### Abstract

Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods (including the popular time reversal algorithm) cannot be used. The inverse problem involving reflecting walls can be solved by the gradual time reversal method we propose here. It consists in solving back in time on the interval the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

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

Article number | 035008 |

Journal | Inverse Problems |

Volume | 31 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2015 |

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### Keywords

- photoacoustic tomography
- reflecting walls
- resonant cavity
- thermoacoustic tomography
- time reversal
- wave equation

### ASJC Scopus subject areas

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

### Cite this

**Gradual time reversal in thermo- and photo-acoustic tomography within a resonant cavity.** / Holman, B.; Kunyansky, Leonid.

Research output: Contribution to journal › Article

*Inverse Problems*, vol. 31, no. 3, 035008. https://doi.org/10.1088/0266-5611/31/3/035008

}

TY - JOUR

T1 - Gradual time reversal in thermo- and photo-acoustic tomography within a resonant cavity

AU - Holman, B.

AU - Kunyansky, Leonid

PY - 2015/3/1

Y1 - 2015/3/1

N2 - Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods (including the popular time reversal algorithm) cannot be used. The inverse problem involving reflecting walls can be solved by the gradual time reversal method we propose here. It consists in solving back in time on the interval the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

AB - Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods (including the popular time reversal algorithm) cannot be used. The inverse problem involving reflecting walls can be solved by the gradual time reversal method we propose here. It consists in solving back in time on the interval the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

KW - photoacoustic tomography

KW - reflecting walls

KW - resonant cavity

KW - thermoacoustic tomography

KW - time reversal

KW - wave equation

UR - http://www.scopus.com/inward/record.url?scp=84923166233&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923166233&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/31/3/035008

DO - 10.1088/0266-5611/31/3/035008

M3 - Article

VL - 31

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 3

M1 - 035008

ER -