### Abstract

Diffuse Optical Tomography (DOT) involves a nonlinear optimization problem to find the tissue optical properties by measuring near-infrared light noninvasively. Many researchers used linearization methods to obtain the optical image in real time. However, the linearization procedure may neglect small but sometimes important regions such as small tumors at an early stage. Therefore, nonlinear optimization methods such as gradient- or Newton- type methods are exploited, resulting in better resolution image than that of linearization methods. But the disadvantage of nonlinear methods is that they need much computation time. To solve this trade-off dilemma between image resolution and computing time, we suggest second order inverse Born expansion algorithm in this paper. It is known that a small perturbation of photon density is represented by Born expansion with respect to the perturbation of optical coefficients, which is an infinite series of integral operators having Robin function kernel. Whereas, inverse Born expansion is an implicit representation of a small perturbation of optical coefficients by an infinite series of the integral operators with respect to the photon density and its perturbation, which is appropriate series expansion for inverse DOT problem. Solving the inverse Born expansion itself and the first order approximation correspond to nonlinear and linear method, respectively. We formulated a second order approximation of the inverse Born expansion explicitly to make numerical implementation possible and showed the convergence order of the proposed method is higher than the linear method.

Original language | English |
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Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Volume | 6850 |

DOIs | |

Publication status | Published - 2008 Apr 21 |

Externally published | Yes |

Event | Multimodal Biomedical Imaging III - San Jose, CA, United States Duration: 2008 Jan 19 → 2008 Jan 21 |

### Other

Other | Multimodal Biomedical Imaging III |
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Country | United States |

City | San Jose, CA |

Period | 08/1/19 → 08/1/21 |

### Fingerprint

### Keywords

- Born expansion
- Diffuse optical tomography
- Robin function

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(Vol. 6850). [68500U] https://doi.org/10.1117/12.762488

**Second order inverse born approximation for diffuse optical tomography.** / Kwon, Kiwoon; Kim, Beop-Min.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*vol. 6850, 68500U, Multimodal Biomedical Imaging III, San Jose, CA, United States, 08/1/19. https://doi.org/10.1117/12.762488

}

TY - GEN

T1 - Second order inverse born approximation for diffuse optical tomography

AU - Kwon, Kiwoon

AU - Kim, Beop-Min

PY - 2008/4/21

Y1 - 2008/4/21

N2 - Diffuse Optical Tomography (DOT) involves a nonlinear optimization problem to find the tissue optical properties by measuring near-infrared light noninvasively. Many researchers used linearization methods to obtain the optical image in real time. However, the linearization procedure may neglect small but sometimes important regions such as small tumors at an early stage. Therefore, nonlinear optimization methods such as gradient- or Newton- type methods are exploited, resulting in better resolution image than that of linearization methods. But the disadvantage of nonlinear methods is that they need much computation time. To solve this trade-off dilemma between image resolution and computing time, we suggest second order inverse Born expansion algorithm in this paper. It is known that a small perturbation of photon density is represented by Born expansion with respect to the perturbation of optical coefficients, which is an infinite series of integral operators having Robin function kernel. Whereas, inverse Born expansion is an implicit representation of a small perturbation of optical coefficients by an infinite series of the integral operators with respect to the photon density and its perturbation, which is appropriate series expansion for inverse DOT problem. Solving the inverse Born expansion itself and the first order approximation correspond to nonlinear and linear method, respectively. We formulated a second order approximation of the inverse Born expansion explicitly to make numerical implementation possible and showed the convergence order of the proposed method is higher than the linear method.

AB - Diffuse Optical Tomography (DOT) involves a nonlinear optimization problem to find the tissue optical properties by measuring near-infrared light noninvasively. Many researchers used linearization methods to obtain the optical image in real time. However, the linearization procedure may neglect small but sometimes important regions such as small tumors at an early stage. Therefore, nonlinear optimization methods such as gradient- or Newton- type methods are exploited, resulting in better resolution image than that of linearization methods. But the disadvantage of nonlinear methods is that they need much computation time. To solve this trade-off dilemma between image resolution and computing time, we suggest second order inverse Born expansion algorithm in this paper. It is known that a small perturbation of photon density is represented by Born expansion with respect to the perturbation of optical coefficients, which is an infinite series of integral operators having Robin function kernel. Whereas, inverse Born expansion is an implicit representation of a small perturbation of optical coefficients by an infinite series of the integral operators with respect to the photon density and its perturbation, which is appropriate series expansion for inverse DOT problem. Solving the inverse Born expansion itself and the first order approximation correspond to nonlinear and linear method, respectively. We formulated a second order approximation of the inverse Born expansion explicitly to make numerical implementation possible and showed the convergence order of the proposed method is higher than the linear method.

KW - Born expansion

KW - Diffuse optical tomography

KW - Robin function

UR - http://www.scopus.com/inward/record.url?scp=42149177893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42149177893&partnerID=8YFLogxK

U2 - 10.1117/12.762488

DO - 10.1117/12.762488

M3 - Conference contribution

SN - 9780819470256

VL - 6850

BT - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

ER -