# Factorization method versus migration imaging in a waveguide

## TL;DR

This paper compares the factorization and migration imaging methods for detecting obstacles in an acoustic waveguide, analyzing their theoretical foundations and performance through simulations.

## Contribution

It provides a detailed analysis and comparison of two qualitative imaging methods in waveguides, highlighting their differences and similarities.

## Key findings

- Factorization method estimates obstacle support using a single frequency.
- Migration method can operate with multiple frequencies and backpropagates waves.
- Analysis shows the connection between the two imaging techniques.

## Abstract

We present a comparative study of two qualitative imaging methods in an acoustic waveguide with sound hard walls. The waveguide terminates at one end and contains unknown obstacles of compact support, to be determined from data gathered by an array of sensors that probe the obstacles with waves and measure the scattered response. The first imaging method, known as the factorization method, is based on the factorization of the far field operator. It is designed to image at single frequency and estimates the support of the obstacles by a Picard range criterion. The second imaging method, known as migration, works either with one or multiple frequencies. It forms an image by backpropagating the measured scattered wave to the search points, using the Green's function in the empty waveguide. We study the connection between these methods with analysis and numerical simulations.