We propose a semismooth Newton-based augmented Lagrangian framework for reconstructing sparse sources in inverse acoustic scattering problems. Rather than working in the unknown source space, our semismooth Newton updates operate in the measurement (adjoint) space, which is especially efficient when the number of measurements is much smaller than the discretized source dimension. The source is then recovered via Fenchel-Rockafellar duality. Our approach substantially accelerates computation and reduces costs. Numerical experiments in two and three dimensions demonstrate the high efficiency of the proposed method.

翻译：本文提出了一种基于半光滑牛顿法的增广拉格朗日框架，用于反声散射问题中的稀疏声源重构。与在未知源空间直接求解不同，我们的半光滑牛顿迭代在测量（伴随）空间中执行，当测量数量远小于离散化源维度时，该方法具有显著计算效率优势。声源最终通过Fenchel-Rockafellar对偶理论进行恢复。该框架大幅提升了计算速度并降低了计算成本。二维与三维数值实验验证了所提方法的高效性。