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基于非局部低秩和加权全变分的图像压缩感知重构算法

赵辉 张静 张乐 刘莹莉 张天骐

引用本文: 赵辉, 张静, 张乐, 刘莹莉, 张天骐. 基于非局部低秩和加权全变分的图像压缩感知重构算法[J]. 电子与信息学报, 2019, 41(8): 2025-2032. doi: 10.11999/JEIT180828 shu
Citation:  Hui ZHAO, Jing ZHANG, Le ZHANG, Yingli LIU, Tianqi ZHANG. Compressed Sensing Image Restoration Based on Non-local Low Rank and Weighted Total Variation[J]. Journal of Electronics and Information Technology, 2019, 41(8): 2025-2032. doi: 10.11999/JEIT180828 shu

基于非局部低秩和加权全变分的图像压缩感知重构算法

    作者简介: 赵辉: 女,1980年生,教授,硕士生导师,研究方向为信号与图像处理;
    张静: 女,1992年生,硕士生,研究方向为信号与图像处理;
    张乐: 女,1993年生,硕士生,研究方向为信号与图像处理;
    刘莹莉: 女,1994年生,硕士生,研究方向为信号与图像处理;
    张天骐: 男,1971年生,博士后,教授,研究方向为通信信号的调制解调、盲处理、语音信号处理、神经网络实现以及FPGA,VLSI实现
    通讯作者: 赵辉,zhaohui@cqupt.edu.cn
  • 基金项目: 国家自然科学基金(61671095)

摘要: 为准确有效地实现自然图像的压缩感知(CS)重构,该文提出一种基于图像非局部低秩(NLR)和加权全变分(WTV)的CS重构算法。该算法考虑图像的非局部自相似性(NSS)和局部光滑特性,对传统的全变分(TV)模型进行改进,只对图像的高频分量设置权重,并用一种差分曲率的边缘检测算子来构造权重系数。此外,算法以改进的TV模型与NLR模型为约束构建优化模型,并分别采用光滑非凸函数和软阈值函数来求解低秩和全变分优化问题,很好地利用了图像的自身性质,保护了图像的细节信息,并提高了算法的抗噪性和适应性。仿真结果表明,与基于NLR的CS算法相比,相同采样率下,该文所提算法的峰值信噪比最高可提高2.49 dB,且抗噪性更强,验证了算法的有效性。

English

    1. [1]

      CANDES E J, ROMBERG J, and TAO T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489–509. doi: 10.1109/TIT.2005.862083

    2. [2]

      DONOHO D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306. doi: 10.1109/TIT.2006.871582

    3. [3]

      石光明, 刘丹华, 高大化, 等. 压缩感知理论及其研究进展[J]. 电子学报, 2009, 37(5): 1070–1081. doi: 10.3321/j.issn:0372-2112.2009.05.028
      SHI Guangming, LIU Danhua, GAO Dahua, et al. Advances in theory and application of compressed sensing[J]. Acta Electronica Sinica, 2009, 37(5): 1070–1081. doi: 10.3321/j.issn:0372-2112.2009.05.028

    4. [4]

      ZHANG Jian, ZHAO Debin, ZHAO Chen, et al. Compressed sensing recovery via collaborative sparsity[C]. 2012 Data Compression Conference, Snowbird, USA, 2012: 287–296.

    5. [5]

      HE Guiqing, XING Siyuan, DONG Dandan, et al. Panchromatic and multi-spectral image fusion method based on two-step sparse representation and wavelet transform[C]. The 9th Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, Kuala Lumpur, Malaysia, 2017: 259–262.

    6. [6]

      RUBINSTEIN R, BRUCKSTEIN A M, and ELAD M. Dictionaries for sparse representation modeling[J]. Proceedings of the IEEE, 2010, 98(6): 1045–1057. doi: 10.1109/JPROC.2010.2040551

    7. [7]

      HONG Tao and ZHU Zhihui. Online learning sensing matrix and sparsifying dictionary simultaneously for compressive sensing[J]. Signal Processing, 2018, 153: 188–196. doi: 10.1016/j.sigpro.2018.05.021

    8. [8]

      EGIAZARIAN K, FOI A, and KATKOVNIK V. Compressed sensing image reconstruction via recursive spatially adaptive filtering[C]. 2007 IEEE International Conference on Image Processing, San Antonio, USA, 2007: I-549-I-552.

