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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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