Navigating unmanned aerial vehicles in precarious environments is of great importance. It is necessary to rely on alternative information processing techniques to attain spatial information that is required for navigation in such settings. This paper introduces a novel deep learning-based approach for navigating that exclusively relies on synthetic aperture radar (SAR) images. The proposed method utilizes deep neural networks (DNNs) for image matching, retrieval, and registration. To this end, we introduce Deep Cosine Similarity Neural Networks (DCSNNs) for mapping SAR images to a global descriptive feature vector. We also introduce a fine-tuning algorithm for DC-SNNs, and DCSNNs are used to generate a database of feature vectors for SAR images that span a geographic area of interest, which, in turn, are compared against a feature vector of an inquiry image. Images similar to the inquiry are retrieved from the database by using a scalable distance measure between the feature vector outputs of DCSNN. Methods for reranking the retrieved SAR images that are used to update position coordinates of an inquiry SAR image by estimating from the best retrieved SAR image are also introduced. Numerical experiments comparing with baselines on the Polarimetric SAR (PolSAR) images are presented.
We propose a two-stage stochastic programming framework for designing or identifying "resilient," or "reparable" structures in graphs whose topology may undergo a stochastic transformation. The reparability of a subgraph satisfying a given property is defined in terms of a budget constraint, which allows for a prescribed number of vertices to be added to or removed from the subgraph so as to restore its structural properties after the observation of random changes to the graph's set of edges. A two-stage stochastic programming model is formulated and is shown to be N P -complete for a broad range of graph-theoretical properties that the resilient subgraph is required to satisfy. A general combinatorial branch-and-bound algorithm is developed, and its computational performance is illustrated on the example of a two-stage stochastic maximum clique problem.
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