Analysis of new direct sampling indicators for far-field measurements

Abstract

This article focuses on the analysis of three direct sampling indicators which can be used for recovering scatterers from the far-field pattern of time-harmonic acoustic measurements. These methods fall under the category of sampling methods where an indicator function is constructed using the far-field operator. Motivated by some recent work, we study the standard indicator using the far-field operator and two indicators derived from the factorization method. We show the equivalence of two indicators previously studied as well as propose a new indicator based on the Tikhonov regularization applied to the far-field equation for the factorization method. Finally, we give some numerical examples to show how the reconstructions compare to other direct sampling methods.

References in corpus (6)

• A novel sampling method for multiple multiscale targets from scattering amplitudes at a fixed frequency
• Direct sampling methods for inverse elastic scattering problems
• Reverse Time Migration for Extended Obstacles: Acoustic Waves
• Reverse Time Migration for Extended Obstacles: Electromagnetic Waves
• The factorization method for a defective region in an anisotropic material
• Linear sampling method for identifying cavities in a heat conductor

Cited by in corpus (2)

• Regularization of the Factorization Method applied to diffuse optical tomography
• Direct sampling method to retrieve small objects from two-dimensional limited-aperture scattered field data