The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization problems in measure space in combination with the Helmholtz equation on a bounded domain is considered. A weighted norm with unbounded weight near the observation points is incorporated into the formulation. Optimality conditions and conditions for recovery in the small noise case are discussed, which motivates concrete choices of the weight. The numerical realization is based on an accelerated conditional gradient method in measure space and a finite element discretization.

中文翻译：

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带界域上具有亥姆霍兹方程的逆点源位置

解决了从有限数量的频率处的相应声压的逐点测量中恢复声源，更具体地为单极子的问题。为此，考虑了在有界域上结合Helmholtz方程在度量空间中的一系列稀疏优化问题。在观察点附近具有无限制权重的加权范数被合并到配方中。讨论了最优条件和小噪声情况下的恢复条件，这促使了权重的具体选择。数值实现基于测量空间中的加速条件梯度法和有限元离散化。