Signed Cumulative Distribution Transform for Parameter Estimation of 1-D Signals
This is an incremental improvement for signal processing researchers, offering a more efficient method for parameter estimation in 1-D signals.
The authors tackled signal parameter estimation by extending the cumulative distribution transform (CDT) to arbitrary signals via the signed cumulative distribution transform (SCDT), enabling Wasserstein-type distance minimization through linear least squares and providing a global minimizer for nonlinear parameter functions.
We describe a method for signal parameter estimation using the signed cumulative distribution transform (SCDT), a recently introduced signal representation tool based on optimal transport theory. The method builds upon signal estimation using the cumulative distribution transform (CDT) originally introduced for positive distributions. Specifically, we show that Wasserstein-type distance minimization can be performed simply using linear least squares techniques in SCDT space for arbitrary signal classes, thus providing a global minimizer for the estimation problem even when the underlying signal is a nonlinear function of the unknown parameters. Comparisons to current signal estimation methods using $L_p$ minimization shows the advantage of the method.