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

2025/10/16 by Tan, Nirui, Sun, Hongpeng
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2510.14805

Abstract

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.

Citations

• An Efficient Augmented Lagrangian Method with Semismooth Newton Solver for Total Generalized Variation
• Quality-Bayesian approach to inverse acoustic source problems with partial data
• Identification of point like objects with multi-frequency sparse data
• An Investigation on Semismooth Newton based Augmented Lagrangian Method for Image Restoration
• A novel integral equation for scattering by locally rough surfaces and application to the inverse problem: the Neumann case
• Sparse Reconstructions of Acoustic Source for Inverse Scattering Problems in Measure Space
• Fast acoustic source imaging using multi-frequency sparse data
• A highly efficient semismooth Newton augmented Lagrangian method for solving Lasso problems
• A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
• The Calderón problem with partial data
• Monotone Operators and the Proximal Point Algorithm
• Multiplier and gradient methods

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• Sparse l1 Regularisation of Matrix Valued Models for Acoustic Source Characterisation
• The linear sampling method for random sources