Signal Processing and Piecewise Convex Estimation

03/14/2018
by   Kurt Riedel, et al.
0

Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage 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 first-stage estimate. This constraint is equivalent to requiring that the third derivative of the second-stage estimate has a single sign in a small neighborhood about each first-stage 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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/11/2018

Piecewise Convex Function Estimation: Pilot Estimators

Given noisy data, function estimation is considered when the unknown fun...
12/07/2021

Change-point regression with a smooth additive disturbance

We assume a nonparametric regression model with signals given by the sum...
12/01/2020

Anisotropic local constant smoothing for change-point regression function estimation

Understanding forest fire spread in any region of Canada is critical to ...
12/07/2021

Change-point Detection for Piecewise Exponential Models

In decision modelling with time to event data, parametric models are oft...
12/06/2021

Cross-validation for change-point regression: pitfalls and solutions

Cross-validation is the standard approach for tuning parameter selection...
09/18/2020

Detection of Change Points in Piecewise Polynomial Signals Using Trend Filtering

While many approaches have been proposed for discovering abrupt changes ...
03/11/2018

Piecewise Convex Function Estimation: Representations, Duality and Model Selection

We consider spline estimates which preserve prescribed piecewise convex ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.