Piecewise Acoustic Source Imaging with Unknown Speed of Sound Using a Level-Set Method

We investigate the following inverse problem:starting from the acoustic wave equation,reconstruct a piecewise constant passive acoustic source from a single boundary temporal measurement without knowing the speed of sound.When the amplitudes of the source are known a priori,we prove a unique determination result of the shape and propose a level set algorithm to reconstruct the singularities.When the singularities of the source are known a priori,we show unique determination of the source amplitudes and propose a least-squares fitting algorithm to recover the source amplitudes.The analysis bridges the low-frequency source inversion problem and the inverse problem of gravimetry.The proposed algorithms are validated and quantitatively evaluated with numerical experiments in 2D and 3D.