# Analysis of new direct sampling indicators for far-field measurements

## TL;DR

This paper analyzes three direct sampling indicators for reconstructing scatterers from far-field acoustic data, demonstrating their equivalence and introducing a new indicator based on Tikhonov regularization, with numerical comparisons.

## Contribution

It introduces a novel indicator based on Tikhonov regularization and establishes the equivalence of existing indicators for far-field scattering reconstruction.

## Key findings

- The new Tikhonov-based indicator performs comparably to existing methods.
- The indicators studied are mathematically equivalent under certain conditions.
- Numerical examples illustrate the effectiveness of the proposed approach.

## 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.