We propose a semismooth Newton-based augmented Lagrangian method for reconstructing sparse sources in inverse acoustic scattering problems. The semismooth Newton method can be iterated in the space of measurements instead of the unknown source to be reconstructed. It is highly efficient, especially when the measurement data is much less than the acoustic source. The source can be calculated from Fenchel-Rockafellar duality theory. We can obtain lots of acceleration and leverage the computational cost. The numerical examples show the high efficiency of the proposed semismooth Newton-based methods.

翻译：本文提出了一种基于半光滑牛顿法的增广拉格朗日方法，用于反声散射问题中的稀疏源重构。该半光滑牛顿法可在测量空间而非待重构的未知源空间中进行迭代，其计算效率显著，尤其在测量数据远少于声源数量的情况下表现突出。声源可通过Fenchel-Rockafellar对偶理论求解。该方法能实现多重加速并有效控制计算成本。数值算例验证了所提出的基于半光滑牛顿法的高效性。