On the Extension of Cameron Decomposition Helicity Asymmetry Parameter From Single-Look to Multi-Look PolSAR Imagery

Abstract

The helicity asymmetry parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> in the Cameron decomposition indicates the degree to wh ich a scatterer deviates from being an ideal symmetric scatterer. However, the solving procedure of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> can only be expressed in terms of single-look Sinclair scattering matrix. In this article, we extend the helicity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> to a generalized helicity parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau _{g} $ </tex-math></inline-formula> , which is appropriate for both the single- and multi-look polarimetric synthetic aperture radar (PolSAR) data. For single-look data, the generalized helicity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau _{g} $ </tex-math></inline-formula> is equivalent to the previous helicity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau $ </tex-math></inline-formula> . In addition, we investigate the relationships among the classical helix/helicity definitions, including the Cameron helicity, the Krogager helix component, and the Yamaguchi helix component. To achieve this, we represent the Cameron and Krogager decompositions in terms of the unified coherent polarimetric decompositions (CTD) model in the format of coherency matrix and revise the expression of Krogager decomposition contributions in function of Huynen parameters. Results show that essentially the Cameron helicity and Krogager helix are two kinds of representation of reflection asymmetry under the same decomposition model, and the Yamaguchi helix contribution is always larger than the Krogager helix contribution. Single-look PolSAR data from L-band ESAR are used for demonstration in this article. Several multi-look datasets are generated by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1\,\,\times \,\,3$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\,\,\times \,\,3$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\,\,\times \,\,5$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\,\,\times \,\,5$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\,\,\times \,\,7$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7\,\,\times \,\,7$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7\,\,\times \,\,9$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9 \times 9$ </tex-math></inline-formula> boxcar average. Two techniques are taken to mitigate reflection symmetry assumption based on helix component and helicity angle, respectively. It will be shown that the technique with the generalized helicity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\tau _{g} $ </tex-math></inline-formula> performs best in terms of efficiency and stability.