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14 September 2015 Phase retrieval
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We answer a number of open problems concerning phase retrieval and phase retrieval by projections. In particular, one main theorem classifies phase retrieval by projections via collections of sequences of vectors allowing norm retrieval. Another key result computes the minimal number of vectors needed to add to a frame in order for it to possess the complement property and hence allow phase retrieval. In furthering this idea, in a third main theorem we show that when a collection of subspaces is one subspace short from allowing phase retrieval, then any partition of these subspaces spans two hyperplanes. We offer many more results in this area as well as provide a large number of examples showing the limitations of the theory.
© (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jameson Cahill, Peter G. Casazza, John Jasper, and Lindsey M. Woodland "Phase retrieval", Proc. SPIE 9597, Wavelets and Sparsity XVI, 95970O (14 September 2015);


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