5 papers
A two-point phase recovering with spherical wave reference
R. G. Novikov, V. N. Sivkin
We consider a reference wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region. We give two-point formulas for…
Discrete non-abelian X-ray transforms
Pranav Gupta, Roman Novikov
We define a discrete version of the non-abelian X-ray transform, going back in particular to Manakov, Zakharov (1981) and Strichartz (1982). We extend to this transform non-overdet…
Inverse scattering for the multipoint potentials of Bethe-Peierls-Thomas-Fermi type
Pei-Cheng Kuo, Roman G. Novikov
We consider the Schrödinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determine…
On non-uniqueness of phase retrieval in multidimensions
Roman Novikov, Tianli Xu
We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensiona…
Inverse source problem for discrete Helmholtz equation
Roman Novikov, Basant Lal Sharma
We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice , . We consider this problem for the cases with…