Signal Processing and Piecewise Convex Estimation
Abstract
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a twostage adaptive estimate. In the first stage, the number and location of the change points is estimated using strong smoothing. In the second stage, a constrained smoothing spline fit is performed with the smoothing level chosen to minimize the MSE. The imposed constraint is that a single change point occurs in a region about each empirical change point of the firststage estimate. This constraint is equivalent to requiring that the third derivative of the secondstage estimate has a single sign in a small neighborhood about each firststage change point. We sketch how PCF may be applied to signal recovery, instantaneous frequency estimation, surface reconstruction, image segmentation, spectral estimation and multivariate adaptive regression.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.05130
 Bibcode:
 2018arXiv180305130R
 Keywords:

 Statistics  Methodology;
 Electrical Engineering and Systems Science  Signal Processing;
 Mathematics  Statistics Theory;
 Physics  Data Analysis;
 Statistics and Probability;
 Statistics  Machine Learning
 EPrint:
 ICIAM Proceedings 1993