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Active Learning in an Information-rich Age

Explore the study of wavelets and signal denoising in an information-rich age. Understand how to use tools like Caveman Did Publish or Perish for scientific research. Dive into small-world phenomenon, Schroder Morlet, Grossmann Mayer, and more. Discover different classes of signals, noise, ECG signals, and noise in nature. Motivate the study of wavelet transforms and gain insights into noise properties in nature.

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Active Learning in an Information-rich Age

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

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

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

  4. Signal Denoising Studyby 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)?

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