)

    Fig.  7  Comparison of reconstruction performance of various algotithms (MR = 0.25, 0.10, 0.04)

    图  8  修正前后的重构图像对比(MR = 0.25)

    Fig.  8  The comparison of reconstructed images before and after refined (MR = 0.25)

    表  1  6幅测试图像在不同算法不同采样率下的PSNR

    Table  1  PSNR values in dB for six testing images by different algorithms at different measurement rates

    图像 算法 MR = 0.25 MR = 0.10 MR = 0.04 MR = 0.01
    w/o BM3D w/BM3D w/o BM3D w/BM3D w/o BM3D w/BM3D w/o BM3D w/BM3D
    Barbara TVAL3 24.19 24.20 21.88 22.21 18.98 18.98 11.94 11.96
    NLR-CS 28.01 28.00 14.80 14.84 11.08 11.56 5.50 5.86
    D-AMP 25.08 25.96 21.23 21.23 16.37 16.37 5.48 5.48
    ReconNet 23.25 23.52 21.89 22.50 20.38 21.02 18.61 19.08
    DR$ ^2 $-Net 25.77 25.99 22.69 22.82 20.70 21.30 18.65 19.10
    MSRNet 26.69 26.91 23.04 23.06 21.01 21.28 18.60 18.90
    Boats TVAL3 28.81 28.81 23.86 23.86 19.20 19.20 11.86 11.88
    NLR-CS 29.11 29.27 14.82 14.86 10.76 11.21 5.38 5.72
    D-AMP 29.26 29.26 21.95 21.95 16.01 16.01 5.34 5.34
    ReconNet 27.30 27.35 24.15 24.10 21.36 21.62 18.49 18.83
    DR$ ^2 $-Net 30.09 30.30 25.58 25.90 22.11 22.50 18.67 18.95
    MSRNet 30.74 30.93 26.32 26.50 22.58 22.79 18.65 18.88
    Flinstones TVAL3 24.05 24.07 18.88 18.92 14.88 14.91 9.75 9.77
    NLR-CS 22.43 22.56 12.18 12.21 8.96 9.29 4.45 4.77
    D-AMP 25.02 24.45 16.94 16.82 12.93 13.09 4.33 4.34
    ReconNet 22.45 22.59 18.92 19.18 16.30 16.56 13.96 14.08
    DR$ ^2 $-Net 26.19 26.77 21.09 21.46 16.93 17.05 14.01 14.18
    MSRNet 26.67 26.89 21.72 21.81 17.28 17.40 13.83 14.10
    Lena TVAL3 28.67 28.71 24.16 24.18 19.46 19.47 11.87 11.89
    NLR-CS 29.39 29.67 15.30 15.33 11.61 11.99 5.95 6.27
    D-AMP 28.00 27.41 22.51 22.47 16.52 16.86 5.73 5.96
    ReconNet 26.54 26.53 23.83 24.47 21.28 21.82 17.87 18.05
    DR$ ^2 $-Net 29.42 29.63 25.39 25.77 22.13 22.73 17.97 18.40
    MSRNet 30.21 30.37 26.28 26.41 22.76 23.06 18.06 18.35
    Monarch TVAL3 27.77 27.77 21.16 21.16 16.73 16.73 11.09 11.11
    NLR-CS 25.91 26.06 14.59 14.67 11.62 11.97 6.38 6.71
    D-AMP 26.39 26.55 19.00 19.00 14.57 14.57 6.20 6.20
    ReconNet 24.31 25.06 21.10 21.51 18.19 18.32 15.39 15.49
    DR$ ^2 $-Net 27.95 28.31 23.10 23.56 18.93 19.23 15.33 15.50
    MSRNet 28.90 29.04 23.98 24.17 19.26 19.48 15.41 15.61
    Peppers TVAL3 29.62 29.65 22.64 22.65 18.21 18.22 11.35 11.36
    NLR-CS 28.89 29.25 14.93 14.99 11.39 11.80 5.77 6.10
    D-AMP 29.84 28.58 21.39 21.37 16.13 16.46 5.79 5.85
    ReconNet 24.77 25.16 22.15 22.67 19.56 20.00 16.82 16.96
    DR$ ^2 $-Net 28.49 29.10 23.73 24.28 20.32 20.78 16.90 17.11
    MSRNet 29.51 29.86 24.91 25.18 20.90 21.16 17.10 17.33
    平均PSNR TVAL3 27.84 27.87 22.84 22.86 18.39 18.40 11.31 11.34
    NLR-CS 28.05 28.19 14.19 14.22 10.58 10.98 5.30 5.62
    D-AMP 28.17 27.67 21.14 21.09 15.49 15.67 5.19 5.23
    ReconNet 25.54 25.92 22.68 23.23 19.99 20.44 17.27 17.55
    DR$ ^2 $-Net 28.66 29.06 24.32 24.71 20.80 21.29 17.44 17.80
    MSRNet 29.48 29.67 25.16 25.38 21.41 21.68 17.54 17.82
    下载: 导出CSV

    表  2  不同算法下11幅测试图像平均SSIM

    Table  2  Mean SSIM values for 11 testing images by different algorithms

    算法 MR = 0.01 MR = 0.04 MR = 0.10 MR = 0.25
    ReconNet 0.4083 0.5266 0.6416 0.7579
    DR$ ^2 $-Net 0.4291 0.5804 0.7174 0.8431
    MSRNet 0.4535 0.6167 0.7598 0.8698
    下载: 导出CSV

    表  3  MSRNet重构图像修正后11幅测试图像的PSNR (dB)和SSIM

    Table  3  The PSNR (dB) and SSIM of 11 test images of refined MSRNet reconstruction

