Robust Estimation for Two-Dimensional Autoregressive Processes Based on Bounded Innovation Propagation Representations

TL;DR

This paper introduces BMM-2D, a robust estimation method for two-dimensional autoregressive models that effectively reduces the impact of outliers, outperforming existing estimators in accuracy and precision, with practical image filtering applications.

Contribution

The paper presents a novel robust estimator for 2D autoregressive models using bounded innovation propagation, improving robustness against contamination.

Findings

BMM-2D outperforms existing estimators in simulations.

The method demonstrates superior accuracy and precision.

Effective in practical image filtering applications.

Abstract

Robust methods have been a successful approach to deal with contaminations and noises in image processing. In this paper, we introduce a new robust method for two-dimensional autoregressive models. Our method, called BMM-2D, relies on representing a two-dimensional autoregressive process with an auxiliary model to attenuate the effect of contamination (outliers). We compare the performance of our method with existing robust estimators and the least squares estimator via a comprehensive Monte Carlo simulation study which considers different levels of replacement contamination and window sizes. The results show that the new estimator is superior to the other estimators, both in accuracy and precision. An application to image filtering highlights the findings and illustrates how the estimator works in practical applications.