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渐近非局部平均图像去噪算法

邢笑笑 王海龙 李健 张选德

邢笑笑, 王海龙, 李健, 张选德. 渐近非局部平均图像去噪算法. 自动化学报, 2020, 46(9): 1952−1960 doi: 10.16383/j.aas.c190294
引用本文: 邢笑笑, 王海龙, 李健, 张选德. 渐近非局部平均图像去噪算法. 自动化学报, 2020, 46(9): 1952−1960 doi: 10.16383/j.aas.c190294
Xing Xiao-Xiao, Wang Hai-Long, Li Jian, Zhang Xuan-De. Asymptotic non-local means image denoising algorithm. Acta Automatica Sinica, 2020, 46(9): 1952−1960 doi: 10.16383/j.aas.c190294
Citation: Xing Xiao-Xiao, Wang Hai-Long, Li Jian, Zhang Xuan-De. Asymptotic non-local means image denoising algorithm. Acta Automatica Sinica, 2020, 46(9): 1952−1960 doi: 10.16383/j.aas.c190294

渐近非局部平均图像去噪算法

doi: 10.16383/j.aas.c190294
基金项目: 国家自然科学基金(61871260, 61362029, 61811530325, 61871259, 61603234)资助
详细信息
    作者简介:

    邢笑笑:陕西科技大学电子信息与人工智能学院硕士研究生. 2017年获得吉林农业大学工学学士学位. 主要研究方向为图像处理, 图像去噪. E-mail: xingxiao_0918@163.com

    王海龙:宁夏师范学院数学与计算机科学学院讲师. 2011年获得香港公开大学教育硕士学位. 主要研究方向为代数. E-mail: wanghailong7903@163.com

    李健:陕西科技大学电子信息与人工智能学院教授. 2002年获得浙江大学工学博士学位. 主要研究方向为图形图像处理, 大数据挖掘与机器学习, 网络与信息安全. E-mail: lijianjsj@sust.edu.cn

    张选德:陕西科技大学电子信息与人工智能学院教授. 2013年获得西安电子科技大学理学博士学位. 主要研究方向为图像恢复, 图像质量评价, 稀疏表示和低秩逼近理论. 本文通信作者. E-mail: zhangxuande@sust.edu.cn

Asymptotic Non-local Means Image Denoising Algorithm

Funds: Supported by National Natural Science Foundation of China (61871260, 61362029, 61811530325, 61871259, 61603234)
  • 摘要: 非局部平均去噪算法(Non-local means denoising algorithm, NLM)是图像处理领域具有里程碑意义的算法, NLM的提出开启了影响深远的非局部方法. 本文从以下两个方面来重新探讨非局部平均算法: 1) 针对NLM算法运算复杂度高的问题, 基于互相关(Cross-correlation, CC)和快速傅里叶变换(Fast Fourier transformation, FFT)构造了一种快速算法; 2) NLM在滤除噪声的同时会模糊图像结构信息, 在强噪声条件下更是如此. 针对这一问题, 提出了一种渐近非局部平均图像去噪算法, 该算法利用方差的性质来控制滤波参数. 数值实验表明, 快速算法较之经典算法, 在标准参数配置下运行速度可提高27倍左右; 渐近非局部平均图像去噪算法较之经典非局部平均图像去噪算法, 去噪效果显著改善.
  • 图  1  像素点i处的取块示意图

    Fig.  1  The schematic of taking blocks at pixel points i

    图  2  滤波参数的大小对权值的影响

    Fig.  2  The influence of filter parameter size on the weight

    图  3  NLM滤波与原图的效果比较

    Fig.  3  Effect comparison of NLM and original image

    图  4  渐近非局部的滤波结果

    Fig.  4  Denoising result of asymptotic non-local

    图  5  三种算法对噪声图像的效果比较

    Fig.  5  Effect comparison of three algorithms on noisy image

    图  6  三种算法对局部噪声图像的效果比较

    Fig.  6  Effect comparison of three algorithms on local noisy image

    表  1  三种去噪算法运行速度的比较

    Table  1  Comparison of running speeds of three denoising algorithms

    图像块
    尺寸
    搜索区域
    尺寸
    NLM运行
    时间 (s)
    NLM-P运行
    时间 (s)
    FNLM运行
    时间 (s)
    NLM与NLM-P
    运行时间之比值
    NLM与FNLM
    运行时间之比值
    NLM-P与FNLM
    运行时间之比值
    3 × 321 × 21232.7919.417.1711.9932.462.71
    3 × 331 × 31505.6442.0110.5312.0448.023.99
    3 × 351 × 51873.02113.0413.957.7262.588.10
    3 × 3101 × 1015 024.73160.1048.4931.38103.623.30
    5 × 521 × 21236.1218.298.6812.9127.202.11
    5 × 531 × 31512.7739.9012.7412.8540.253.13
    5 × 551 × 51911.16108.0416.198.4356.286.67
    5 × 5101 × 1015 159.80154.8353.1333.3397.122.91
    7 × 721 × 21250.7719.2111.2813.0522.231.70
    7 × 731 × 31547.5042.2916.5112.9533.162.56
    7 × 751 × 151913.15114.3719.755.5846.245.79
    7 × 7101 × 1015 328.55163.5659.9632.5888.872.73
    9 × 921 × 21256.4918.5413.4013.8319.141.38
    9 × 931 × 31560.1739.6320.7014.1327.061.91
    9 × 951 × 51969.08108.7423.358.9141.504.66
    9 × 9101 × 1015 516.60154.7567.4135.6581.842.30
    下载: 导出CSV

