Adaptive data analysis via nonlinear compressed sensing

Thursday, November 4, 2010 - 3:00pm - 3:45pm
Keller 3-180
Thomas Hou (California Institute of Technology)
We introduce a new adaptive data analysis method to analyze
multiscale nonlinear and non-stationary data. The purpose of this
work is to find the sparsest representation of a multiscale signal
using basis that is adapted to the data instead of being prescribed
a priori. Using a variation approach base on nonlinear L1 optimization,
our method defines trends and Instantaneous Frequency of amultiscale signal. One advantage of performing such decomposition is to preserve some intrinsic physical property of the signal without
introducing artificial scales or harminics. For multiscale data that have a nonlinear sparse representation, we prove that
our nonlinear optimization method converges to the exact signal with
the sparse representation. Moreover, we will show that our method is
insensitive to noise and robust enough to apply to realistic physical
data. For general data that do not have a sparse representation,
our method will give an approximate decomposition and the accuracy
is controlled by the scale separation property of the original signal.