DSP seminar: Oct 9, 1997

Speaker: Michael Kramer

Title: Nonlinear Transform Domain De-noising

Abstract:

Nonlinear wavelet based techniques for signal de-noising have been
extensively studied recently and show great promise at recovering
certain classes of signals.  Additionally, similar threshold based
schemes have been used with Fourier type bases to recover stationary
signals, also with good results.
  Rather than address which type of basis should be used, we consider
an analysis of applying a non-linear thresholding operation to general
frame expansions (i.e. transform domain de-noising) with the Fourier and
wavelet based techniques being special cases.  The frames we are considering
are typicaly overdetermined, consisting of several sub-frames to help match a
variety of signals.
  After introducing the frame-based notation and reviewing current work
in de-noising, we present theoretical threshold bounds for worst-case
and expected performace measures as well as some alternative schemes
for signal reconstruction given the same threshold non-linearity.