### Abstract

We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function f from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these means can be expressed through the solution of the wave equation with the initial pressure equal to f.) An explicit solution of this inverse problem is obtained in 3D for the surface that is the boundary of an open octet, and in 2D for the case when the centers of integration circles lie on two rays starting at the origin and intersecting at the angle equal to , . Our formulas reconstruct the Radon projections of a function closely related to f, from the values of on the measurement surface. Then, function f can be found by inverting the Radon transform.

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

Article number | 095001 |

Journal | Inverse Problems |

Volume | 31 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2015 |

### Fingerprint

### Keywords

- explicit inversion formula
- optoacoustic tomography
- photoacoustic tomography
- spherical means
- thermoacoustic tomography
- wave equation

### ASJC Scopus subject areas

- Signal Processing
- Computer Science Applications
- Applied Mathematics
- Mathematical Physics
- Theoretical Computer Science

### Cite this

**Inversion of the spherical means transform in corner-like domains by reduction to the classical Radon transform.** / Kunyansky, Leonid.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Inversion of the spherical means transform in corner-like domains by reduction to the classical Radon transform

AU - Kunyansky, Leonid

PY - 2015/9/1

Y1 - 2015/9/1

N2 - We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function f from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these means can be expressed through the solution of the wave equation with the initial pressure equal to f.) An explicit solution of this inverse problem is obtained in 3D for the surface that is the boundary of an open octet, and in 2D for the case when the centers of integration circles lie on two rays starting at the origin and intersecting at the angle equal to , . Our formulas reconstruct the Radon projections of a function closely related to f, from the values of on the measurement surface. Then, function f can be found by inverting the Radon transform.

AB - We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function f from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these means can be expressed through the solution of the wave equation with the initial pressure equal to f.) An explicit solution of this inverse problem is obtained in 3D for the surface that is the boundary of an open octet, and in 2D for the case when the centers of integration circles lie on two rays starting at the origin and intersecting at the angle equal to , . Our formulas reconstruct the Radon projections of a function closely related to f, from the values of on the measurement surface. Then, function f can be found by inverting the Radon transform.

KW - explicit inversion formula

KW - optoacoustic tomography

KW - photoacoustic tomography

KW - spherical means

KW - thermoacoustic tomography

KW - wave equation

UR - http://www.scopus.com/inward/record.url?scp=84940563009&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940563009&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/31/9/095001

DO - 10.1088/0266-5611/31/9/095001

M3 - Article

AN - SCOPUS:84940563009

VL - 31

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 9

M1 - 095001

ER -