Detecting Markov Random Fields Hidden in White Noise

TL;DR

This paper addresses the challenge of detecting Gaussian Markov random fields embedded in white noise, providing theoretical bounds and near-optimal detection methods for applications in time series and image analysis.

Contribution

It introduces minimax lower bounds and develops near-optimal tests for detecting hidden Gaussian Markov random fields in noisy environments.

Findings

Derived minimax lower bounds for detection

Proposed near-optimal detection tests

Applicable to time series and image analysis

Abstract

Motivated by change point problems in time series and the detection of textured objects in images, we consider the problem of detecting a piece of a Gaussian Markov random field hidden in white Gaussian noise. We derive minimax lower bounds and propose near-optimal tests.