Parameter selection in sparsity-driven SAR imaging

We consider a recently developed sparsity-driven synthetic aperture radar (SAR) imaging approach which can produce superresolution, feature-enhanced images. However, this regularization-based approach requires the selection of a hyper-parameter in order to generate such high-quality images. In this paper we present a number of techniques for automatically selecting the hyper-parameter involved in this problem. In particular, we propose and develop numerical procedures for the use of Stein’s unbiased risk estimation, generalized cross-validation, and L-curve techniques for automatic parameter choice. We demonstrate and compare the effectiveness of these procedures through experiments based on both simple synthetic scenes, as well as electromagnetically simulated realistic data. Our results suggest that sparsity-driven SAR imaging coupled with the proposed automatic parameter choice procedures offers significant improvements over conventional SAR imaging

Time-variant nonparametric extreme quantile estimation with application to US temperature data

Statistical modelling for several years of daily temperature data is somewhat challenging due to remarkable variations of negative and positive temperatures throughout the year. A scatter plot of day and daily temperature shows the high magnitude of variations among data points as dots fall only in the first and fourth quadrants. One parametric modelling approach to this data is to use quantile regression to obtain regression lines on different quantiles. However, these quantile lines cannot make reliable predictions on extreme quantiles when time-variant quantiles differ significantly. In this paper, we develop several two-step nonparametric smoothing estimators and show their superiority over quantile regression for smoothing estimation of nonparametric quantiles with a novel application to temperature data. Narrower bootstrap confidence bands, smaller Minimum Absolute Distance (MAD), smaller bias and MSE, and higher coverage from the application and simulation results show that smoothing curves obtained from these smoothing estimators outperform the quantile regression line

Parameter selection in non-quadratic regularization-based SAR imaging

Many remote sensing applications such as weather forecasting and automatic target recognition (ATR) require high-resolution images. Synthetic Aperture Radar (SAR) has become an important imaging technology for these remote sensing tasks through its all-weather, day and night imaging capability. However the effectiveness of SAR imaging for a specific decision making task depends on the quality of certain features in the formed imagery. For example, in order to be able to successively use a SAR image in an ATR system, the SAR image should exhibit features of the objects in the scene that are relevant for ATR. Recently, advanced SAR image formation techniques have been developed to produce feature-enhanced SAR images. In this thesis, we focus on one such technique, in particular a non-quadratic regularization-based approach which aims to produce so-called “point-enhanced SAR images”. The idea behind this approach is to emphasize appropriate features by means of regularizing the solution. The stability of the solution is ensured through a scalar parameter, called the regularization parameter, balancing the contribution of the data and the a priori constraints on the formed image. Automatic selection of the regularization parameter is an important issue since SAR images are ideally aimed to be used in fully automated systems. However this issue has not been addressed in previous work. To address the parameter selection problem in this image formation algorithm, we propose the use of Stein’s unbiased risk estimation, generalized cross-validation, and L-curve techniques which have been mostly used in quadratic regularization methods previously. We have adapted these methods to the SAR imaging framework, and have developed a number of numerical tools to enable their usage. We demonstrate the effectiveness of the applied methods through experiments based on both synthetic as well as electromagnetically simulated realistic data