SURE shrinkage of Gaussian paths and signal identification

TL;DR

This paper develops a new method for estimating and de-noising signals affected by continuous-time Gaussian noise, using a Stein Unbiased Risk Estimator based on Gaussian process properties.

Contribution

It introduces a novel SURE-based approach leveraging local and occupation times for Gaussian process drift estimation and signal de-noising.

Findings

Effective signal estimation in Gaussian noise environments

New SURE estimator for Gaussian process drift

Improved de-noising performance demonstrated

Abstract

Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed by a continuous-time Gaussian noise.