arXiv subjects

Siamak RabieniaHaratbar

Publications and source records attributed to Siamak RabieniaHaratbar.

3 recordsLinked to original sources

arXiv2019

Inverse Scattering and Stability Estimates for The Biharmonic Operator

We study an inverse scattering problem of a perturbed biharmonic operator. we show that the high-frequency asymptotic of scattering amplitude of the biharmonic operator uniquely determine the curl A and {V -1/2 nablaA}. We also study the near-field scattering problem and show that the high-frequency asymptotic expansion up to a certain error in terms of frequency lambda recovers the same two above quantities with no additional information about A and V. We also prove stability estimates for curl A and {V -1/2 nablaA}.

math.AP↗

arXiv2018

Invertibility and Stability for A Generic class of Radon Transforms with Applications to Dynamic Operators

Let X be an open subset of R^2. We study the dynamic operator, A, integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be recovered by the data-set. Our results show that not all singularities can be recovered, as the object moves with a speed lower than the X-ray source. We establish stability estimates and prove that the injectivity and stability are of a generic set if the dynamic operator satisfies the visibility, no conjugate points, and local Bolker conditions. We also show this results can be implemented to Fan beam geometry.

math.AP↗

arXiv2018

Support Theorem for the Light Ray Transform on Minkowski Spaces

We study the Light-Ray transform of integrating vector fields on the Minkowski time-space R^{1+n}, n bigger than equal 2, with the Minkowski metric. We prove a support theorem for vector fields vanishing on an open set of light-like geodesics.

math.AP↗