| In this talk, we introduce a new method for analysing nonlinear and
non-stationary data. This method is partly inspired by the EMD method
developed by N. E. Huang et al.. We apply the idea of sparse representation
and multiscale analysis to analyze the nonlinear and non-stationary data.
The key part of the method is to find the adaptive base function and
minimise the total variation to get the mean and envelop. The adaptive base
function is obtained through a normalization operator. The adaptive base
function is totally based on the local characteristic time scale of the
data, so it is applicable to nonlinear and non-stationary processes. Once
the adaptive base function is known, the mean and envelop can be computed by
minimizing the total variation. This is an L_1 minimization problem, which
is studied very much recently in the research of compressive sensing. By
processing normalization and optimization iteratively until converge, we can
get a decomposition of the original nonlinear and non-stationary data. This
method can be seen as a mathematical formulation of the EMD method or a
nonlinear generalization of the compressive sensing. This is a joint work
with Prof. Thomas Y. Hou. |
