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An optimized direction statistics for detecting and removing random-valued impulse noise

  • * Corresponding author: Leiting Chen

    * Corresponding author: Leiting Chen
Abstract Full Text(HTML) Figure(7) / Table(5) Related Papers Cited by
  • In this paper, we propose a robust local image statistic based on optimized direction, by which we can distinguish image details and edges from impulse noise effectively. Therefore it can identify noisy pixels more accurately. Meanwhile, we combine it with the edge-preserving regularization to remove random-valued impulse noise in the cause of precise estimated value. Simulation results show that our method can preserve edges and details efficiently even at high noise levels.

    Mathematics Subject Classification: Primary: 94A08; Secondary: 47A52.

    Citation:

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  • Figure 1.  two kinds of edge contained in neighbor, (a) vertical edge, (b) slope edge

    Figure 2.  Directions and hops

    Figure 3.  The mean PSNR values associated with different $\alpha$ values

    Figure 4.  Total error detection

    Figure 5.  Results obtained by different algorithms for restoring the test lena image corrupted by random-valued impulse noise with 40 % noise density. (a) Noisy image, (b) ACWM, (c) Luo's method, (d) ASWM, (e) DWM, (f) ROAD-Trilateral, (g) ROR-NLM, (h) ROLD-EPR, (i) Proposed Method.

    Figure 6.  Run time of detection vs. removal noises with different density

    Figure 7.  Run time of detection vs. removal noises with different scale image

    Table 1.  sets along the $l^{th}$ direction and hop count $h$

    $ S^{(1)}_{1}=\{ (-1,-1); (0, 0); (1, 1) \} $ $ S^{(1)}_{2}=\{ (-2,-2); (-1,-1); (0, 0); (1, 1); (2, 2) \} $
    $ S^{(2)}_{1}=\{ (0,-1); (0, 0); (0, 1) \} $ $ S^{(2)}_{2}=\{(0,-2); (0,-1); (0, 0); (0, 1); (0, 2)\}$
    $ S^{(3)}_{1}=\{ (1,-1); (0, 0); (-1, 1 \}$ $S^{(3)}_{2}=\{(2,-2); (1,-1); (0, 0); (-1, 1); (-2, 2)\}$
    $ S^{(4)}_{1}=\{ (-1, 0); (0, 0); (1, 0) \} $ $ S^{(4)}_{2}=\{(-2, 0); (-1, 0); (0, 0); (1, 0); (2, 0) \} $
     | Show Table
    DownLoad: CSV

    Table 2.  Comparison of noise detection results for image "Lena" with various ratios of random-valued impulse noise

    Method40%50%60%
    MissFalse-hitTotalMissFalse-hitTotalMissFalse-hitTotal
    ACWM[13]142491928161772059636022419831165666837833
    Luo[24]143651713160782059621352237133374288636260
    CEF[17]147276141208681749077452523521314865729971
    ASWM[2]73811104218423106141205022664195771684536422
    DWM[15]1160079371953715035865223687153731421529588
    ROR-NLM[32]124433056154991577836551943321601591727518
    ROAD[16]1347680792155513771100552382617212933026542
    ROLD[14]139877471214581633178752420617245922326468
    Proposed101585234153921130265831788515234762322857
     | Show Table
    DownLoad: CSV

    Table 3.  Comparison of restoration results in PSNR for images corrupted with random-valued impulse noise

    Method"Lena" image"Bridge" image"Pentagon" image
    40 %50 %60 %40 %50 %60 %40 %50 %60 %
    ACWM[13]29.5824.6320.4023.5221.4119.1227.0925.4723.41
    Luo[24]30.7727.1622.6223.5921.6219.1727.0025.3322.78
    CEF[17]32.1129.7625.9023.8522.7921.4127.1626.2425.12
    ASWM[2]32.2929.2325.0423.9722.5821.1127.2926.2024.98
    DWM[15]32.3429.3225.4924.0722.5821.1327.2326.0725.03
    ROR-NLM[32]32.9730.0225.6024.1822.8421.1927.6826.5625.36
    ROAD[16]32.0730.2427.4223.7323.0921.8826.6125.9224.82
    ROLD[14]32.7531.1228.9824.5123.5122.5227.5826.6525.61
    Proposed33.6231.7329.5624.9823.8222.7927.9226.9825.93
     | Show Table
    DownLoad: CSV

    Table 4.  Run time of detection vs. removal noises with different density

    Noise DensityRun Time(s)
    DetectionRemovalTotal
    30 % 4.7234.6939.41
    40 % 4.8373.3078.13
    50 %4.67163.53168.20
    60 % 4.65239.58244.23
    70 % 4.87271.64276.51
     | Show Table
    DownLoad: CSV

    Table 5.  Run time of detection vs. removal noises with different scale image

    Image ScaleRun Time(s)
    DetectionRemoval
    64×640.385.5
    128× 1281.1314.28
    256×2564.2734.69
    512×51217.19111.64
     | Show Table
    DownLoad: CSV
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