Convex recovery from interferometric measurements

Laurent Demanet; Vincent Jugnon

doi:10.1109/tci.2017.2688923

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arXiv · 1307.6864

Convex recovery from interferometric measurements

Laurent Demanet·Vincent Jugnon

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Abstract

This note formulates a deterministic recovery result for vectors $x$ from quadratic measurements of the form $(Ax)_i \overline{(Ax)_j}$ for some left-invertible $A$. Recovery is exact, or stable in the noisy case, when the couples $(i,j)$ are chosen as edges of a well-connected graph. One possible way of obtaining the solution is as a feasible point of a simple semidefinite program. Furthermore, we show how the proportionality constant in the error estimate depends on the spectral gap of a data-weighted graph Laplacian. Such quadratic measurements have found applications in phase retrieval, angular synchronization, and more recently interferometric waveform inversion.

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Laurent Demanet, Vincent Jugnon. 2013-07-25. Convex recovery from interferometric measurements. https://doi.org/10.1109/tci.2017.2688923

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