Symmetries, inversion formulas, and image reconstruction for optical tomography.

We consider the image reconstruction problem for optical tomography with diffuse light. The associated inverse scattering problem is analyzed by making use of particular symmetries of the scattering data. The effects of sampling and limited data are analyzed for several different experimental modalities, and computationally efficient reconstruction algorithms are obtained. These algorithms are suitable for the reconstruction of images from very large data sets.

[1]  G. C. Pomraning,et al.  Linear Transport Theory , 1967 .

[2]  Britton Chance,et al.  Proceedings of optical tomography and spectroscopy of tissue : theory, instrumentation, model, and human studies II : 9-12 February 1997, San Jose, California , 1997 .

[3]  Vadim A. Markel,et al.  Near-field tomography without phase retrieval. , 2001, Physical review letters.

[4]  M. V. Rossum,et al.  Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion , 1998, cond-mat/9804141.

[5]  John C. Schotland,et al.  Effects of sampling and limited data in optical tomography , 2002 .

[6]  R. Aronson,et al.  Boundary conditions for diffusion of light. , 1995, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7]  R R Alfano,et al.  Time-resolved Fourier optical diffuse tomography. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  John C Schotland,et al.  Scanning paraxial optical tomography. , 2002, Optics letters.

[9]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[10]  G. Müller,et al.  Medical Optical Tomography: Functional Imaging and Monitoring , 1993 .

[11]  Vadim A. Markel,et al.  Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[12]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[13]  Vadim A. Markel,et al.  Inverse problem in optical diffusion tomography. II. Role of boundary conditions. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[14]  Britton Chance,et al.  Proceedings of optical tomography and spectroscopy of tissue III : 24-28 January 1999, San Jose, California , 1999 .

[15]  Vadim A. Markel,et al.  Inverse scattering with diffusing waves. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[16]  Andrew G. Glen,et al.  APPL , 2001 .

[17]  M. V. Berry,et al.  Optics of Fractal Clusters Such as Smoke , 1986 .

[18]  L. Apresyan,et al.  Radiation transfer : statistical and wave aspects , 1996 .

[19]  V A Markel,et al.  Inverse scattering for the diffusion equation with general boundary conditions. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.