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Atomic norm algorithms for blind spectral super-resolution problems
Helland, Jonathan W.
Helland, Jonathan W.
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2019
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This thesis focuses on the development of atomic norm based algorithms for particular instances of blind super-resolution problems appearing in wireless communications, modal analysis in sensor networks, and target localization in radar signal processing. Blind super- resolution problems are a harder version of canonical super-resolution problems in that they include more degrees of freedom that must be resolved due to additional sources of blurring via unknown linear transformations. Our atomic norm algorithms focus on leveraging special sparsity structure with respect to certain dictionaries inherent in the signals of interest. We first provide a relatively self-contained introduction to and review of the atomic norm’s use in non-blind and blind super-resolution problems. We then develop theoretical tools towards establishing guaranteed blind super-resolution for a problem which we refer to as multi-band line spectral estimation – an extension of line spectral estimation to signals whose composite waveforms occupy continuous frequency bands rather than discrete spikes. We introduce a generic signal model that can be used to model multi-sensor blind super- resolution problems, which are of particular interest in radar signal processing and sensor networks. We establish some theoretical results about computationally tractable techniques for computing the atomic norms that arise from our proposed multi-sensor signal models. We next apply our multi-sensor atomic norm algorithm to the problem of modal analysis from vibrational measurements – a blind super-resolution problem arising in structural health monitoring and acoustics. We finally apply our multi-sensor atomic norm algorithm to the problem of extended target localization in stepped-frequency radar signal processing. This problem is relevant to near-field radar imaging including through-the-wall radar imaging.
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