Orbit separation and invariant theory : degree bounds and algorithms
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The goal of this thesis is to contribute to the growing number of applications of computational invariant theory to problems in signal processing and statistics. Our focus is on problems of both sample complexity and the construction of algorithms for explicit signal recovery. The primary statistical model we study is the multi-reference alignment (MRA) problema fundamental challenge in statistical signal processing--in which one seeks to recover an unknown signal from many noisy and transformed copies. We use tools from invariant theory, particularly the method of moments, to analyze signal identifiability and to develop practical recovery algorithms.
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Ph. D