39 research outputs found
Uniqueness in inverse scattering with phaseless near-field data generated by superpositions of two incident plane waves
This paper is concerned with the uniqueness in inverse acoustic and
electromagnetic scattering with phaseless near-field data generated by
superpositions of two incident plane waves at a fixed frequency. It can be
proved that the unknown scatterer can be uniquely determined by the phaseless
near-field data. The proof is based on the analysis of the phase information
and the application of Rellich's lemma together with the Green's formula for
the radiating solutions to the Helmholtz equation or the Stratton--Chu formula
for the radiating solutions to the Maxwell equations
Convex recovery from interferometric measurements
This note formulates a deterministic recovery result for vectors from
quadratic measurements of the form for some
left-invertible . Recovery is exact, or stable in the noisy case, when the
couples 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