Uniqueness, stability and algorithm for an inverse wave-number-dependent source problem

Abstract This paper is concerned with an inverse wave-number-/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but independent on one spatial variable. The dependence of the source function on wave-number/frequency is supposed to be unknown. Based on the Fourier-transform and Dirichlet-Laplacian methods, we develop two efficient non-iterative numerical algorithms to recover the wave-number-dependent source. Uniqueness proof and increasing stability analysis are carried out if the boundary measurement data of Dirichlet kind are available. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed methods.