2-D Rayleigh Autoregressive Moving Average Model for SAR Image Modeling

TL;DR

This paper introduces a novel 2-D Rayleigh ARMA model tailored for SAR image data, addressing non-Gaussian, positive, and asymmetric signal characteristics, with extensive simulations and experiments demonstrating its effectiveness.

Contribution

The paper develops the first 2-D Rayleigh ARMA model specifically for SAR images, including derivation, inference methods, and validation through simulations and practical experiments.

Findings

The 2-D RARMA model accurately captures SAR image statistics.

The model outperforms traditional 2-D ARMA in anomaly detection.

Simulation results confirm reliable parameter estimation.

Abstract

Two-dimensional (2-D) autoregressive moving average (ARMA) models are commonly applied to describe real-world image data, usually assuming Gaussian or symmetric noise. However, real-world data often present non-Gaussian signals, with asymmetrical distributions and strictly positive values. In particular, SAR images are known to be well characterized by the Rayleigh distribution. In this context, the ARMA model tailored for 2-D Rayleigh-distributed data is introduced -- the 2-D RARMA model. The 2-D RARMA model is derived and conditional likelihood inferences are discussed. The proposed model was submitted to extensive Monte Carlo simulations to evaluate the performance of the conditional maximum likelihood estimators. Moreover, in the context of SAR image processing, two comprehensive numerical experiments were performed comparing anomaly detection and image modeling results of the proposed model with traditional 2-D ARMA models and competing methods in the literature.