    表  2  三种去噪算法对灰度图像的效果比较

    Table  2  Effect comparison of three denoising algorithms on gray images

    图像算法25305075100
    PSNR/SSIMPSNR/SSIMPSNR/SSIMPSNR/SSIMPSNR/SSIM
    Camera 256 × 256NLM28.23/0.7727.27/0.7324.26/0.5721.82/0.4120.17/0.30
    PNLM28.39/0.8227.58/0.7924.96/0.7122.59/0.6121.02/0.52
    ANLM28.07/0.8327.43/0.8125.35/0.7323.32/0.6421.80/0.56
    Lena 512 × 512NLM30.11/0.8929.13/0.8726.21/0.7823.75/0.6722.00/0.58
    PNLM30.58/0.8929.72/0.8827.18/0.8125.07/0.7323.65/0.67
    ANLM30.59/0.9029.80/0.8927.57/0.8325.72/0.7724.35/0.71
    Boat 512 × 512NLM28.17/0.8527.21/0.8224.53/0.7222.48/0.6121.04/0.53
    PNLM28.40/0.8527.51/0.8224.99/0.7223.17/0.6322.07/0.56
    ANLM28.55/0.8627.74/0.8425.50/0.7523.73/0.6722.58/0.61
    Finger 512 × 512NLM26.57/0.9325.43/0.9121.84/0.7919.18/0.6317.73/0.51
    PNLM26.41/0.9325.45/0.9122.15/0.7819.22/0.5717.64/0.40
    ANLM26.41/0.9425.63/0.9323.00/0.8320.40/0.6818.58/0.52
    B Fly 512 × 512NLM28.09/0.8527.12/0.8223.88/0.6920.61/0.5418.39/0.41
    NLM27.78/0.8826.98/0.8624.32/0.7921.44/0.68 18.99/0.56
    ANLM27.61/0.8926.84/0.8724.65/0.8022.44/0.7220.45/0.63
    Man 512 × 512NLM28.28/0.8527.39/0.8224.87/0.7122.83/0.6121.35/0.53
    PNLM28.45/0.8427.62/0.8125.32/0.7123.61/0.6222.51/0.56
    ANLM28.63/0.8627.89/0.8325.83/0.7524.20/0.6723.08/0.61
    Baboon 512 × 512NLM24.53/0.8123.66/0.7721.60/0.6320.27/0.5219.36/0.44
    PNLM24.61/0.8123.75/0.7621.51/0.5920.23/0.4719.61/0.40
    ANLM24.62/0.8323.88/0.7921.83/0.6420.57/0.5319.90/0.45
    Straw 256 × 256NLM24.67/0.8023.50/0.7420.71/0.5519.16/0.3918.27/0.31
    PNLM24.94/0.8123.78/0.7520.66/0.5118.96/0.3218.25/0.24
    ANLM24.96/0.8324.04/0.7821.23/0.5819.37/0.4018.51/0.32
    Barbara 512 × 512NLM28.26/0.8927.11/0.8724.05/0.7621.92/0.6520.54/0.57
    PNLM28.76/0.9027.64/0.8824.51/.07822.45/0.6821.30/0.60
    ANLM28.72/0.9127.82/0.8925.08/0.8123.02/0.7121.82/0.65
    Montage 256 × 256NLM30.31/0.8329.17/0.7825.54/0.6222.21/0.4420.24/0.33
    PNLM30.56/0.8829.50/0.8626.41/0.7923.51/0.6921.31/0.59
    ANLM30.60/0.8929.65/0.8727.04/0.8024.50/0.7122.28/0.62
    House 256 × 256NLM30.60/0.7829.43/0.7425.92/0.5723.20/0.4121.43/0.30
    PNLM31.30/0.8330.26/0.8126.97/0.7324.31/0.6222.74/0.54
    ANLM31.28/0.8430.47/0.8227.85/0.7525.35/0.6623.58/0.58
    Hill 512 × 512NLM28.21/0.8327.33/0.7924.94/0.6823.08/0.5821.68/0.51
    PNLM28.37/0.8227.51/0.7825.31/0.6623.87/0.5723.01/0.52
    ANLM28.69/0.8427.94/0.8125.86/0.7124.38/0.6223.44/0.57
    Couple 512 × 512NLM27.50/0.8426.52/0.8024.03/0.6922.16/0.5820.84/0.50
    PNLM27.76/0.8426.74/0.8024.27/0.6722.68/0.5721.71/0.51
    ANLM28.12/0.8627.21/0.8324.79/0.7223.22/0.6222.20/0.56
    Peppers 256 × 256NLM28.61/0.7927.58/0.7524.45/0.6021.76/0.4520.00/0.34
    PNLM29.04/0.8328.08/0.8025.12/0.7222.40/0.6220.64/0.53
    ANLM28.75/0.8427.93/0.8125.51/0.7423.34/0.6521.64/0.57
    下载: 导出CSV
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  • 收稿日期:  2019-04-11
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