Complex-Valued Multi-Layer Perceptrons – An Application to Polarimetric SAR Data

Multi-Layer Perceptrons (MLPS) are powerful function approximators. In the last decades they were successfully applied to many different regression and classification problems. Their characteristics and convergence properties are well studied and relatively well understood, but they were originally designed to work with real-valued data. The main focus of this paper is the classification of polarimetric synthetic aperture radar (POLSAR) data which are a complex-valued signal. Instead of using an arbitrarily projection of this complex-valued data to the real domain, the paper proposes the usage of complex-valued MLPS (CV-MLPS), which are an extension of MLPS to the complex domain. The paper provides a detailed yet general derivation of the complex backpropagation algorithm and mentions related problems as well as possible solutions. Furthermore, it evaluates the performance of CV-MLPS in a land-cover classification task in POLSAR images under several learning conditions, and compares the proposed classifier with standard methods. The experimental results show that CV-MLPS are successfully applicable to classification tasks in POLSAR data. They show good convergence properties and a better performance if compared to real-valued MLPS.