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分块压缩感知的全变差正则化重构算法

谌德荣 吕海波 李秋富 宫久路 厉智强 韩肖君

引用本文: 谌德荣, 吕海波, 李秋富, 宫久路, 厉智强, 韩肖君. 分块压缩感知的全变差正则化重构算法[J]. 电子与信息学报, 2019, 41(9): 2217-2223. doi: 10.11999/JEIT180931 shu
Citation:  Derong CHEN, Haibo LÜ, Qiufu LI, Jiulu GONG, Zhiqiang LI, Xiaojun HAN. Total Variation Regularized Reconstruction Algorithms for Block Compressive Sensing[J]. Journal of Electronics and Information Technology, 2019, 41(9): 2217-2223. doi: 10.11999/JEIT180931 shu

分块压缩感知的全变差正则化重构算法

    作者简介: 谌德荣: 女,1966年生,博士,教授,研究方向为信息处理、自动目标识别等;
    吕海波: 男,1993年生,硕士生,研究方向为图像压缩处理等;
    宫久路: 男,1983年生,博士,讲师,研究方向为数字信号处理、模式识别等;
    通讯作者: 宫久路,lujiugong@bit.edu.cn
摘要: 针对分块压缩感知(BCS)重建图像质量较差问题,该文提出一种最小化l0范数的分块压缩感知全变差(TV)正则化迭代阈值图像重构算法(BCS-TVIT)。BCS-TVIT算法考虑图像的局部平滑、有界变差等性质,将最小化l0范数与图像的全变差TV正则项结合,构建目标函数。针对目标函数中l0范数项和分块测量约束项无法直接优化问题,采用迭代阈值法使重构图像l0范数最小化,并通过凸集投影保证满足约束条件,完成了目标函数的优化求解。实验表明,与基于l0范数最小化的分块压缩感知平滑投影算法(BCS-SPL)相比,BCS-TVIT算法重构图像峰值信噪比提高2 dB,能消除BCS-SPL的“亮斑”效应,且在视觉效果上明显优于BCS-SPL算法;与最小全变差算法相比,BCS-TVIT算法重构图像峰值信噪比提升1 dB,且能降低重构时间约2个数量级。

English

    1. [1]

      CANDÈS E J, ELDAR Y C, NEEDELL D, et al. Compressed sensing with coherent and redundant dictionaries[J]. Applied and Computational Harmonic Analysis, 2010, 31(1): 59–73. doi: 10.1016/j.acha.2010.10.002

    2. [2]

      KABANAVA M and RAUHUT H. Cosparsity in Compressed Sensing[M]. Cham: Birkhäuser, 2015: 315–339.

    3. [3]

      ZHOU Chengwei, GU Yujie, ZHANG Y D, et al. Compressive sensing-based coprime array direction-of-arrival estimation[J]. IET Communications, 2017, 11(11): 1719–1724. doi: 10.1049/iet-com.2016.1048

    4. [4]

      GAN Lu. Block compressed sensing of natural images[C]. 2007 5th International Conference on Digital Signal Processing, Cardiff, UK, 2007: 403–406.

    5. [5]

      VAN CHIEN T, DINH K Q, JEON B, et al. Block compressive sensing of image and video with nonlocal Lagrangian multiplier and patch-based sparse representation[J]. Signal Processing: Image Communication, 2017, 54: 93–106. doi: 10.1016/j.image.2017.02.012

    6. [6]

      MUN S and FOWLER J E. Block compressed sensing of images using directional transforms[C]. The 16th IEEE International Conference on Image Processing, Cairo, Egypt, 2009: 3021–3024.

    7. [7]

      唐朝伟, 王雪锋, 杜永光. 一种稀疏度自适应分段正交匹配追踪算法[J]. 中南大学学报(自然科学版), 2016, 47(3): 784–792. doi: 10.11817/j.issn.1672-7207.2016.03.011
      TANG Chaowei, WANG Xuefeng, and DU Yongguang. A sparsity adaptive stagewise orthogonal matching pursuit algorithm[J]. Journal of Central South University (Science and Technology), 2016, 47(3): 784–792. doi: 10.11817/j.issn.1672-7207.2016.03.011

    8. [8]

      CANDES E J and TAO T. Near-optimal signal recovery from random projections: Universal encoding strategies[J]. IEEE Transactions on Information Theory, 2006, 52(12): 5406–5425. doi: 10.1109/TIT.2006.885507

    9. [9]

      EFTEKHARI A and WAKIN M B. New analysis of manifold embeddings and signal recovery from compressive measurements[J]. Applied and Computational Harmonic Analysis, 2015, 39(1): 67–109. doi: 10.1016/j.acha.2014.08.005

    10. [10]

      陈勇, 吴春婷, 刘焕淋. 基于改进压缩感知的缺损光纤Bragg光栅传感信号修复方法[J]. 电子与信息学报, 2018, 40(2): 386–393. doi: 10.11999/JEIT170424
      CHEN Yong, WU Chunting, and LIU Huanlin. A repaired algorithm based on improved compressed sensing to repair damaged fiber bragg grating sensing signal[J]. Journal of Electronics &Information Technology, 2018, 40(2): 386–393. doi: 10.11999/JEIT170424

    11. [11]

      BLUMENSATH T and DAVIES M E. Iterative hard thresholding for compressed sensing[J]. Applied and Computational Harmonic Analysis, 2009, 27(3): 265–274. doi: 10.1016/j.acha.2009.04.002

    12. [12]

      宋和平, 王国利. 稀疏信号重构的阈值化迭代检测估计[J]. 电子与信息学报, 2014, 36(10): 2431–2437. doi: 10.3724/SP.J.1146.2013.01696
      SONG Hepin and WANG Guoli. Sparse signal recovery via iterative detection estimation with thresholding[J]. Journal of Electronics &Information Technology, 2014, 36(10): 2431–2437. doi: 10.3724/SP.J.1146.2013.01696