    9. [9]

      BUADES A, COLL B, and MOREL J M. A review of image denoising algorithms, with a new one[J]. Multiscale Modeling & Simulation, 2005, 4(2): 490–530. doi: 10.1137/040616024

    10. [10]

      LIU Hangfan, XIONG Ruiqin, ZHANG Xinfeng, et al. Nonlocal gradient sparsity regularization for image restoration[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2017, 27(9): 1909–1921. doi: 10.1109/TCSVT.2016.2556498

    11. [11]

      YU Jun and DONG Shumin. Nonlocal variational method application for image denoising[C]. 2017 IEEE International Conference on Signal Processing, Communications and Computing, Xiamen, China, 2017: 1–6.

    12. [12]

      DONG Weisheng, SHI Guangming, LI Xin, et al. Compressive sensing via nonlocal low-rank regularization[J]. IEEE Transactions on Image Processing, 2014, 23(8): 3618–3632. doi: 10.1109/TIP.2014.2329449

    13. [13]

      宋云, 李雪玉, 沈燕飞, 等. 基于非局部相似块低秩的压缩感知图像重建算法[J]. 电子学报, 2017, 45(3): 695–703. doi: 10.3969/j.issn.0372-2112.2017.03.029
      SONG Yun, LI Xueyu, SHEN Yanfei, et al. Compressed sensing image reconstruction based on low rank of non-local similar patches[J]. Acta Electronica Sinica, 2017, 45(3): 695–703. doi: 10.3969/j.issn.0372-2112.2017.03.029

    14. [14]

      LIU Hangfan, XIONG Ruiqin, LIU Dong, et al. Low rank regularization exploiting intra and inter patch correlation for image denoising[C]. 2017 IEEE Visual Communications and Image Processing, USA, 2017: 1–4.

    15. [15]

      GU Shuhang, XIE Qi, MENG Deyu, et al. Weighted nuclear norm minimization and its applications to low level vision[J]. International Journal of Computer Vision, 2017, 121(2): 183–208. doi: 10.1007/s11263-016-0930-5

    16. [16]

      RUDIN L I, OSHER S, and FATEMI E. Nonlinear total variation based noise removal algorithms[C]. The 11th Annual International Conference of the Center for Nonlinear Studies on Experimental mathematics: Computational Issues in Nonlinear Science, Los Alamos, USA, 1992: 259–268.

    17. [17]

      LI Chengbo, YIN Wotao, and ZHANG Yin. TVAL3: TV minimization by augmented lagrangian and alternating direction algorithms[EB/OL]. http://www.caam.rice.edu/~optimization/L1/TVAL3/, 2013.

    18. [18]

      CHEN Qiang, MONTESINOS P, SUN Quansen, et al. Adaptive total variation denoising based on difference curvature[J]. Image and Vision Computing, 2010, 28(3): 298–306. doi: 10.1016/j.imavis.2009.04.012

    19. [19]

      ZHANG Jian, LIU Shaohui, XIONG Ruiqin, et al. Improved total variation based image compressive sensing recovery by nonlocal regularization[C]. 2013 IEEE International Symposium on Circuits and Systems, Beijing, China, 2013: 2836–2839.

    20. [20]

      CANDèS E J, WAKIN M B, and BOYD S P. Enhancing sparsity by reweighted ${\ell _1}$ minimization[J]. Journal of Fourier Analysis and Applications, 2008, 14(5/6): 877–905. doi: 10.1007/s00041-008-9045-x

    21. [21]

      WANG Ting, NAKAMOTO K, ZHANG Heye, et al. Reweighted anisotropic total variation minimization for limited-angle CT reconstruction[J]. IEEE Transactions on Nuclear Science, 2017, 64(10): 2742–2760. doi: 10.1109/TNS.2017.2750199

    22. [22]

      LI Yan. Sparse hyperspectral unmixing combined L1/2 norm and reweighted total variation regularization[C]. The Ninth International Conference on Digital Image Processing, Hong Kong, China, 2017: 1042046.

