Abstract

A condition on nonuniqueness in optical tomography is stated. The main result applies to steady-state (dc) diffusion-based optical tomography, wherein we demonstrate that simultaneous unique recovery of diffusion and absorption coefficients cannot be achieved. A specific example of two images that give identical dc data is presented. If the refractive index is considered an unknown, then nonuniqueness also occurs in frequency-domain and time-domain optical tomography, if the underlying model of the diffusion approximation is employed.

© 1998 Optical Society of America

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  1. J. C. Hebden, S. R. Arridge, and D. T. Delpy, Phys. Med. Biol. 42, 825 (1997).
  2. S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).
  3. H. Jiang, K. D. Paulsen, and U. L. Osterberg, Phys. Med. Biol. 41, 1483 (1996).
  4. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).
  5. S. R. Arridge and M. Schweiger, Proc. SPIE 2389, 378 (1995).
  6. J. Sylvester and G. Uhlmann, Ann. Math. 125, 153 (1987).
  7. V. Isakov, Inverse Problems 9, 579 (1993).
  8. B. J. Hoenders, J. Opt. Soc. Am. A 14, 262 (1997).
  9. M. R. Ostermeyer and S. L. Jacques, J. Opt. Soc. Am. A 14, 255 (1997).
  10. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).
  11. V. Isakov, Inverse Problems in Partial Differential Equations (Springer, New York, 1998).
  12. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

1998

V. Isakov, Inverse Problems in Partial Differential Equations (Springer, New York, 1998).

1997

M. R. Ostermeyer and S. L. Jacques, J. Opt. Soc. Am. A 14, 255 (1997).

B. J. Hoenders, J. Opt. Soc. Am. A 14, 262 (1997).

1995

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

S. R. Arridge and M. Schweiger, Proc. SPIE 2389, 378 (1995).

1993

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

1987

J. Sylvester and G. Uhlmann, Ann. Math. 125, 153 (1987).

Arridge, S. R.

S. R. Arridge and M. Schweiger, Proc. SPIE 2389, 378 (1995).

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

J. C. Hebden, S. R. Arridge, and D. T. Delpy, Phys. Med. Biol. 42, 825 (1997).

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).

J. C. Hebden, S. R. Arridge, and D. T. Delpy, Phys. Med. Biol. 42, 825 (1997).

Deply, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

Hebden, J. C.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, Phys. Med. Biol. 42, 825 (1997).

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

Hoenders, B. J.

B. J. Hoenders, J. Opt. Soc. Am. A 14, 262 (1997).

Isakov, V.

V. Isakov, Inverse Problems in Partial Differential Equations (Springer, New York, 1998).

V. Isakov, Inverse Problems 9, 579 (1993).

Jacques, S. L.

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

H. Jiang, K. D. Paulsen, and U. L. Osterberg, Phys. Med. Biol. 41, 1483 (1996).

Osterberg, U. L.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

H. Jiang, K. D. Paulsen, and U. L. Osterberg, Phys. Med. Biol. 41, 1483 (1996).

Ostermeyer, M. R.

Patterson, M. S.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

Paulsen, K. D.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

H. Jiang, K. D. Paulsen, and U. L. Osterberg, Phys. Med. Biol. 41, 1483 (1996).

Pogue, B. W.

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

Schweiger, M.

S. R. Arridge and M. Schweiger, Proc. SPIE 2389, 378 (1995).

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

Sylvester, J.

J. Sylvester and G. Uhlmann, Ann. Math. 125, 153 (1987).

Uhlmann, G.

J. Sylvester and G. Uhlmann, Ann. Math. 125, 153 (1987).

Ann. Math.

J. Sylvester and G. Uhlmann, Ann. Math. 125, 153 (1987).

Inverse Problems

V. Isakov, Inverse Problems 9, 579 (1993).

J. Opt. Soc. Am. A

B. J. Hoenders, J. Opt. Soc. Am. A 14, 262 (1997).

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, J. Opt. Soc. Am. A 13, 253 (1995).

J. Opt. Soc. Am. A

Med. Phys.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Deply, Med. Phys. 20, 299 (1993).

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, Med. Phys. 22, 1779 (1995).

Phys. Med. Biol.

J. C. Hebden, S. R. Arridge, and D. T. Delpy, Phys. Med. Biol. 42, 825 (1997).

S. R. Arridge and J. C. Hebden, Phys. Med. Biol. 42, 841 (1997).

H. Jiang, K. D. Paulsen, and U. L. Osterberg, Phys. Med. Biol. 41, 1483 (1996).

Proc. SPIE

S. R. Arridge and M. Schweiger, Proc. SPIE 2389, 378 (1995).

Other

V. Isakov, Inverse Problems in Partial Differential Equations (Springer, New York, 1998).

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