Quantum computational approaches to some classic target identification and localization algorithms, especially for radar images, are investigated, and are found to raise a number of quantum statistics and quantum measurement issues with much broader applicability. Such algorithms are computationally intensive, involving coherent processing of large sensor data sets in order to extract a small number of low profile targets from a cluttered background. Target enhancement is accomplished through accurate statistical characterization of the environment, followed by optimal identification of statistical outliers. The key result of the work is that the environmental covariance matrix estimation and manipulation at the heart of the statistical analysis actually enables a highly efficient quantum implementation. The algorithm is inspired by recent approaches to quantum machine learning, but requires significant extensions, including previously overlooked `quantum analog--digital conversion steps (which are found to substantially increase the required number of qubits), `quantum statistical generalization of the classic phase estimation and Grover search algorithms, and careful consideration of projected measurement operations. Application regimes where quantum efficiencies could enable significant overall algorithm speedup are identified. Key possible bottlenecks, such as data loading and conversion, are identified as well.
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