A new regular grid-based spatial process on the log-symmetric model for speckled clutter

Solving remote sensing (RS) problems is crucial for society when it comes to environmental and climate dynamics, to name just a few examples. An efficient RS source is the use of synthetic aperture radar (SAR) to describe natural and man-made phenomena through imagery. Our approach is to understand the data behind SAR images as outcomes of random variables, and then use statistics to solve RS problems. In this paper, we consider the input of a SAR image as a random variable in regular space and describe the nature of SAR intensity (a strictly positive and asymmetric feature that is affected by speckle noise and prevents direct interpretation) using a new proposal for a log-symmetric (LOGSYM) regression model in two dimensions, the 2-D LOGSYM autoregressive moving-average (2-D LOGSYMARMA) model. Besides a discussion on the physical relationship between the proposed model and SAR intensity (mentioning that it can extend a commonly used lognormal law), we derive some mathematical properties of 2-D LOGSYMARMA: matrix-based score function and Fisher information. We discuss in detail the conditional maximum likelihood (CML) estimation for the 2-D LOGSYMARMA parameters. We conduct a Monte Carlo study to quantify the performance of the resulting estimates and to verify that the asymptotic behavior expected from CML estimators is achieved. Finally, we perform an application to real SAR data, where our proposal is applied to different types of regions – ocean, forest, and urban areas – utilizing the versatility of the log-symmetric family. Results of both artificial and real experiments show that our model is an important tool for the extraction and classification of spatial information in SAR images.