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Directional Lifting-Based Wavelet Transform

Directional Lifting-Based Wavelet Transform. Arian Maleki Shirin Jalali EE398 final project March, 2005. Outline. Transform coding 2D wavelet Directional lifting Image compression based on directional lifting Directional invariant denoising. Transform Coding. Advantages:

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Directional Lifting-Based Wavelet Transform

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  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 (cont’d)

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

  10. Denoising (Cont’d) • 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.

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