    图像 MR = 0.25 MR = 0.10 MR = 0.04
    PSNR SSIM PSNR SSIM PSNR SSIM
    Monarch 29.74 0.9189 24.40 0.8078 19.62 0.6400
    Parrots 30.13 0.9054 25.15 0.8240 22.06 0.7311
    Barbara 27.53 0.8553 23.28 0.6630 21.39 0.5524
    Boats 31.63 0.8999 26.73 0.7753 22.86 0.6355
    C-man 27.17 0.8433 23.33 0.7400 20.51 0.6378
    Fingerprint 28.75 0.9280 23.18 0.7777 18.81 0.5212
    Flinstones 27.77 0.8529 22.14 0.7114 17.46 0.4824
    Foreman 35.85 0.9297 31.71 0.8740 26.97 0.7939
    House 34.15 0.8891 29.55 0.8196 25.60 0.7443
    Lena 30.95 0.9019 26.68 0.7965 23.16 0.6882
    Peppers 30.67 0.8898 25.43 0.7811 21.28 0.6382
    平均值 30.39 0.8922 25.59 0.7791 21.79 0.6423
    下载: 导出CSV

    表  4  不同卷积方式在图 5的测试集中重构图像的平均PSNR (dB)

    Table  4  Mean PSNR in dB for testing set in Fig. 5 by different convolution

    卷积形式 MR = 0.01 MR = 0.04 MR = 0.10 MR = 0.25
    普通卷积 17.50 21.23 24.79 29.05
    扩张卷积 17.54 21.41 25.16 29.48
    下载: 导出CSV

    表  5  不同卷积方式在BSD500测试集中重构图像平均PSNR (dB)

    Table  5  Mean PSNR in dB for BSD500 testing set by different convolution

    算法 MR = 0.01 MR = 0.04 MR = 0.10 MR = 0.25
    普通卷积 19.34 22.14 24.48 27.78
    扩张卷积 19.35 22.25 24.73 27.93
    下载: 导出CSV

    表  6  重构一幅$ 256 \times 256 $图像的运行时间(s)

    Table  6  Time (in seconds) for reconstruction a single $ 256 \times 256 $ image

    算法 MR = 0.01 (CPU/GPU) MR = 0.04 (CPU/GPU) MR = 0.10 (CPU/GPU) MR = 0.25 (CPU/GPU)
    ReconNet 0.5363/0.0107 0.5369/0.0100 0.5366/0.0101 0.5361/0.0105
    DR$ ^2 $-Net 1.2039/0.0317 1.2064/0.0317 1.2096/0.0314 1.2176/0.0326
    MSRNet 0.4884/0.0121 0.5172/0.0124 0.5152/0.0117 0.5206/0.0126
    下载: 导出CSV

    表  7  不同算法在BSD500测试集的平均PSNR (dB)和平均SSIM

    Table  7  Mean PSNR in dB and SSIM values for BSD500 testing images by different algorithms

    模型 MR = 0.01 MR = 0.04 MR = 0.10 MR = 0.25
    PSNR SSIM PSNR SSIM PSNR SSIM PSNR SSIM
    ReconNet 19.17 0.4247 21.40 0.5149 23.28 0.6121 25.48 0.7241
    DR$ ^2 $-Net 19.34 0.4514 21.86 0.5501 24.26 0.6603 27.56 0.7961
    MSRNet 19.35 0.4541 22.25 0.5696 24.73 0.6837 27.93 0.8121
    下载: 导出CSV

    表  8  比较ReconNet、DR$ ^2 $-Net和MSRNet三种算法对高斯噪声的鲁棒性(图 5中11幅测试图像)

    Table  8  Comparison of robustness to Gaussian noise among of ReconNet, DR$ ^2 $-Net, MSRNet (11 testing images in Fig. 5)

    模型 MR = 0.25 MR = 0.10
    $ \sigma $ = 0.01 $ \sigma $ = 0.05 $ \sigma $ = 0.10 $ \sigma $ = 0.25 $ \sigma $ = 0.01 $ \sigma $ = 0.05 $ \sigma $ = 0.10 $ \sigma $ = 0.25
    ReconNet 25.44 23.81 20.81 14.15 22.63 21.64 19.54 14.17
    DR$ ^2 $-Net 28.49 25.63 21.45 14.32 24.17 22.70 20.04 14.54
    MSRNet 29.28 26.50 22.63 18.46 25.06 23.56 21.11 15.46
    下载: 导出CSV

    表  9  比较ReconNet、DR$ ^2 $-Net和MSRNet三种算法对高斯噪声的鲁棒性(BSD500数据集)

    Table  9  Comparison of robustness to Gaussian noise among of ReconNet, DR$ ^2 $-Net, MSRNet (BSD500 dataset)

    模型 MR = 0.25 MR = 0.10
    $ \sigma $ = 0.01 $ \sigma $ = 0.05 $ \sigma $ = 0.10 $ \sigma $ = 0.25 $ \sigma $ = 0.01 $ \sigma $ = 0.05 $ \sigma $ = 0.10 $ \sigma $ = 0.25
    ReconNet 25.38 22.03 20.72 14.03 23.22 22.06 19.85 14.51
    DR$ ^2 $-Net 27.40 24.99 21.32 14.47 24.17 22.74 20.26 14.85
    MSRNet 27.78 25.53 22.37 18.38 24.67 23.34 21.22 16.37
    下载: 导出CSV
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  • 收稿日期:  2017-09-26
  • 录用日期:  2018-01-29
  • 刊出日期:  2019-11-20

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