Scalar and homoskedastic models for SAR and POLSAR data - Le, Thanh-Hai (2014)
SAR and POLSAR data are stochastic multiplicative and heteroskedastic in their natural domain. It is hence desirable to establish additive and homoskedastic models, such that the benefits of homoskedastic statistical estimation framework can be demonstrated and realized for practical applications such as speckle filtering. In addition, the processing of multidimensional POLSAR data requires the establishment of discrimination observables which are to be scalar and statistically consistent. Moreover, these same scalar observable quantities also need to be naturally representative for the multidimensional POLSAR data. In this thesis, the effects of homoskedasticity on SAR and POLSAR speckle filtering within the framework of computational and statistical estimation are extensively studied. Concurrently, the statistical behaviour of the determinant of POLSAR covariance matrix is also explored, where it is shown to be the representative scalar observable for the multidimensional POLSAR, similar to the role of the intensity in SAR. As a result of these studies, several scalar statistical models based on the determinant of POLSAR covariance matrix, namely the determinant and the determinant-ratio models, are proposed and validated. These generic models for POLSAR are also shown to be both multiplicative and heteroskedastic, similar to the models for SAR intensity. Subsequently, logarithmic transformation is applied onto both SAR and POLSAR models to convert them into additive and homoskedastic models. These models includes: the log-determinant, the log-distance, the dispersion and the contrast models. Since the full POLSAR data is multi-dimensional and the proposed models are scalar, they are not perfect. Specifically, they suffers from a loss of dimension. Still there are several beneficial implications of the models proposed in this thesis. Since the scalar and representative models for POLSAR extend the traditional models for SAR’s intensity, its main benefit is that it enables the adaptation of many existing SAR data processing techniques for POLSAR data. Similarly, the homoskedastic model carries additional benefits. For example, for inexperienced researchers (such as this author when he began this research), this thesis proposes additive and homoskedastic models for both SAR and POLSAR data, which are simpler and more familiar. They are helpful by keeping these inexperienced researchers from falling into several common traps in (POL)SAR data processing. For more experienced researchers, besides the unified scalar statistical theory for both SAR and POLSAR, this thesis also proposes several ways that homoskedastic data processing can be used to neutralize certain existing negative impacts of heteroskedasticity on the statistical estimation framework for (POL)SAR.