• Journal of Infrared and Millimeter Waves
  • Vol. 44, Issue 2, 297 (2025)
Jun-Gang YANG1, Ting LIU1,2,*, Yong-Xian LIU1,**, Bo-Yang LI1..., Ying-Qian WANG1, Wei-Dong SHENG1 and Wei AN1|Show fewer author(s)
Author Affiliations
  • 1College of Electronic Science and Technology,National University of Defense Technology,Changsha 410073,China
  • 2College of Automation and Electronic Information,Xiangtan University,Xiangtan 411100,China
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    DOI: 10.11972/j.issn.1001-9014.2025.02.017 Cite this Article
    Jun-Gang YANG, Ting LIU, Yong-Xian LIU, Bo-Yang LI, Ying-Qian WANG, Wei-Dong SHENG, Wei AN. Infrared small target detection method based on nonconvex low-rank Tuck decomposition[J]. Journal of Infrared and Millimeter Waves, 2025, 44(2): 297 Copy Citation Text show less
    The overall flow chart of the proposed method
    Fig. 1. The overall flow chart of the proposed method
    Comparison of ADMM algorithm and sGSADMM algorithm:(a)ADMM algorithm;(b)sGSADMM algorithm
    Fig. 2. Comparison of ADMM algorithm and sGSADMM algorithm:(a)ADMM algorithm;(b)sGSADMM algorithm
    The convergence curve of the proposed method on Sequence 6
    Fig. 3. The convergence curve of the proposed method on Sequence 6
    The qualitative experimental results of the proposed method and eight compared methods on Sequences 1-3(red rectangular box represents targets,blue oval represents background clutters and false alarm)
    Fig. 4. The qualitative experimental results of the proposed method and eight compared methods on Sequences 1-3(red rectangular box represents targets,blue oval represents background clutters and false alarm)
    The qualitative experimental results of the proposed method and eight compared methods on Sequences 4-6(where red rectangular box represents targets,blue oval represents background clutters and false alarm)
    Fig. 5. The qualitative experimental results of the proposed method and eight compared methods on Sequences 4-6(where red rectangular box represents targets,blue oval represents background clutters and false alarm)
    3D ROC curves for the proposed method and compared methods on Sequences 1-6. Each row from left to right represents 3D ROC,2D ROC Fa,Pd,2D ROC τ,Pd,2D ROC τ,Fa
    Fig. 6. 3D ROC curves for the proposed method and compared methods on Sequences 1-6. Each row from left to right represents 3D ROC,2D ROC Fa,Pd,2D ROC τ,Pd,2D ROC τ,Fa

    算法1 本文的NFTD-sGSADMM算法

      1.输入. 红外图像序列,OB0=S0=0,LHλ1λ2ρ0=0.01ρmax=1e7μ=1.5ζ=1e-6

      2.重复以下步骤,直到满足停止条件:

