An Augmented Lagrangian Method-Based Framework in the Adjoint Space for Sparse Reconstruction of Acoustic Sources

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.