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.