Developing Fast Accurate and Robust Numerical Algorithms

Developing Fast Accurate and Robust Numerical Algorithms Developing Fast, Accurate, and Robust Numerical Algorithms for Extracting Actionable Information from Acquiring Sensing Data The main objective of the proposed research is to construct fast, accurate, and robust numerical algorithms that extract actionable information from acquired sensing data. The PIs will study synthetic aperture radar (SAR) as the prototype sensing system, with the focus on the detection, classification, and tracking of targets, and the extraction of important image information. SAR data are typically acquired as samples in the Fourier domain. Flight path variations, clutter, jamming, occlusion and other practical considerations affecting data collection may lead to irregular and incomplete sampling, which has negative implications on accuracy, robustness, and computational efficiency. One critical component of the proposed research is to thoroughly analyze current localized feature detection and image reconstruction methods so that it is possible to develop new algorithms that are effective under such non-idyllic circumstances. Moreover, since transforms other than Fourier, e.g. wavelets and short time Fourier transforms (STFT), also arise in sensing, this proposal seeks to expand current localized feature detection and imaging techniques, when possible, to a framework amenable to other relevant representations. Finally, this proposal will also develop algorithms for solving partial differential equations (PDEs) on complicated domains where non-standard data may be more suitable for computations, especially in situations where accurate terrain representation is critical for the given AF sensing system.