24 August 2017 Phase retrieval from local measurements in two dimensions
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The phase retrieval problem has appeared in a multitude of applications for decades. While ad hoc solutions have existed since the early 1970s, recent developments have provided algorithms that offer promising theoretical guarantees under increasingly realistic assumptions. Motivated by ptychographic imaging, we generalize a recent result on phase retrieval of a one dimensional objective vector x ∈ ℂd to recover a two dimensional sample Q ∈ ℂd x d from phaseless measurements, using a tensor product formulation to extend the previous work.
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Mark Iwen, Mark Iwen, Brian Preskitt, Brian Preskitt, Rayan Saab, Rayan Saab, Aditya Viswanathan, Aditya Viswanathan, } "Phase retrieval from local measurements in two dimensions", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103940X (24 August 2017); doi: 10.1117/12.2274355; https://doi.org/10.1117/12.2274355

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