    13. [13]

      XIAO Yunhai, YANG Junfeng, and YUAN Xiaoming. Alternating algorithms for total variation image reconstruction from random projections[J]. Inverse Problems & Imaging, 2012, 6(3): 547–563. doi: 10.3934/ipi.2012.6.547

    14. [14]

      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

    15. [15]

      CANDÈS E J, ROMBERG J K, and TAO T. Stable signal recovery from incomplete and inaccurate measurements[J]. Communications on Pure and Applied Mathematics, 2006, 59(8): 1207–1223. doi: 10.1002/cpa.20124

    16. [16]

      CHEN Gao, LI Gang, and ZHANG Jiashu. Tensor compressed video sensing reconstruction by combination of fractional-order total variation and sparsifying transform[J]. Signal Processing: Image Communication, 2017, 55: 146–156. doi: 10.1016/j.image.2017.03.021

    17. [17]

      USC. The USC-SIPI image database[EB/OL]. http://sipi.usc.edu/database/database.php?volume=misc&image=12, 2018.

    18. [18]

      CHEN Duo, WAN Suiren, XIANG Jing, et al. A high-performance seizure detection algorithm based on Discrete Wavelet Transform (DWT) and EEG[J]. PLoS One, 2017, 12(3): e0173138. doi: 10.1371/journal.pone.0173138

    19. [19]

      YANG Jingyu, XU Wenli, DAI Qionghai, et al. Image compression using 2D Dual-tree Discrete Wavelet Transform (DDWT)[C]. 2007 IEEE International Symposium on Circuits and Systems, New Orleans, USA, 2007: 297–300.

    20. [20]

      SAI N S T and PATIL R C. Image retrieval using 2D dual-tree discrete wavelet transform[J]. International Journal of Computer Applications, 2011, 14(6): 1–8. doi: 10.5120/1891-2513

    21. [21]

      SENDUR L and SELESNICK I W. Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency[J]. IEEE Transactions on Signal Processing, 2002, 50(11): 2744–2756. doi: 10.1109/TSP.2002.804091

    22. [22]

      GOMATHI R, and SELVAKUMARAN S. A new bivariate shrinkage denoising of remotely sensed images with Discrete Shearlet Transform (DST)[C]. 2018 Second International Conference on Intelligent Computing and Control Systems (ICICCS), Madurai, India, 2018: 173–175.

    23. [23]

      ZHANG Fuqiang and LIU Zengli. Image denoising based on the bivariate model of dual tree complex wavelet transform[C]. The 11th International Conference on Computational Intelligence and Security, Shenzhen, China, 2015: 171–174. doi: 10.1109/CIS.2015.49.

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  • 图 1  0.1采样率下BCS-SPL, BCS-TV, BCS-TVIT重构图像

    图 2  红外图像序列

    表 1  各算法的重构PSNR (dB)

    算法采样率
    0.10.20.30.40.5
    BCS-SPL[6]22.5024.0225.6427.2828.91
    BarbaraBCS-TV[15]22.3823.5224.4825.5626.73
    BCS-TVIT22.6724.4126.4628.7331.58
    BCS-SPL[6]23.7325.3026.5727.7229.01
    LaxBCS-TV[15]23.7526.0528.0629.9331.77
    BCS-TVIT24.1626.8828.6930.5032.28
    BCS-SPL[6]25.5427.1028.2729.3930.59
    BuildingBCS-TV[15]25.4527.9929.8831.6933.50
    BCS-TVIT26.2828.9930.6332.1933.74
    BCS-SPL[6]23.3725.3226.8028.3129.56
    AerialBCS-TV[15]23.2225.6327.6729.4231.41
    BCS-TVIT24.0227.2829.5731.5633.26
    下载: 导出CSV

    表 2  各算法的重构时间(s)

    算法采样率
    0.10.20.30.40.5
    BCS-SPL[6]521612129
    BarbaraBCS-TV[15]12101514175921362690
    BCS-TVIT7057322121
    BCS-SPL[6]3528272524
    LaxBCS-TV[15]11791499173720972638
    BCS-TVIT3930282925
    BCS-SPL[6]5135252421
    BuildingBCS-TV[15]12221539178121532684
    BCS-TVIT5338262622
    BCS-SPL[6]5030262418
    AerialBCS-TV[15]11701492175021252666
    BCS-TVIT5130282319
    下载: 导出CSV

    表 3  重构图像PSNR (dB)

    算法采样率
    0.10.20.30.40.5
    第100帧BCS-SPL[6]32.3840.3543.0544.7346.25
    BCS-TVIT37.7040.5442.4545.0645.63
    第400帧BCS-SPL[6]33.4735.2037.2338.9340.51
    BCS-TVIT33.7836.5438.4940.1641.75
    下载: 导出CSV

    表 4  重构图像PSNR (dB)的统计结果

    算法采样率
    0.10.20.30.40.5
    平均值BCS-SPL[6]25.7128.5830.5632.2333.83
    BCS-TVIT25.9829.8232.0734.2036.51
    最大值BCS-SPL[6]31.8135.6437.3939.2241.00
    BCS-TVIT32.5536.9939.4741.4144.41
    最小值BCS-SPL[6]15.4719.2222.2723.1824.23
    BCS-TVIT18.6022.1323.4924.7126.01
    下载: 导出CSV
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文章相关
  • 通讯作者:  宫久路, lujiugong@bit.edu.cn
  • 收稿日期:  2018-09-30
  • 录用日期:  2019-02-18
  • 网络出版日期:  2019-03-23
  • 刊出日期:  2019-09-01
通讯作者: 陈斌, bchen63@163.com
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