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                    漸近非局部平均圖像去噪算法

                    邢笑笑 王海龍 李健 張選德

                    邢笑笑, 王海龍, 李健, 張選德. 漸近非局部平均圖像去噪算法. 自動化學報, 2020, 46(9): 1952?1960 doi: 10.16383/j.aas.c190294
                    引用本文: 邢笑笑, 王海龍, 李健, 張選德. 漸近非局部平均圖像去噪算法. 自動化學報, 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

                    漸近非局部平均圖像去噪算法

                    doi: 10.16383/j.aas.c190294
                    基金項目: 國家自然科學基金(61871260, 61362029, 61811530325, 61871259, 61603234)資助
                    詳細信息
                      作者簡介:

                      邢笑笑:陜西科技大學電子信息與人工智能學院碩士研究生. 2017年獲得吉林農業大學工學學士學位. 主要研究方向為圖像處理, 圖像去噪. E-mail: xingxiao_0918@163.com

                      王海龍:寧夏師范學院數學與計算機科學學院講師. 2011年獲得香港公開大學教育碩士學位. 主要研究方向為代數. E-mail: wanghailong7903@163.com

                      李?。宏兾骺萍即髮W電子信息與人工智能學院教授. 2002年獲得浙江大學工學博士學位. 主要研究方向為圖形圖像處理, 大數據挖掘與機器學習, 網絡與信息安全. E-mail: lijianjsj@sust.edu.cn

                      張選德:陜西科技大學電子信息與人工智能學院教授. 2013年獲得西安電子科技大學理學博士學位. 主要研究方向為圖像恢復, 圖像質量評價, 稀疏表示和低秩逼近理論. 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)是圖像處理領域具有里程碑意義的算法, NLM的提出開啟了影響深遠的非局部方法. 本文從以下兩個方面來重新探討非局部平均算法: 1) 針對NLM算法運算復雜度高的問題, 基于互相關(Cross-correlation, CC)和快速傅里葉變換(Fast Fourier transformation, FFT)構造了一種快速算法; 2) NLM在濾除噪聲的同時會模糊圖像結構信息, 在強噪聲條件下更是如此. 針對這一問題, 提出了一種漸近非局部平均圖像去噪算法, 該算法利用方差的性質來控制濾波參數. 數值實驗表明, 快速算法較之經典算法, 在標準參數配置下運行速度可提高27倍左右; 漸近非局部平均圖像去噪算法較之經典非局部平均圖像去噪算法, 去噪效果顯著改善.
                    • 圖  1  像素點i處的取塊示意圖

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

                      圖  2  濾波參數的大小對權值的影響

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

                      圖  3  NLM濾波與原圖的效果比較

                      Fig.  3  Effect comparison of NLM and original image

                      圖  4  漸近非局部的濾波結果

                      Fig.  4  Denoising result of asymptotic non-local

                      圖  5  三種算法對噪聲圖像的效果比較

                      Fig.  5  Effect comparison of three algorithms on noisy image

                      圖  6  三種算法對局部噪聲圖像的效果比較

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

                      表  1  三種去噪算法運行速度的比較

                      Table  1  Comparison of running speeds of three denoising algorithms

                      圖像塊
                      尺寸
                      搜索區域
                      尺寸
                      NLM運行
                      時間 (s)
                      NLM-P運行
                      時間 (s)
                      FNLM運行
                      時間 (s)
                      NLM與NLM-P
                      運行時間之比值
                      NLM與FNLM
                      運行時間之比值
                      NLM-P與FNLM
                      運行時間之比值
                      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
                      下載: 導出CSV

                      表  2  三種去噪算法對灰度圖像的效果比較

                      Table  2  Effect comparison of three denoising algorithms on gray images

                      圖像算法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
                      下載: 導出CSV
                      360彩票
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