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## State-estimation approach to the nonstationary optical tomography problem

Ville Kolehmainen, Simon Prince, Simon R. Arridge, and Jari P. Kaipio »View Author Affiliations

Ville Kolehmainen, Jari P. Kaipio

*Department of Applied Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland*

*Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 113576*

*Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK*

JOSA A, Vol. 20, Issue 5, pp. 876-889 (2003)

http://dx.doi.org/10.1364/JOSAA.20.000876

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### Abstract

We propose a new numerical approach to the nonstationary optical (diffusion) tomography (OT) problem. The assumption in the method is that the absorption and/or diffusion coefficients are nonstationary in the sense that they may exhibit significant changes during the time that is needed to measure data for one traditional image frame. In the proposed method, the OT problem is formulated as a state-estimation problem. Within the state-estimation formulation, the absorption and/or diffusion coefficients are considered a stochastic process. The objective is to estimate a sequence of states for the process when the state evolution model for the process, the observation model for OT experiments, and data on the exterior boundary are given. In the proposed method, the state estimates are computed by using Kalman filtering techniques. The performance of the proposed method is evaluated on the basis of synthetic data. The simulations also illustrate that further improvements to the results in nonstationary applications can be obtained by adjustment of the measurement protocol.

© 2003 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.6960) Medical optics and biotechnology : Tomography

**Citation**

Ville Kolehmainen, Simon Prince, Simon R. Arridge, and Jari P. Kaipio, "State-estimation approach to the nonstationary optical tomography problem," J. Opt. Soc. Am. A **20**, 876-889 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-876

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**Abdoulaev, G.**

**Alcouffe, R. E.**

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**Alfano, R. R.**

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**Andronica, R.**

**Arif, I.**

**Aronson, R.**

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**Arridge, S. R.**

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**Barbour, D.-L. S.**

**Barbour, R. L.**

- A. V. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001); http://www.opticsexpress.org.
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- B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, and R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. R. Alfano, eds., Proc. SPIE 2389, 16–28 (1995).

**Barbour, S. S.**

**Benaron, D. A.**

- J. P. van Houten, D. A. Benaron, S. Splilman, and D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).

**Bernarding, J.**

- C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, and A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).
- R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, and A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).

**Bluestone, A.**

**Bluestone, A. V.**

**Boas, D. A.**

- D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
- R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
- M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).

**Boretsky, R.**

- B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, and R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).

**Bouman, C. A.**

**Brazy, J. E.**

- J. E. Brazy, D. V. Lewis, M. H. Mitnick, and F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).

**Brooks, D. H.**

- D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
- R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, and D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).

**Bucy, R. S.**

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**Bui-Mong-Hung,**

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- Semi-Three-Dimensional Algorithm for Time-Resolved Diffuse Optical Tomography by Use of the Generalized Pulse Spectrum Technique (AO)
- Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography (OL)
- Three-Dimensional Optical Tomographic Imaging of Supersonic Jets through Inversion of Phase Data Obtained through the Transport-of-Intensity Equation (AO)

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