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Redundant Wavelet Transform and its Application in Denoising and Predication

Redundant Wavelet Transform and its Application in Denoising and Predication. Jiajun Gu May 15, 2003. Outline:. Definition Redundant Wavelet Transform Relationship with Discrete Wavelet Transform Relationship with Continuous Wavelet Transform Application Denoising Predication.

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Redundant Wavelet Transform and its Application in Denoising and Predication

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  1. Redundant Wavelet Transform and its Application in Denoising and Predication Jiajun Gu May 15, 2003

  2. Outline: • Definition Redundant Wavelet Transform • Relationship with Discrete Wavelet Transform • Relationship with Continuous Wavelet Transform • Application • Denoising • Predication

  3. Definition of Redundant Wavelet Transform Simple Idea: Undecimated DWT We do not decimate the coefficients after decomposition. Instead, modify the filters at each level by upsampling!

  4. Redundant Wavelet Transform

  5. Relationship with DWT Redundant Wavelet Transform contains the coefficients of DWT of Shifted Signal.

  6. Relationship with CWT Redundant wavelet transform is Discretizated version of CWT CWT: Discretize: It is Redundant Wavelet transform coefficient!

  7. Inverse Redundant Wavelet Transform Method 1: Choose one shift value, find the DWT coefficients and do IDWT Method 2: For every shift value, find the DWT coefficients and do IDWT. Average them!

  8. Denoising Why Redundant Wavelet can perform better? It is shift invariant!

  9. Examples

  10. Prediction Discretized version of CWT decomposition of signal in different frequency bands

  11. Predication Method Short term predication Neural Network Predication 12 inputs 4 hidden layers 1 output Use Real value to predict the next step

  12. Prediction Results MSE error 0.232 30% less than non transformed prediction

  13. A Close Look

  14. Conclusion • Advantage: shift-invariant • Disadvantage: more computation • N - N*log(N) • Application: • Denoising • Signal Exploration

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