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Assessment of the Wavelet Transform in Reduction of Noise from Simulated PET Images

Bahareh Shalchian, Hossein Rajabi and Hamid Soltanian-Zadeh
Journal of Nuclear Medicine Technology December 2009, 37 (4) 223-228; DOI: https://doi.org/10.2967/jnmt.109.067454

Article Figures & Data

Figures

  • FIGURE 1. 
    FIGURE 1. 

    Images obtained using DWT method: reference image (A), corresponding noisy image (B), image denoised using only approximation reconstruction procedure (C), and image denoised using approximation and diagonal reconstruction procedure (D). Corresponding line profiles are shown beneath images (at level 1 of decomposition).

  • FIGURE 2. 
    FIGURE 2. 

    Same test image as in Figure 1 has been denoised using solely approximation (SWT method): level 1 (A), level 2 (B), and level 3 (C) of decomposition. Corresponding line profiles are shown beneath images.

  • FIGURE 3. 
    FIGURE 3. 

    Same test image as in Figure 1 has been denoised using global thresholding: level 1 (A), level 2 (B), and level 3 (C) of decomposition. Corresponding line profiles are shown beneath images.

  • FIGURE 4. 
    FIGURE 4. 

    Same test image as in Figure 1 has been denoised using level-dependent soft thresholding procedures: default procedure (A), penalhi procedure (B), penalme procedure (C), and penallo procedure (D). Corresponding line profiles are shown beneath images.

Tables

  • TABLE 1

    Relative RMSE in DWT Using Different Combinations of Approximation and Details at 1 Level of Decomposition

    Reconstruction procedureRelative RMSE (mean ± SD)
    Only approximation0.315 ± 0.007
    Approximation and horizontal detail0.585 ± 0.013
    Approximation and vertical detail0.588 ± 0.008
    Approximation and diagonal detail0.446 ± 0.002
  • TABLE 2

    Relative RMSE in SWT Using Solely Approximation at Different Levels

    Decomposition levelRelative RMSE (mean ± SD)
    Level 10.196 ± 0.005
    Level 20.086 ± 0.009
    Level 30.119 ± 0.025
  • TABLE 3

    Relative RMSE at Different Levels of Global Thresholding

    Decomposition levelRelative RMSE (mean ± SD)
    Level 10.316 ± 0.007
    Level 20.104 ± 0.007
    Level 30.097 ± 0.012
  • TABLE 4

    Relative RMSE in Different Methods of Level-Dependent Thresholding at 1 Level of Decomposition

    Level-dependent thresholdRelative RMSE (mean ± SD)
    Default procedure0.418 ± 0.005
    Penalhi procedure0.315 ± 0.007
    Penalme procedure0.318 ± 0.007
    Penallo procedure0.320 ± 0.006
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