Detection and inferences in non-gaussian signals

Abstract

Signal detection is a fundamental task in the field of signal and image processing, being pivotal for decision whether a signal is present or identify the different land cover type in synthetic aperture radar (SAR) images. Over the years, detection schemes have been developed assuming the Gaussian distribution. However, in the real world, most of signals are non-Gaussian, and the Gaussianity assumption may not be enough to model several practical contexts. In particular, quantized discrete-time sampled data and amplitude values of a SAR image pixels constitute clear examples of non-Gaussian data. Thus, in this thesis, we derived tools for non-Gaussian signals, such as (i) a new regression model based on the Rayleigh distribution; (ii) bias-adjusted estimators for the Rayleigh regression model parameters; (iii) a new two-dimensional autoregressive moving average model based on the Rayleigh distribution; (iv) a new time series model assuming the beta binomial distribution; and (v) the use of a stack of SAR images to obtain a ground scene prediction (GSP) image. The proposed Rayleigh regression model was applied in detection schemes of land cover type in SAR images and the obtained results were compared to the measurements from Gaussian-, Gamma-, and Weibull-based regression models. The Rayleigh regression model was the only model that could detect the difference among the three tested regions. The two-dimensional Rayleigh autoregressive moving average model were applied to detect changes in SAR images. For comparison purposes, we also obtained the detection results based on the two-dimensional Gaussian model. The proposed method detected 24 in a total of 25 military vehicles, while the Gaussian-based scheme detected only 16 military vehicles. The derived beta binomial autoregressive moving average model was employed in nonrandom signals detection showing a higher probability of detection and a lower probability of false alarm in comparison to the traditional Gaussian based methods. The obtained GPS image based on the median method was considered in a change detection algorithm displaying a probability of detection of 97% and a false alarm rate of 0:11=km², when considering military vehicles concealed in a forest.