Publications

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Scanning electron microscopes (SEMs) are used in neuroscience and materials science to image square centimeters of sample area at nanometer scales. Since imaging rates are in large part SNR-limited. imaging time is proportional to the number of measurements taken of each sample; in a traditional SEM. large collections can lead to weeks of around-the-clock imaging time. We previously reported a single-beam sparse sampling approach that we have demonstrated on an operational SEM for collecting "smooth" images. In this paper, we analyze how measurements from a hypothetical multi-beam system would compare to the single-beam approach in a compressed sensing framework. To that end. multi-beam measurements are synthesized on a single-beam SEM. and fidelity of reconstructed images are compared to the previously demonstrated approach. Since taking fewer measurements comes at the cost of reduced SNR, image fidelity as a function of undersampling ratio is reported.

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For this paper, we consider the problem of classifying a test sample given incomplete information. This problem arises naturally when data about a test sample is collected over time, or when costs must be incurred to compute the classification features. For example, in a distributed sensor network only a fraction of the sensors may have reported measurements at a certain time, and additional time, power, and bandwidth is needed to collect the complete data to classify. A practical goal is to assign a class label as soon as enough data is available to make a good decision. We formalize this goal through the notion of reliability—the probability that a label assigned given incomplete data would be the same as the label assigned given the complete data, and we propose a method to classify incomplete data only if some reliability threshold is met. Our approach models the complete data as a random variable whose distribution is dependent on the current incomplete data and the (complete) training data. The method differs from standard imputation strategies in that our focus is on determining the reliability of the classification decision, rather than just the class label. We show that the method provides useful reliability estimates of the correctness of the imputed class labels on a set of experiments on time-series data sets, where the goal is to classify the time-series as early as possible while still guaranteeing that the reliability threshold is met.

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