A Bragg-Like Point Extraction Method for Co-polarization Channel Imbalance Calibration

Abstract

Calibration by distributed targets is an important part of polarimetric calibration (PolCAL) without corner reflectors (CRs). Currently, both the correlation of HH and VV ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{\rm{hhvv}}$</tex-math></inline-formula> ) and the equivalent number of looks (ENL) constitute the common method for the extraction of Bragg-like points (BLPs) in order to calibrate the co-polarization channel imbalance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> . However, strict assumptions about distributed targets and complex mathematical expressions regarding ENL limit the impact analysis of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{\rm{hhvv}}$</tex-math></inline-formula> and ENL; thus, the fixed thresholds for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{\mathrm{hhvv}}$</tex-math></inline-formula> and ENL can be obtained only by comparing the calibration errors with the CRs or simulated values in order to calibrate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> accurately. In some Earth observation and lunar exploration without CRs, the above conditions are not satisfied. In this article, a BLP extraction method is proposed for calibrating co-polarization channel imbalance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> in PolCAL. <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H}/{\bar{\alpha }}$</tex-math></inline-formula> decomposition is utilised to deduce the specific scattering impacts of BLPs by different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> values first. Then, a dynamic selection method is proposed to reduce the influence of fixed thresholds and improve the extraction accuracy. Multi-scene polarimetric synthetic aperture radar (PolSAR) images from AIRSAR, ALOS, and GF-3 are utilised to verify the effectiveness of the proposed algorithm in the extraction of BLPs and the calibration results of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> obtained by applying the extracted BLPs (ext. BLPs).