Model-based Tensor Decompositions for Geophysical Parameter Retrieval from Multidimensional SAR Data

Abstract

Tensor decompositions are mathematical methods for joint analysis and information extraction from multidimensional data. This work combines model-free algebraic tensor decompositions with physical synthetic aperture radar (SAR) models and introduces a novel framework for geophysical parameter retrieval from multidimensional SAR tensors. To demonstrate parameter retrieval, we combine information from polarimetric, temporal, and spatial data dimensions and invert soil moisture over vegetated agricultural areas. We formulate parameter inversion as a constrained optimization problem and retrieve the parameters by fitting the physical model to the observed SAR tensor. Compared to methods that operate on matrices, multidimensional tensors offer a larger observation space, reduce inversion ambiguities, and allow inversion of more complex models that cover a larger range of field conditions and crop types. The proposed method represents the signal as a sum of three components, separates the surface, dihedral, and volume signal contributions, and allows estimation of crop-specific volume scattering polarimetric signatures. With the increasing availability of multidimensional SAR data, model-based tensor decompositions gain relevance and provide a flexible, extensible, and explainable way to jointly analyze the information across multiple data dimensions.