Inverse medium problems, saddle point formulation

TL;DR

This paper introduces an improved direct sampling method for inverse medium problems using saddle point formulations, enabling efficient and direct imaging of media by solving saddle point problems.

Contribution

It develops a novel saddle point formulation-based probing method that enhances direct sampling techniques for inverse medium imaging.

Findings

Improved probing functions for direct sampling.

Efficient imaging of media using saddle point solutions.

Applicable to a broad class of inverse medium problems.

Abstract

In this paper we discuss inverse medium problems. We develop the direct sampling method based on probing indices using the saddle point formulation. The medium is constructed by solutions of saddle point problems. The method improves the probing functions for the direct sampling method and directly images the medium. The method is very efficient and can be applied to a general class of inverse medium problems.