Novos modelos estatísticos para processamento e monitoramento de imagens de radar de abertura sintética

Abstract

The study and correct interpretation of Synthetic Aperture Radar (SAR) images are relevant in the context of remote sensing and can be of great value to civil and military interests. This thesis addresses aspects of modeling and monitoring SAR images. More specifically, into three independent self-contained articles, new statistical models for modeling SAR images are introduced, as well as tools for detecting anomalies, based on probabilistic models. The first article introduces the concept of control charts for detecting anomalies in digital images. It is based on a reparameterization of the Burr XII distribution. This distribution has, as particular cases, usual models for SAR images in the intensity and amplitude format: the single-look G 0 I and single-look G 0 A distributions. Several properties and statistical measures useful for describing SAR images are presented. Through numerical studies on simulated and real images, it is shown that the proposed control chart is potentially useful for detecting anomalies in SAR images. More importantly, it presents the lowest occurrence of false alarms compared to analogous applications of other distributions in the context of SAR. Articles 2 and 3 introduce new probability distributions for modeling SAR images. The area of knowledge related to proposing probability models has been extensively investigated. However, to the best of our knowledge, it is not fully explored in the context of SAR images. Article 2 introduces the exponentiated transmuted-inverted beta distribution (ET-IB). It is a generalization of the inverted beta distribution, an important texture model among the well-known multiplicative models for SAR images. Properties are presented, such as measures based on the quantiles of the distribution: median, skewness, and kurtosis coefficients. Next, simulation studies and applications to real data are carried out, showing the potential of the ET-IB distribution for modeling amplitude-format images from forest and ocean regions. In article 3 an approximation to the G 0 A distribution, called distribution LA, is proposed. The G 0 A distribution is known as the universal model for modeling SAR images in amplitude format. However, it has some analytical limitations. Our proposal is an analytically more tractable alternative since it does not present any special function in its probability density, cumulative distribution, and quantile functions. This tractability is useful for proposing remote sensing tools based on distribution quantiles, as well as for real-time applications. Several useful measures are calculated and presented, all without analytical limitations, for describing SAR images related to central tendency, variability, and density shape. Still, such measures’ behavior is verified in the face of the variation of the parameters that index the distribution. Finally, numerical studies are conducted to compare the performance of the G 0 A and LA distributions. Images referring to regions of forest, ocean, urban, industrial, vegetation, and railways are considered. In general, the results show a better performance of the LA distribution. It is expected that the contributions of this thesis can be helpful in future studies and applications related to the context of remote sensing.