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.
翻译:我们用签名的累计分布变换(SCDT)描述一种信号参数估计方法,这是最近采用的一种基于最佳运输理论的信号表示工具。这种方法以最初为正分布而采用的累计分布变换(CDT)的信号估计为基础。具体地说,我们表明,仅使用在SCDT空间的线性最小方位技术来任意信号类别,即可进行瓦森斯坦式距离最小化,因此即使基本信号是未知参数的非线性功能,也为估算问题提供了一个全球最小化工具。与使用$L_p$最小化的当前信号估计方法进行比较,显示了该方法的优势。