  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.
