### Abstract

We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen’s method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and nonconvex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, we ensure that each least squares calculation is well-conditioned so that an iterative solver can be effectively applied. Each matrix-vector product involves the solution of a large number of forward scattering problems, for which we have created a new, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately 1 million partial differential equations were solved, requiring approximately 2 days to compute using a parallel MATLAB implementation on a multicore workstation.

Original language | English (US) |
---|---|

Pages (from-to) | 641-664 |

Number of pages | 24 |

Journal | SIAM Journal on Imaging Sciences |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - 2017 |

### Fingerprint

### Keywords

- Acoustics
- Electromagnetics
- Fast direct solvers
- Inverse scattering
- Recursive linearization

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Imaging Sciences*,

*10*(2), 641-664. https://doi.org/10.1137/16M1093562

**High resolution inverse scattering in two dimensions using recursive linearization.** / Borges, Carlos; Gillman, Adrianna; Greengard, Leslie.

Research output: Contribution to journal › Article

*SIAM Journal on Imaging Sciences*, vol. 10, no. 2, pp. 641-664. https://doi.org/10.1137/16M1093562

}

TY - JOUR

T1 - High resolution inverse scattering in two dimensions using recursive linearization

AU - Borges, Carlos

AU - Gillman, Adrianna

AU - Greengard, Leslie

PY - 2017

Y1 - 2017

N2 - We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen’s method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and nonconvex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, we ensure that each least squares calculation is well-conditioned so that an iterative solver can be effectively applied. Each matrix-vector product involves the solution of a large number of forward scattering problems, for which we have created a new, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately 1 million partial differential equations were solved, requiring approximately 2 days to compute using a parallel MATLAB implementation on a multicore workstation.

AB - We describe a fast, stable algorithm for the solution of the inverse acoustic scattering problem in two dimensions. Given full aperture far field measurements of the scattered field for multiple angles of incidence, we use Chen’s method of recursive linearization to reconstruct an unknown sound speed at resolutions of thousands of square wavelengths in a fully nonlinear regime. Despite the fact that the underlying optimization problem is formally ill-posed and nonconvex, recursive linearization requires only the solution of a sequence of linear least squares problems at successively higher frequencies. By seeking a suitably band-limited approximation of the sound speed profile, we ensure that each least squares calculation is well-conditioned so that an iterative solver can be effectively applied. Each matrix-vector product involves the solution of a large number of forward scattering problems, for which we have created a new, spectrally accurate, fast direct solver. For the largest problems considered, involving 19,600 unknowns, approximately 1 million partial differential equations were solved, requiring approximately 2 days to compute using a parallel MATLAB implementation on a multicore workstation.

KW - Acoustics

KW - Electromagnetics

KW - Fast direct solvers

KW - Inverse scattering

KW - Recursive linearization

UR - http://www.scopus.com/inward/record.url?scp=85021674780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021674780&partnerID=8YFLogxK

U2 - 10.1137/16M1093562

DO - 10.1137/16M1093562

M3 - Article

AN - SCOPUS:85021674780

VL - 10

SP - 641

EP - 664

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 2

ER -