Directional LiftingBased Wavelet Transform

1
Directional Lifting-Based Wavelet Transform

• Arian Maleki
• Shirin Jalali
• EE398 final project
• March, 2005

2
Outline

• Transform coding
• 2D wavelet
• Directional lifting
• Image compression based on directional lifting
• Directional invariant denoising

3
Transform Coding

• Advantages
• Signal decorrelation
• Sparse representation
• Fourier versus wavelet

4
2D Wavelet

• Separable filters
• Question How can edges be represented more
  efficiently?

5
Lifting structure

• 2-D lifting
• Predict
• Update

6
Directional Lifting

• Proposed by Ding et al (2004).
• Vertical lifting
• Horizontal lifting
• Lowpass 9 directions
• Highpass one direction
• 3 different modes one 16x16 , four 8x8 or
  sixteen 4x4
• Modes and directions are selected based on the
  Lagrangian cost function

7
Simulation results compression

• Simulation setup
• 5/3 biorthogonal wavelet
• Comparing the mean absolute value of each band

8
Simulation results compression (contd)
9
Denoising

• Old method Lowpass filtering
• Wavelet-based method
• Applying 2D wavelet to the noisy image
• Soft/hard thresholding
• Inverse 2D wavelet

10
Denoising (Contd)

• Applying thresholding algorithm to the DSP
  Wavelet
• Directional Invariant Denoising (DI) Denoising
  in all possible directions and taking the
  average.
• Simulation setup
• 9/7 biorthogonal wavelet
• Hard thresholding with same threshold for all the
  subbands

11
Denoising simulation results
Average of all directions
Direction 90
PSNR 26.3 dB
PSNR 27.7 dB
12
Conclusion

• Directional lifting based wavelet was discussed
• Its application in image compression was
  investigated
• Even more than 1.3 dB PSNR improvement can be
  achieved for some special images.
• In addition, the denoisng application of the
  directional lifting based wavelet was examined.
• It was observed that by averaging among all the
  directions, about 1.5dB PSNR gain can be
  obtained.