    23. [23]

      BOYD S, PARIKH N, CHU E, et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations and Trends in Machine Learning, 2011, 3(1): 1–122. doi: 10.1561/2200000016

    24. [24]

      ZHANG Mingli, DESROSIERS C, and ZHANG Caiming. Effective compressive sensing via reweighted total variation and weighted nuclear norm regularization[C]. 2017 IEEE International Conference on Acoustics, Speech and Signal Processing, New Orleans, LA, United States, 2017: 1802–1806.

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  • 图 1  Barbara仿真效果对比图

    图 2  Parrots仿真效果对比图

    图 3  6幅测试图在不同采样率下各种算法的PSNR平均值

    图 4  算法测量值含噪的PSNR值比较

    表 1  基于非局部低秩和加权全变分的图像压缩感知重构算法(NLR-WTV)

     输入: 从原始图像${{u}}$采样得到的压缩感知测量值${{y}}$
     初始化:${{{u}}_0} = {{{Φ}} ^{\rm{T}}}{{y}}$, ${{a}}$, ${{b}}$, ${{c}}$, ${\lambda _1}$, ${\lambda _2}$, ${\mu _1}$, ${\mu _2}$;
     Outer loop for $k{\rm{ }} = 1, {\rm{ }}2, ·\!·\!·, K$
      (1) 根据块匹配法找到图像各相似像素点的位置;
      (2) 根据式(6)、式(7)和式(8)计算图像的低频分量${{{u}}_{\rm{L}}}$和高频分
    量${{{u}}_{\rm{R}}}$;
      (3) if $k \le {K_{{0}}}$, ${{{w}}_i} = 1$ else 根据式(9)计算${{{w}}_i}$;end if
     Inner loop for $t{\rm{ }} = 1, {\rm{ }}2, ·\!·\!·, T\;$
        (a) 根据式(17)计算${{{L}}_i}^{(k + 1)}$;
        (b) 根据式(19)计算${{{x}}^{(k + 1)}}$;
        (c) 分别根据式(21)和式(22)计算图像在低频和高频的梯度
    ${{{z}}_1}^{(k + 1)}$和${{{z}}_2}^{(k + 1)}$;
        (d) 根据式(25)计算${{{u}}^{(k + 1)}}$;
       end for
       根据式(14)更新${{a}}$, ${{b}}$和${{c}}$;
     end for
     输出:重构图像${ {{ u} } \!\,\!\! { { {\widehat} }= { {{u} }^{(k + 1)} }$
    下载: 导出CSV

    表 2  不同算法重构图像的PSNR(dB)和SSIM比较

    采样率算法性能指标MonarchBarbaraLenaBoatsParrotsCameraman
    5%TVAL3PSNR20.0619.7923.0822.3822.8722.89
    SSIM0.5080.4120.5600.5430.5930.605
    BM3D-CSPSNR22.7321.3424.1223.3124.1323.76
    SSIM0.6420.5230.6930.6100.6920.658
    TVNLRPSNR23.0222.6525.4124.7925.8924.39
    SSIM0.7510.5680.7450.6960.8000.737
    NLR-CSPSNR26.3827.9430.6429.8131.7125.38
    SSIM0.8480.8300.8750.8300.8850.770
    NLR-WTVPSNR28.2129.1030.8330.1432.3127.87
    SSIM0.8830.8620.8790.8570.8910.817
    下载: 导出CSV

    表 3  算法测量值含噪的SSIM值比较

    图像算法1520253035
    MonarchNLR-CS0.3740.5500.7480.8740.939
    NLR-WTV0.3870.5690.7610.8900.948
    BoatsNLR-CS0.2760.4520.6720.8240.904
    NLR-WTV0.2810.4660.6810.8440.927
    下载: 导出CSV
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文章相关
  • 通讯作者:  赵辉, zhaohui@cqupt.edu.cn
  • 收稿日期:  2018-08-22
  • 录用日期:  2019-01-28
  • 网络出版日期:  2019-02-25
  • 刊出日期:  2019-08-01
通讯作者: 陈斌, bchen63@163.com
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