Constrained Tensor Decompositions for SAR Data: Agricultural Polarimetric Time Series Analysis

Tensor decompositions are a powerful tool for multidimensional data analysis, interpretation, and signal processing. This work develops a constrained tensor decomposition framework for complex multidimensional synthetic aperture radar (SAR) data. The framework generalizes the canonical polyadic (CP) decomposition by formulating it as an optimization problem and allows precise control over the shape and properties of the output factors. The implementation supports complex tensors, automatic differentiation, and different loss functions and optimizers. We discuss the importance of constraints for physical validity, interpretability, and uniqueness of the decomposition results. To illustrate the framework, we formulate a polarimetric time series decomposition and apply it to data acquired over agricultural areas to analyze the development of four crop types at the X-, C-, and L-bands over the period of 12 weeks. The obtained temporal factors describe the changes in the crops in a compact way and show a correlation to certain crop parameters. We extend the existing polarimetric time series change analysis with the decomposition to show the changes in more detail and provide an interpretation through the polarimetric factors. The decomposition framework is extensible and promising for joint information extraction from multidimensional SAR data.