Abstract
Following the pioneering work of Schapira, we consider topological Radon-type integral transforms on constructible -valued functions using the Euler characteristic as a measure. Contributions include: (1) application of the Schapira inversion formula to target localization and classification problems in sensor networks; (2) extension and application of the inversion formula to weighted Radon transforms; and (3) pseudo-inversion formulae for inverting annuli (sets of Euler measure zero).
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