Bounds on the stably recoverable information for the Helmholtz equation in R²
Mirza Karamehmedovic (Technical University of Denmark, Denmark)

Linearisation casts inverse boundary problems in terms of inverse source problems (ISP). For the ISP with the two-dimensional Helmholtz equation, the singular value decomposition of the forward operator reveals a sharp cutoff in the stably recoverable information. We prove and numerically validate lower and upper bounds on this cutoff. Our result explicitly links the amount of stably recoverable information with the size parameter of the problem and with the zeros of the Bessel functions Jm and Ym.