$\mathcal {H}$ Distribution for Multilook Polarimetric SAR Data

Polarimetric synthetic aperture radar (PolSAR) is an advanced imaging radar system, for which the acquired data provide not only the information of each channel but also the correlation between channels. To fully utilize and accurately model the multilook PolSAR data, a novel compound distribution, named the <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> distribution, is proposed based on the generalized Fisher distribution (<inline-formula> <tex-math notation="LaTeX">$\text{G}\mathcal {F}\text{D}$ </tex-math></inline-formula>). Specifically, the <inline-formula> <tex-math notation="LaTeX">$\text{G}\mathcal {F}\text{D}$ </tex-math></inline-formula> introduces a power parameter to the ordinary Fisher distribution. With one more free parameter, the <inline-formula> <tex-math notation="LaTeX">$\text{G}\mathcal {F}\text{D}$ </tex-math></inline-formula> is flexible and versatile enough to characterize different kinds of texture. Then, by assuming the generalized-Fisher-distributed texture and the Wishart-distributed speckle, the <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> distribution is derived, whose closed-form expression is obtained with the help of Fox’s H-function. As such, the <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> distribution has a compact form and is conveniently applied to practical problems, such as modeling and classification of PolSAR data. The effectiveness of this method is tested by modeling the multilook PolSAR data and performing image classification. The experimental results demonstrate that the <inline-formula> <tex-math notation="LaTeX">$\mathcal {H}$ </tex-math></inline-formula> distribution is a flexible and effective way to model multilook PolSAR data.