### Abstract

Exterior inverse problem for the circular means transform (CMT) arises in the intravascular photoacoustic imaging (IVPA), in the intravascular ultrasound imaging (IVUS), as well as in radar and sonar. The reduction of the IPVA to the CMT is quite straightforward. As shown in the paper, in IVUS the circular means can be recovered from measurements by solving a certain Volterra integral equation. Thus, a tomography reconstruction in both modalities requires solving the exterior problem for the CMT. Numerical solution of this problem usually is not attempted due to the presence of "invisible" wavefronts, which results in severe instability of the reconstruction. The novel inversion algorithm proposed in this paper yields a stable partial reconstruction: it reproduces the "visible" part of the image and blurs the "invisible" part. If the image contains little or no invisible wavefronts (as frequently happens in the IVPA and IVUS) the reconstruction is quantitatively accurate. The presented numerical simulations demonstrate the feasibility of tomography-like reconstruction in these modalities.

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

Pages (from-to) | 339-359 |

Number of pages | 21 |

Journal | Inverse Problems and Imaging |

Volume | 8 |

Issue number | 2 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Circular means
- Exterior problem
- Intravas-cular imaging
- Photoacoustic tomography
- Radon transform

### ASJC Scopus subject areas

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

### Cite this

**Exterior/interior problem for the circular means transform with applications to intravascular imaging.** / Ambartsoumian, Gaik; Kunyansky, Leonid.

Research output: Contribution to journal › Article

*Inverse Problems and Imaging*, vol. 8, no. 2, pp. 339-359. https://doi.org/10.3934/ipi.2014.8.339

}

TY - JOUR

T1 - Exterior/interior problem for the circular means transform with applications to intravascular imaging

AU - Ambartsoumian, Gaik

AU - Kunyansky, Leonid

PY - 2014

Y1 - 2014

N2 - Exterior inverse problem for the circular means transform (CMT) arises in the intravascular photoacoustic imaging (IVPA), in the intravascular ultrasound imaging (IVUS), as well as in radar and sonar. The reduction of the IPVA to the CMT is quite straightforward. As shown in the paper, in IVUS the circular means can be recovered from measurements by solving a certain Volterra integral equation. Thus, a tomography reconstruction in both modalities requires solving the exterior problem for the CMT. Numerical solution of this problem usually is not attempted due to the presence of "invisible" wavefronts, which results in severe instability of the reconstruction. The novel inversion algorithm proposed in this paper yields a stable partial reconstruction: it reproduces the "visible" part of the image and blurs the "invisible" part. If the image contains little or no invisible wavefronts (as frequently happens in the IVPA and IVUS) the reconstruction is quantitatively accurate. The presented numerical simulations demonstrate the feasibility of tomography-like reconstruction in these modalities.

AB - Exterior inverse problem for the circular means transform (CMT) arises in the intravascular photoacoustic imaging (IVPA), in the intravascular ultrasound imaging (IVUS), as well as in radar and sonar. The reduction of the IPVA to the CMT is quite straightforward. As shown in the paper, in IVUS the circular means can be recovered from measurements by solving a certain Volterra integral equation. Thus, a tomography reconstruction in both modalities requires solving the exterior problem for the CMT. Numerical solution of this problem usually is not attempted due to the presence of "invisible" wavefronts, which results in severe instability of the reconstruction. The novel inversion algorithm proposed in this paper yields a stable partial reconstruction: it reproduces the "visible" part of the image and blurs the "invisible" part. If the image contains little or no invisible wavefronts (as frequently happens in the IVPA and IVUS) the reconstruction is quantitatively accurate. The presented numerical simulations demonstrate the feasibility of tomography-like reconstruction in these modalities.

KW - Circular means

KW - Exterior problem

KW - Intravas-cular imaging

KW - Photoacoustic tomography

KW - Radon transform

UR - http://www.scopus.com/inward/record.url?scp=84900457033&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84900457033&partnerID=8YFLogxK

U2 - 10.3934/ipi.2014.8.339

DO - 10.3934/ipi.2014.8.339

M3 - Article

AN - SCOPUS:84900457033

VL - 8

SP - 339

EP - 359

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

SN - 1930-8337

IS - 2

ER -