Noisy data

 Noise comes in two distinct flavors. First is erratic bursty noise which is difficult to fit into a statistical model. It bursts out of our simple models. To handle this noise we need ``robust'' estimation procedures which we consider first.

Next is noise that has a characteristic spectrum, temporal spectrum, spatial spectrum, or dip spectrum. Such noise is called ``stationary'' noise. A special case of stationary noise is low frequency drift of the mean value of a signal.

In real life, we need to handle both bursty noise and stationary noise at the same time. We'll try that now.

 

• MEANS, MEDIANS, PERCENTILES AND MODES
  • Percentiles and Hoare's algorithm
  • The weighted mean
  • Weighted L.S. conjugate-direction template
  • Multivariate $\ell^1$ estimation by iterated reweighting
  • Nonlinear L.S. conjugate-direction template
  • Minimizing the Cauchy function
• NOISE BURSTS
  • De-spiking with median smoothing
  • De-bursting
• MEDIAN BINNING
• ROW NORMALIZED PEF
• DEBURST
  • Potential seismic applications of two-stage infill
• TWO 1-D PEFS VERSUS ONE 2-D PEF
• ALTITUDE OF SEA SURFACE NEAR MADAGASCAR
• ELIMINATING NOISE AND SHIP TRACKS IN GALILEE
  • Attenuation of noise bursts and glitches
  • Preconditioning for accelerated convergence
  • $\ell^1$ norm
  • Abandoned strategy for attenuating tracks
  • Modeling data acquisition drift
  • Regridding