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基于高斯平滑压缩感知分数阶全变分算法的图像重构

覃亚丽 梅济才 任宏亮 胡映天 常丽萍

覃亚丽, 梅济才, 任宏亮, 胡映天, 常丽萍. 基于高斯平滑压缩感知分数阶全变分算法的图像重构[J]. 电子与信息学报. doi: 10.11999/JEIT200376
引用本文: 覃亚丽, 梅济才, 任宏亮, 胡映天, 常丽萍. 基于高斯平滑压缩感知分数阶全变分算法的图像重构[J]. 电子与信息学报. doi: 10.11999/JEIT200376
Yali QIN, Jicai MEI, Hongliang REN, Yingtian HU, Liping CHANG. Image Reconstruction Based on Gaussian Smooth Compressed Sensing Fractional Order Total Variation Algorithm[J]. Journal of Electronics and Information Technology. doi: 10.11999/JEIT200376
Citation: Yali QIN, Jicai MEI, Hongliang REN, Yingtian HU, Liping CHANG. Image Reconstruction Based on Gaussian Smooth Compressed Sensing Fractional Order Total Variation Algorithm[J]. Journal of Electronics and Information Technology. doi: 10.11999/JEIT200376

基于高斯平滑压缩感知分数阶全变分算法的图像重构

doi: 10.11999/JEIT200376
基金项目: 国家自然科学基金 (61675184, 61275124);浙江省自然科学基金(LY18F010023)
详细信息
    作者简介:

    覃亚丽:女,1963年生,教授,研究方向为光学信号处理

    梅济才:男,1994年生,硕士生,研究方向为压缩感知信号处理

    任宏亮:男,1978年生,副教授,研究方向为信号与信息处理

    胡映天:女,1991年生,讲师,研究方向为光纤传感

    常丽萍:女,1980年生,副教授,研究方向为压缩感知信号处理

    通讯作者:

    梅济才 2111703012@zjut.edu.cn

  • 中图分类号: TP391.41

Image Reconstruction Based on Gaussian Smooth Compressed Sensing Fractional Order Total Variation Algorithm

Funds: The National Natural Science Foundation of China (61675184, 61275124), The Natural Science Foundation of Zhejiang Province (LY18F010023)
  • 摘要: 针对全变分(TV)算法梯度效应造成图像纹理细节丢失和单像素成像系统中的环境噪声问题,该文给出基于高斯平滑压缩感知分数阶全变分(FOTVGS)算法的图像重构。分数阶微分损失图像低频分量的同时增加了图像的高频分量,达到增强图像细节的目的,高斯平滑滤波算子更新拉格朗日梯度算子滤除了微分算子导致的加性高斯白噪声高频分量的增加。仿真结果表明,对比其他4种同类算法,在相同的采样率和噪声水平下,该算法能取得最大的峰值信噪比(PSNR)和结构相似度(SSIM)。采样率为0.2时,对比分数阶全变分(FOTV)算法,在无噪声(测量值${\rm{SNR}} = \infty $)和有噪声(测量值${\rm{SNR}} = 25\;{\rm{dB}}$)情况下提高的最大峰值信噪比和结构相似度分别是1.39 dB(0.035)和3.91 dB(0.098)。可见,此算法在无噪声和有噪声情况下均能提高图像的重构质量,尤其是在有噪声情况下对图像重构质量有较大提高。该算法为单像素成像等计算成像系统中由于环境造成的噪声的图像重构提供了可行的解决方案。
  • 图  1  分数阶次$\alpha $对信号幅频特性的影响

    图  2  实验原始图

    图  3  高斯平滑算子加入前后,梯度算子更新变化对比图

    图  4  无噪声和噪声环境下重构对比图

    图  5  采样率为0.2情况下5种算法的重构SSIM曲线

    图  6  无噪声和噪声环境下5种算法在不同采样率下平均重构时间对比图

    表  1  改进算法流程

     输入:测量矩阵${{A}}$,测量值${{y}}$,相关参数${{\nu}} $, ${{\lambda}} $, $\beta $, $\gamma $, $\alpha $
     初始化:${{u}} = {{{A}}^{\rm T}}{{y}}$, ${{\nu}} = {\bf{0}}$, ${{\lambda}} = {\bf{0}}$, $\beta = {2^6}$, $\gamma = {2^7}$, $\alpha = {2^7}$
     While (目标函数式(8)未达到最优解) do
       While ${\left\| { { {{u} }^{(k + 1)} } - { {{u} }^k} } \right\|_2} \ge \varepsilon$ do
         利用式(12)求解${{w}}$子问题
         利用式(13)求解${{u}}$子问题
       End while
     利用式(10),使用高斯平滑滤波算子$G$更新拉格朗日梯度算子
     使用式(4),将输入图像的像素值作为权重,乘以相关核
     将上面各步得到的结果相加后输出
     End while
     输出:恢复的图像${{u}}$
    下载: 导出CSV

