General Four-Component Scattering Power Decomposition With Unitary Transformation of Coherency Matrix

This paper presents a new general four-component scattering power decomposition method by implementing a set of unitary transformations for the polarimetric coherency matrix. There exist nine real independent observation parameters in the 3 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\times$</tex></formula> 3 coherency matrix with respect to the second-order statistics of polarimetric information. The proposed method accounts for all observation parameters in the new scheme. It is known that the existing four-component decomposition method reduces the number of observation parameters from nine to eight by rotation of the coherency matrix and that it accounts for six parameters out of eight, leaving two parameters (i.e., the real and imaginary parts of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$T_{13}$</tex></formula> component) unaccounted for. By additional special unitary transformation to this rotated coherency matrix, it became possible to reduce the number of independent parameters from eight to seven. After the unitary transformation, the new four-component decomposition is carried out that accounts for all parameters in the coherency matrix, including the remaining <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$T_{13}$</tex> </formula> component. Therefore, the proposed method makes use of full utilization of polarimetric information in the decomposition. The decomposition also employs an extended volume scattering model, which discriminates volume scattering between dipole and dihedral scattering structures caused by the cross-polarized <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$HV$</tex></formula> component. It is found that the new method enhances the double-bounce scattering contributions over the urban areas compared with those of the existing four-component decomposition, resulting from the full utilization of polarimetric information, which requires highly improved acquisitions of the cross-polarized <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$HV$</tex></formula> component above the noise floor.