### Abstract

We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors placed on a circle (in 2D) or a sphere (in 3D) surrounding the object of interest. The third inversion algorithm works with the data measured by the integrating line detectors arranged in a cylindrical assembly rotating around the object. The number of operations required by these techniques is equal to O(n ^{3} log n) and O(n ^{3} log ^{2}n) for the 3D techniques (assuming the reconstruction grid with n ^{3} nodes) and to O(n ^{2} log n) for the 2D problem with n × n discretizetion grid. Numerical simulations show that on large computational grids our methods are at least two orders of magnitude faster than the finite-difference time reversal techniques. The results of reconstructions from real measurements done by the integrating line detectors are also presented, to demonstrate the practicality of our algorithms.

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

Pages (from-to) | 111-131 |

Number of pages | 21 |

Journal | Inverse Problems and Imaging |

Volume | 6 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2012 |

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### Keywords

- Fast algorithms
- Integrating detectors
- Radon transform
- Spherical means
- Thermoacoustic tomography

### ASJC Scopus subject areas

- Analysis
- Control and Optimization
- Discrete Mathematics and Combinatorics
- Modeling and Simulation

### Cite this

**Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries.** / Kunyansky, Leonid.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries

AU - Kunyansky, Leonid

PY - 2012/2

Y1 - 2012/2

N2 - We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors placed on a circle (in 2D) or a sphere (in 3D) surrounding the object of interest. The third inversion algorithm works with the data measured by the integrating line detectors arranged in a cylindrical assembly rotating around the object. The number of operations required by these techniques is equal to O(n 3 log n) and O(n 3 log 2n) for the 3D techniques (assuming the reconstruction grid with n 3 nodes) and to O(n 2 log n) for the 2D problem with n × n discretizetion grid. Numerical simulations show that on large computational grids our methods are at least two orders of magnitude faster than the finite-difference time reversal techniques. The results of reconstructions from real measurements done by the integrating line detectors are also presented, to demonstrate the practicality of our algorithms.

AB - We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors placed on a circle (in 2D) or a sphere (in 3D) surrounding the object of interest. The third inversion algorithm works with the data measured by the integrating line detectors arranged in a cylindrical assembly rotating around the object. The number of operations required by these techniques is equal to O(n 3 log n) and O(n 3 log 2n) for the 3D techniques (assuming the reconstruction grid with n 3 nodes) and to O(n 2 log n) for the 2D problem with n × n discretizetion grid. Numerical simulations show that on large computational grids our methods are at least two orders of magnitude faster than the finite-difference time reversal techniques. The results of reconstructions from real measurements done by the integrating line detectors are also presented, to demonstrate the practicality of our algorithms.

KW - Fast algorithms

KW - Integrating detectors

KW - Radon transform

KW - Spherical means

KW - Thermoacoustic tomography

UR - http://www.scopus.com/inward/record.url?scp=84857171095&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857171095&partnerID=8YFLogxK

U2 - 10.3934/ipi.2012.6.111

DO - 10.3934/ipi.2012.6.111

M3 - Article

AN - SCOPUS:84857171095

VL - 6

SP - 111

EP - 131

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 1

ER -