Roman G. Novikov

An inversion formula for the attenuated X-ray transformation

The problem of inversion of the attenuated X-ray transformation is solved by an explicit formula. Several subsequent results are also given.

The -approach to approximate inverse scattering at fixed energy in three dimensions

We develop the d-bar approach to inverse scattering at fixed energy in dimensions

On the range characterization for the two-dimensional attenuated x-ray transformation

d\ge 3

The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential

of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential

Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials

v

Formulae and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

from its scattering amplitude

Small angle scattering andX-ray transform in classical mechanics

f

Rapidly converging approximation in inverse quantum scattering in dimension 2

at fixed energy

A noise property analysis of single-photon emission computed tomography data

E>0

On determination of the Fourier transform of a potential from the scattering amplitude

in dimension