1. Active Learning in an Information-rich Age Early 20 th century, how do you study physics? Early 21 st century, how do you study wavelets?

2. Use Tools Like Caveman Did http://www.harzing.com/resources.htm#/pop.htm Publish or Perish (a good tool for scientific research)

3. Small-World Phenomenon Donoho Johnstone Coifman Vertteli DeVore Daubechies Sweldens Mallat Mayer Morlet, Grossmann Vaidyanathan Schröder

4. Signal Denoising Study by Toy Examples taken from Donoho’s paper “Translation-invariant Denoising”

5. Four Classes of Signals

6. Noisy Observations Y=X+W W~N(0,1)

7. An Easy Attack Use a Low-Pass filter such as moving averaging Why low-pass? What if noise is periodic? How far are we from the optimal performance?

8. A Different Class of Signal

9. A Different Class of Noise ECG signal

10. Signal in Nature Self-similar property (Global) –1/f noise is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency Transient/nonstationary property (Local) –Changes in space and time –Motivate the study of wavelet transforms

11. Noise in Nature Always Gaussian? Stationary or transient? Random or structural (perceptually meaningful)?