## UC Berkeley / Lawrence Berkeley Laboratory

#### Adaptive Data Analysis via Nonlinear Compressed Sensing

**Tom Hou, Caltech**

##### April 22nd, 2010 at 2PM–3PM in 740 Evans Hall [Map]

We introduce an Instantaneous Fourier 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 a multiscale 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.