## Linear single-step image reconstruction in the presence of nonscattering regions

JOSA A, Vol. 19, Issue 6, pp. 1162-1171 (2002)

http://dx.doi.org/10.1364/JOSAA.19.001162

Acrobat PDF (1142 KB)

### Abstract

There is growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in using this technique for obtaining tomographic images of the neonatal head, with the view of determining the level of oxygenated and deoxygenated blood within the brain. Because of computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases where a nonscattering region exists. We present reconstructed images, using linear algorithms, of models that contain a nonscattering region within a diffusing material. The forward data are calculated by using the radiosity-diffusion model, and the inverse problem is solved by using either the radiosity-diffusion model or the diffusion-only model. When using data from a model containing a clear layer and reconstructing with the correct model, one can reconstruct the anomaly, but the qualitative accuracy and the position of the reconstructed anomaly depend on the size and the position of the clear regions. If the inverse model has no information about the clear regions (i.e., it is a purely diffusing model), an anomaly can be reconstructed, but the resulting image has very poor qualitative accuracy and poor localization of the anomaly. The errors in quantitative and localization accuracies depend on the size and location of the clear regions.

© 2002 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(170.3660) Medical optics and biotechnology : Light propagation in tissues

**Citation**

H. Dehghani and D. T. Delpy, "Linear single-step image reconstruction in the presence of nonscattering regions," J. Opt. Soc. Am. A **19**, 1162-1171 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-6-1162

Sort: Year | Journal | Reset

### References

- J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, and S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
- B. W. Pogue, K. D. Paulsen, C. Abele, and H. Kaufman, “Calibration of near-infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
- S. Fantini, M. A. Franceschini, E. Gratton, D. Hueber, W. Rosenfeld, D. Maulik, P. G. Stubblefield, and M. R. Stankovic, “Non-invasive optical mapping of the piglet in real time,” Opt. Express 4, 308–314 (1999).
- H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamaru, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
- J. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997).
- J. C. Hebden, S. R. Arridge, and D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
- S. R. Arridge, “Topical review: optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
- S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
- V. Ntziachristos and B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. Treatment 3, 41–46 (2001).
- C. H. Schmitz, H. L. Graber, H. B. Luo, I. Arif, J. Hira, Y. L. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, S. L. S. Barbour, and R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6486 (2000).
- M. A. Franceschini, V. Toronov, M. E. Filiaci, E. Gratton, and S. Fantini, “On-line optical imaging of the human brain with 160-ms temporal resolution,” Opt. Express 6, 49–57 (2000), http://www.opticsexpress.org.
- D. A. Boas, T. Gaudette, G. Strangman, X. F. Cheng, J. J. A. Marota, and J. B. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
- S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
- M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
- H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
- J. S. Wyatt, D. T. Delpy, M. Cope, S. Wray, and E. O. R. Reynolds, “Quantification of cerebral oxygenation and haemodynamics in sick newborn infants by near infrared spectroscopy,” Lancet ii, 1063–1066 (1986).
- A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogenous tissue,” Phys. Med. Biol. 43, 1285–1302 (1998).
- S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
- J. Riley, H. Dehghani, M. Schweiger, S. R. Arridge, J. Ripoll, and M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express 7, 462–467 (2000), http://www.opticsexpress.org.
- H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1670 (2000).
- J. Ripoll, S. R. Arridge, H. Dehghani, and M. Nieto-Vesperinas, “Boundary conditions for light propagation in diffusive media with non-scattering regions,” J. Opt. Soc. Am. A 17, 1671–1681 (2000).
- J. Ripoll, M. Nieto-Vesperinas, and S. R. Arridge, “Effect of roughness in nondiffusive regions within diffusive media,” J. Opt. Soc. Am. A 18, 940–947 (2001).
- A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
- O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).
- M. Vauhkonen, “Electrical impedance tomography and priori information,” Ph.D. dissertation (University of Kuopio, Kuopio, Finland, 1997).
- Y. Pei, H. L. Graber, and R. L. Barbour, “Normalized-constrained algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express 9, 97–109 (2001), http://www.opticsexpress.org.
- M. Schweiger and S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97 Proceedings), Vol. 1230 of Lecture Notes in Computer Science, J. Duncan and G. Gindi, eds. (Springer-Verlag, Berlin, 1997).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
- S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2:finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
- M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.