      步骤1. 根据式(11)更新Un

      步骤2. 根据式(14)更新Wn

      步骤3. 根据式(16)更新B

      步骤4. 根据式(19)更新G

      步骤5. 根据式(21)更新S

      步骤6. 根据式(16)更新B

      步骤7. 根据式(14)更新Wn

      步骤8. 根据式(11)更新Un

      步骤9 根据式(22)更新δnn=1NΓΛ

      步骤10. 根据式(23)更新ρ

      步骤11. 检查是否达到收敛条件O-B-SF2OF2ζ

      3.输出. 背景图像B,目标图像S

    Table 0. [in Chinese]
    LHAUCFa,FdAUCτ,PdAUCτ,FaAUCOAAUCSNPR
    380.99160.96830.00201.9579484.15
    480.99990.99660.00201.9945498.30
    580.99990.99950.00201.9974499.75
    680.99990.86080.00221.8585391.27
    780.99990.79800.00371.7942215.68
    880.99990.79800.00521.7927153.46
    LHAUCFa,FdAUCτ,PdAUCτ,FaAUCOAAUCSNPR
    520.99990.88040.11331.76707.7705
    540.99990.85290.03351.819325.460
    560.99990.81760.00781.8097104.82
    580.99990.99950.00201.9974499.75
    5100.99990.99740.00201.9953498.70
    Table 1. AUC metrics for different L and H values in sequence 1
    场景指标Top-hatNRAMECASTTMSLSTIPTASTTV-NTLAIMNN-LWECSRSTT4D-TTNFTD-sGSADMM
    0.99990.99580.99990.99990.99990.99580.99990.99990.9999
    0.99410.98350.95770.90000.98630.99360.78630.80590.9995
    序列10.05120.00200.00820.07520.03000.00200.00200.00200.0020
    1.94281.97731.94941.82471.95621.98741.78421.80381.9974
    19.416491.75116.7911.96832.877496.80393.15402.95499.75
    0.99990.99990.99990.99990.99990.99990.99990.99990.9999
    0.79020.71570.96820.98660.94310.85690.76670.88820.9830
    序列20.02700.00200.00220.28670.04390.00200.00200.00200.0020
    1.76311.71361.96591.69981.89911.85481.76461.88611.9809
    29.267357.85440.093.441221.483428.45383.35444.10491.50
    0.99990.99990.99980.99990.99990.99150.99990.99990.9999
    0.96170.95490.70650.82550.81760.90560.82160.81760.9667
    序列30.03090.00200.00510.06430.04550.00220.00200.00200.0020
    1.93071.95281.70121.76111.77201.89491.81951.81551.9646
    31.123477.45138.5312.83817.969411.64410.80408.80483.35
    0.99990.99990.99990.99990.99990.99990.99990.99990.9999
    0.96670.93530.97660.94710.99840.98630.95100.93920.9947
    序列40.02470.00200.00340.07410.02040.00200.00200.00200.0020
    1.94191.93321.97311.87291.97791.98421.94891.93711.9926
    39.138467.65287.2412.78148.941493.15475.50469.60497.35
    0.99990.89990.99950.99990.99990.99160.99990.99990.9999
    0.98780.78550.71300.98460.99760.98530.96670.96270.9911
    序列50.04790.00220.00990.34270.13840.00200.00200.00200.0020
    1.93981.68321.70261.64181.85911.97491.96461.96061.9890
    20.622357.0572.0202.87317.2081492.65483.35481.35495.55
    0.99990.98740.99990.99990.99990.98330.99990.99990.9999
    1.00000.76140.81750.90000.99760.92900.85290.93920.9812
    序列60.05210.00210.00750.13860.17760.00210.00200.00200.0020
    1.94781.74671.80991.76131.81991.91021.85081.93711.9791
    19.194362.57109.006.49355.6171442.38426.45469.60490.60
    Table 2. Evaluation of detection performance of different methods on Sequences 1-6.
    场景指标FTD-ADMMFTD-sGSADMMNFTD-ADMMNFTD-sGSADMM
    0.98330.99990.99990.9999
    0.88880.98810.98650.9947
    序列40.00200.00200.00200.0020
    1.87011.98601.98441.9926
    444.40494.05493.25497.35
    0.99990.99580.99990.9999
    0.99410.97510.98140.9911
    序列50.01990.00200.00200.0020
    1.97411.96891.97931.9890
    49.955487.55490.70495.55
    0.99990.97490.99160.9999
    0.93140.94110.96000.9812
    序列60.02170.00200.00200.0020
    1.90961.91401.94961.9791
    42.922470.55480.00490.60
    Table 3. Performance evaluation related to ablation experiments
    序列1序列2序列3序列4序列5序列6
    Top-hat0.0043s0.0042s0.0042s0.0042s0.0050s0.0041s
    NRAM1.3736s0.9492s1.3235s1.4354s1.2867s1.3546s
    ECASTT4.7305s4.8508s4.7872s4.7385s4.9369s4.6887s
    MSLSTIPT2.1905s2.2949s2.2691s2.2357s2.2702s2.2541s
    ASTTV-NTLA1.9818s1.8454s1.8661s1.7746s1.8840s1.8520s
    IMNN-LWEC2.5232s2.5428s2.5530s2.6821s2.5472s2.7229s
    SRSTT13.994s12.236s13.235s14.389s14.287s14.566s
    4D-TT0.9129s0.9272s0.9319s0.9310s0.9881s0.9635s
    NFTD-sGSADMM0.1807s0.1795s0.2418s0.1778s0.4583s0.4309s
    Table 4. Time comparison of the proposed method and compared methods in six scenes.
    Jun-Gang YANG, Ting LIU, Yong-Xian LIU, Bo-Yang LI, Ying-Qian WANG, Wei-Dong SHENG, Wei AN. Infrared small target detection method based on nonconvex low-rank Tuck decomposition[J]. Journal of Infrared and Millimeter Waves, 2025, 44(2): 297
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