Efficient Computation of Extended Surface Sources

TL;DR

This paper introduces an efficient method for solving inverse wave propagation problems by using a preconditioned iterative approach that leverages a variant of time reversal, demonstrated with a 2D acoustic surface source example.

Contribution

It presents a novel preconditioning technique based on time reversal for faster convergence in source extension inverse problems.

Findings

Preconditioner accelerates Krylov space iteration.

Effective for sources supported on surfaces with point constraints.

Demonstrated with a 2D acoustic example.

Abstract

Source extension is a reformulation of inverse problems in wave propagation, that at least in some cases leads to computationally tractable iterative solution methods. The core subproblem in all source extension methods is the solution of a linear inverse problem for a source (right hand side in a system of wave equations) through minimization of data error in the least squares sense with soft imposition of physical constraints on the source via an additive quadratic penalty. A variant of the time reversal method from photoacoustic tomography provides an approximate solution that can be used to precondition Krylov space iteration for rapid convergence to the solution of this subproblem. An acoustic 2D example for sources supported on a surface, with a soft contraint enforcing point support, illustrates the effectiveness of this preconditioner.