Target reconstruction with a reference point scatterer using phaseless far field patterns

TL;DR

This paper introduces a hybrid method combining phase retrieval and direct sampling to reconstruct target locations using phaseless far field data, overcoming translation invariance issues with a reference point scatterer.

Contribution

The paper proposes a novel approach that integrates a reference point scatterer with phase retrieval and direct sampling, enabling accurate target reconstruction from phaseless data.

Findings

Effective phase retrieval algorithm developed

Method overcomes translation invariance in phaseless data

Numerical examples demonstrate robustness and accuracy

Abstract

An important property of the phaseless far field patterns with incident plane waves is the translation invariance. Thus it is impossible to reconstruct the location of the underlying scatterers. By adding a reference point scatterer into the model, we design a novel direct sampling method using the phaseless data directly. The reference point technique not only overcomes the translation invariance, but also brings a practical phase retrieval algorithm. Based on this, we propose a hybrid method combining the novel phase retrieval algorithm and the classical direct sampling methods. Numerical examples in two dimensions are presented to demonstrate their effectiveness and robustness.