Piecewise acoustic source imaging with unknown speed of sound using a level-set method. (English) Zbl 1541.65137
Summary: 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.
MSC:
| 65N21 | Numerical methods for inverse problems for boundary value problems involving PDEs |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 15A23 | Factorization of matrices |
| 65F50 | Computational methods for sparse matrices |
| 65R10 | Numerical methods for integral transforms |
Keywords:
inverse gravimetry; acoustic source imaging; inversion of sound speed; level-set method; inverse problemSoftware:
k-WaveReferences:
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