    表  2  在无噪声(测量值SNR=${{ \infty }}$)和有噪声情况下5种算法图像重构峰值信噪比(PSNR: dB)

    采样率0.10.2
    SNR (dB)1020253035$\infty $1020253035$\infty $
    BarbaraTV12.5316.2618.7719.3920.4322.0613.6217.2519.8320.4821.6624.12
    TVNR13.5016.7318.9219.8321.5323.0614.5417.8220.2321.5622.2325.05
    FOTV10.8315.5516.3918.2819.8624.3512.9116.7718.1019.2420.0425.56
    TVGS13.1016.5718.4318.7620.0421.5314.1217.7319.9419.5220.6223.21
    FOTVGS14.3217.9319.1720.3622.3025.2815.2518.3720.7722.1023.3126.35
    LenaTV16.6520.4822.5323.9624.0325.2918.3322.1023.4325.2426.9428.42
    TVNR17.8721.4223.1024.4025.1526.3419.5423.0324.9326.9427.5528.93
    FOTV15.9319.4021.5822.7823.4427.8117.2121.2222.3024.1925.1229.38
    TVGS17.2820.9822.7823.5223.8724.7218.8822.7424.2325.1426.2128.02
    FOTVGS18.6922.5924.4125.4226.4627.9320.3924.4725.3827.5828.2030.77
    BoatsTV14.7518.5820.1321.3022.5123.2115.5719.3821.0022.9124.2826.66
    TVNR15.9319.7420.9921.9423.0123.7516.5520.3422.8823.6524.8727.12
    FOTV13.5117.3718.8920.8621.3924.6014.2118.7520.7821.9323.9327.86
    TVGS15.3319.0020.2321.0222.0623.0116.0219.9321.2122.8224.0126.03
    FOTVGS17.1020.8622.3723.5524.3725.4617.8223.2624.6925.1526.8428.69
    PeppersTV16.6620.5121.1922.5423.5324.0317.8921.7523.2424.6525.3026.06
    TVNR17.5221.7922.3623.1124.0024.7818.7723.2324.8825.9426.2327.83
    FOTV15.7519.1320.2321.4722.7225.6616.5120.9622.4123.7124.5128.41
    TVGS17.2121.5521.2422.3123.1723.8418.2522.5523.9424.7125.0225.87
    FOTVGS18.6322.3523.7924.4725.3226.3319.5424.7725.4426.1127.3228.88
    采样率0.30.4
    SNR (dB)1020253035$\infty $1020253035$\infty $
    BarbaraTV14.6918.5521.0522.5023.4026.3316.5520.4523.6424.9825.9028.11
    TVNR15.7719.4921.9723.8724.5827.3317.6322.3724.5325.7826.4529.49
    FOTV13.9318.5619.0421.5122.5427.9515.3419.2422.2123.4824.2429.98
    TVGS15.4319.0321.2422.4723.2126.0017.2121.2324.0125.0725.7927.91
    FOTVGS16.8320.3622.4524.3425.1428.5718.5623.6625.4926.0327.8630.47
    LenaTV19.4123.9025.7227.4228.0131.1421.3125.8027.8629.7330.0132.62
    TVNR21.3225.4526.1128.0129.2131.9522.4126.9728.9930.0131.5233.43
    FOTV18.3322.9724.5025.9327.1832.6620.4524.8525.0627.1129.9934.53
    TVGS20.7824.3525.9627.5127.9430.9922.1726.6527.9929.7029.8832.39
    FOTVGS22.4526.3627.6929.0230.0333.1023.5827.5129.7331.4832.8935.36
    BoatsTV17.8823.0124.1925.2726.5528.3519.2325.3626.0027.4128.2829.87
    TVNR19.5324.9425.2426.4527.1428.8320.8226.6527.2128.7729.5630.29
    FOTV17.0222.9423.1224.5625.5129.2518.8824.1625.7826.0327.6430.68
    TVGS18.7724.6824.2325.1026.3528.0120.5926.1826.5527.4628.0029.51
    FOTVGS20.4525.4926.2227.1828.0329.6721.9627.4228.6929.1530.2431.43
    PeppersTV18.6123.4024.2225.0426.7427.9619.9724.0625.6126.9728.1629.71
    TVNR19.9324.8225.9626.9227.7128.3221.3225.3626.9927.9828.7229.92
    FOTV17.4420.6722.5824.2325.3529.1118.5423.6624.9726.0527.1430.51
    TVGS19.6624.5424.4225.0226.4527.3120.8625.8825.9726.8729.0329.41
    FOTVGS21.2325.3526.7927.4728.8929.4222.3926.7727.4428.3529.1130.89
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-05-12
  • 修回日期:  2020-11-06
  • 网络出版日期:  2020-11-11

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