Fast Matrix Inversion and Determinant Computation for Polarimetric Synthetic Aperture Radar

TL;DR

This paper presents a GPU-accelerated algorithm for rapid inversion and determinant calculation of small matrices in PolSAR image analysis, offering about twice the speed of traditional Cholesky-based methods.

Contribution

A novel fast algorithm leveraging matrix symmetry and adjoint computation for efficient matrix inversion and determinant calculation in PolSAR processing.

Findings

Achieves approximately twofold speedup over Cholesky factorization.

Applicable to various platforms due to general expression formulation.

Validated with simulated and real PolSAR data.

Abstract

This paper introduces a fast algorithm for simultaneous inversion and determinant computation of small sized matrices in the context of fully Polarimetric Synthetic Aperture Radar (PolSAR) image processing and analysis. The proposed fast algorithm is based on the computation of the adjoint matrix and the symmetry of the input matrix. The algorithm is implemented in a general purpose graphical processing unit (GPGPU) and compared to the usual approach based on Cholesky factorization. The assessment with simulated observations and data from an actual PolSAR sensor show a speedup factor of about two when compared to the usual Cholesky factorization. Moreover, the expressions provided here can be implemented in any platform.