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Wavelet Decomposition

  • Wavelets: A math tool for space-efficient hierarchical decomposition of functions
  • S = [2, 2, 0, 2, 3, 5, 4, 4] can be transformed to

    \[ S^ = [2\frac{3}{4}, -1\frac{1}{4}, \frac{1}{2}, 0, 0, -1, -1, 0] \]
  • Compression: many small detail coefficients can be replaced by 0’s, and only the significant coefficients are retained
 

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