Abstract

A nonparametric deconvolution algorithm for recovering the photon time-of-flight distribution (TOFD) from time-resolved (TR) measurements is described. The algorithm combines wavelet denoising and a two-stage deconvolution method based on generalized singular value decomposition and Tikhonov regularization. The efficacy of the algorithm was tested on simulated and experimental TR data and the results show that it can recover the photon TOFD with high fidelity. Combined with the microscopic Beer–Lambert law, the algorithm enables accurate quantification of absorption changes from arbitrary time-of-flight windows, thereby optimizing the depth sensitivity provided by TR measurements.

© 2012 Optical Society of America

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2011 (1)

M. Makitalo and A. Foi, IEEE Trans. Image Process 20, 99 (2011).
[CrossRef]

2010 (1)

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

2008 (1)

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

2007 (1)

P. C. Hansen, Numer. Algorithms 46, 189 (2007).
[CrossRef]

2006 (2)

2005 (1)

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

2004 (1)

2003 (1)

A. Liebert, H. Wabnitz, D. Grosenick, and R. Macdonald, J. Biomed. Opt. 8, 512 (2003).
[CrossRef]

2001 (1)

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

1999 (1)

1997 (1)

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988).
[CrossRef]

Bérubé-Lauzière, Y.

G. Bodi and Y. Bérubé-Lauzière, in European Conference on Biomedical Optics (Optical Society of America, 2009), p. 7369.

Boas, D. A.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

Bodi, G.

G. Bodi and Y. Bérubé-Lauzière, in European Conference on Biomedical Optics (Optical Society of America, 2009), p. 7369.

Chabrier, R.

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988).
[CrossRef]

Contini, D.

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, Opt. Express 14, 5418 (2006).
[CrossRef]

H. Wabnitz, A. Liebert, D. Contini, L. Spinelli, and A. Torricelli, in Biomedical Optics (Optical Society of America, 2008), p. BMD9.

Cubeddu, R.

Diop, M.

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

Dogariu, A.

Elliott, J. T.

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

Foi, A.

M. Makitalo and A. Foi, IEEE Trans. Image Process 20, 99 (2011).
[CrossRef]

Franceschini, M. A.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

Gagnon, L.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

Gauthier, C.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

Grosenick, D.

A. Liebert, H. Wabnitz, D. Grosenick, and R. Macdonald, J. Biomed. Opt. 8, 512 (2003).
[CrossRef]

Hansen, P. C.

P. C. Hansen, Numer. Algorithms 46, 189 (2007).
[CrossRef]

P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (Society for Industrial and Applied Mathematics, 2010).

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988).
[CrossRef]

Hoge, R. D.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

Kienle, A.

Lawrence, K. St.

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

Lee, T. Y.

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

Lesage, F.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

Liebert, A.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, Appl. Opt. 43, 3037 (2004).
[CrossRef]

A. Liebert, H. Wabnitz, D. Grosenick, and R. Macdonald, J. Biomed. Opt. 8, 512 (2003).
[CrossRef]

H. Wabnitz, A. Liebert, D. Contini, L. Spinelli, and A. Torricelli, in Biomedical Optics (Optical Society of America, 2008), p. BMD9.

Macdonald, R.

Makitalo, M.

M. Makitalo and A. Foi, IEEE Trans. Image Process 20, 99 (2011).
[CrossRef]

Migueis, M.

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

Moller, M.

Montcel, B.

Obrig, H.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, Appl. Opt. 43, 3037 (2004).
[CrossRef]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

Paglia, F.

Patterson, M. S.

Pifferi, A.

Pine, D. J.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988).
[CrossRef]

Popescu, G.

Poulet, P.

Rinneberg, H.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, Appl. Opt. 43, 3037 (2004).
[CrossRef]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

Selb, J.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

Sorensen, A. G.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

Spinelli, L.

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, Opt. Express 14, 5418 (2006).
[CrossRef]

H. Wabnitz, A. Liebert, D. Contini, L. Spinelli, and A. Torricelli, in Biomedical Optics (Optical Society of America, 2008), p. BMD9.

Steinbrink, J.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, Appl. Opt. 43, 3037 (2004).
[CrossRef]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

Stott, J. J.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

Tichauer, K. M.

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

Torricelli, A.

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, Opt. Express 14, 5418 (2006).
[CrossRef]

H. Wabnitz, A. Liebert, D. Contini, L. Spinelli, and A. Torricelli, in Biomedical Optics (Optical Society of America, 2008), p. BMD9.

Villringer, A.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, Appl. Opt. 43, 3037 (2004).
[CrossRef]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

Wabnitz, H.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, Appl. Opt. 43, 3037 (2004).
[CrossRef]

A. Liebert, H. Wabnitz, D. Grosenick, and R. Macdonald, J. Biomed. Opt. 8, 512 (2003).
[CrossRef]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

H. Wabnitz, A. Liebert, D. Contini, L. Spinelli, and A. Torricelli, in Biomedical Optics (Optical Society of America, 2008), p. BMD9.

Weitz, D. A.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Image Process (1)

M. Makitalo and A. Foi, IEEE Trans. Image Process 20, 99 (2011).
[CrossRef]

J. Biomed. Opt. (4)

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, J. Biomed. Opt. 10, 11013 (2005).
[CrossRef]

A. Liebert, H. Wabnitz, D. Grosenick, and R. Macdonald, J. Biomed. Opt. 8, 512 (2003).
[CrossRef]

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, J. Biomed. Opt. 13, 054019 (2008).
[CrossRef]

M. Diop, K. M. Tichauer, J. T. Elliott, M. Migueis, T. Y. Lee, and K. St. Lawrence, J. Biomed. Opt. 15, 057004 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

Numer. Algorithms (1)

P. C. Hansen, Numer. Algorithms 46, 189 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Med. Biol. (1)

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, Phys. Med. Biol. 46, 879 (2001).
[CrossRef]

Phys. Rev. Lett. (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988).
[CrossRef]

Other (4)

“MathWorks,” http://www.mathworks.com/ .

H. Wabnitz, A. Liebert, D. Contini, L. Spinelli, and A. Torricelli, in Biomedical Optics (Optical Society of America, 2008), p. BMD9.

P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (Society for Industrial and Applied Mathematics, 2010).

G. Bodi and Y. Bérubé-Lauzière, in European Conference on Biomedical Optics (Optical Society of America, 2009), p. 7369.

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