Abstract

An optimal statistical approach is applied to the task of image reconstruction in photoacoustics. The physical essence of the task is as follows: Pulse laser irradiation induces an ultrasound wave on the inhomogeneities inside the investigated volume. This acoustic wave is received by the set of receivers outside this volume. It is necessary to reconstruct a spatial image of these inhomogeneities. Developed mathematical techniques of the radio location theory are used for solving the task. An algorithm of maximum likelihood is synthesized for the image reconstruction. The obtained algorithm is investigated by digital modeling. The number of receivers and their disposition in space are arbitrary. Results of the synthesis are applied to noninvasive medical diagnostics (breast cancer). The capability of the algorithm is tested on real signals. The image is built with use of signals obtained in vitro. The essence of the algorithm includes (i) summing of all signals in the image plane with the transform from the time coordinates of signals to the spatial coordinates of the image and (ii) optimal spatial filtration of this sum. The results are shown in the figures.

© 2000 Optical Society of America

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References

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  1. A. Rosencwaig, “Photoacoustic spectroscopy,” Anal. Chem. 46, 592–602 (1975).
    [CrossRef]
  2. R. A. Kruger, “Photoacoustic ultrasound,” Med. Phys. 21, 127–131 (1994).
    [CrossRef] [PubMed]
  3. R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
    [CrossRef] [PubMed]
  4. P. Liu, “Image reconstruction from photoacoustic pressure signals,” in Laser–Tissue Interaction VII, S. L. Jacques, ed., Proc. SPIE2681, 285–296 (1996).
    [CrossRef]
  5. R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).
  6. G. G. A. Hoelen, F. F. M. de Mul, R. Pongers, R. Dekker, “Three-dimensional photoacoustic imaging of blood vessels in tissue,” Opt. Lett. 23, 648–650 (1998).
    [CrossRef]
  7. R. A. Kruger, D. R. Reinecke, G. A. Kruger, “Thermoacoustic computed tomography,” Med. Phys. 26, 1832–1837 (1999).
    [CrossRef] [PubMed]
  8. P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.
  9. P. A. Bakut, Y. V. Julina, N. A. Ivanchuk, “Detection of mobile objects,” (Sovetskoye Radio, Moscow, 1980), in Russian.
  10. D. B. Ivashov, Y. V. Julina, “Potentials of the radioimage reconstruction algorithms,” Radiotekh. Elecktron. 41, 1–22 (1996), in Russian.
  11. I. S. Gradstein, I. M. Ryshik, Tables of Integrals, Sums, Series and Products (Physics-Mathematician State Publishing House, Moscow, 1962), in Russian.
  12. K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
    [CrossRef] [PubMed]

1999 (1)

R. A. Kruger, D. R. Reinecke, G. A. Kruger, “Thermoacoustic computed tomography,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

1998 (2)

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

G. G. A. Hoelen, F. F. M. de Mul, R. Pongers, R. Dekker, “Three-dimensional photoacoustic imaging of blood vessels in tissue,” Opt. Lett. 23, 648–650 (1998).
[CrossRef]

1996 (1)

D. B. Ivashov, Y. V. Julina, “Potentials of the radioimage reconstruction algorithms,” Radiotekh. Elecktron. 41, 1–22 (1996), in Russian.

1995 (1)

R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

1994 (1)

R. A. Kruger, “Photoacoustic ultrasound,” Med. Phys. 21, 127–131 (1994).
[CrossRef] [PubMed]

1975 (1)

A. Rosencwaig, “Photoacoustic spectroscopy,” Anal. Chem. 46, 592–602 (1975).
[CrossRef]

Appledorn, C. R.

R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

Bakut, P. A.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

P. A. Bakut, Y. V. Julina, N. A. Ivanchuk, “Detection of mobile objects,” (Sovetskoye Radio, Moscow, 1980), in Russian.

Bolshakov, I. A.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

de Mul, F. F. M.

Dekker, R.

Esenaliev, R. O.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Fang, Y. R.

R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

Fantini, S.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Fornage, B. D.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Franceschini, M.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Gerasimov, B. M.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

Gradstein, I. S.

I. S. Gradstein, I. M. Ryshik, Tables of Integrals, Sums, Series and Products (Physics-Mathematician State Publishing House, Moscow, 1962), in Russian.

Hoelen, G. G. A.

Ivanchuk, N. A.

P. A. Bakut, Y. V. Julina, N. A. Ivanchuk, “Detection of mobile objects,” (Sovetskoye Radio, Moscow, 1980), in Russian.

Ivashov, D. B.

D. B. Ivashov, Y. V. Julina, “Potentials of the radioimage reconstruction algorithms,” Radiotekh. Elecktron. 41, 1–22 (1996), in Russian.

Jess, H.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Julina, Y. V.

D. B. Ivashov, Y. V. Julina, “Potentials of the radioimage reconstruction algorithms,” Radiotekh. Elecktron. 41, 1–22 (1996), in Russian.

P. A. Bakut, Y. V. Julina, N. A. Ivanchuk, “Detection of mobile objects,” (Sovetskoye Radio, Moscow, 1980), in Russian.

Karabutov, A. A.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Kaschke, M.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Kruger, G. A.

R. A. Kruger, D. R. Reinecke, G. A. Kruger, “Thermoacoustic computed tomography,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

Kruger, R. A.

R. A. Kruger, D. R. Reinecke, G. A. Kruger, “Thermoacoustic computed tomography,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

R. A. Kruger, “Photoacoustic ultrasound,” Med. Phys. 21, 127–131 (1994).
[CrossRef] [PubMed]

Kuriksha, A. A.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

Liu, P.

R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

P. Liu, “Image reconstruction from photoacoustic pressure signals,” in Laser–Tissue Interaction VII, S. L. Jacques, ed., Proc. SPIE2681, 285–296 (1996).
[CrossRef]

Moesta, K. T.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Oraevsky, A. A.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Pongers, R.

Reinecke, D. R.

R. A. Kruger, D. R. Reinecke, G. A. Kruger, “Thermoacoustic computed tomography,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

Repin, V. G.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

Rosencwaig, A.

A. Rosencwaig, “Photoacoustic spectroscopy,” Anal. Chem. 46, 592–602 (1975).
[CrossRef]

Ryshik, I. M.

I. S. Gradstein, I. M. Ryshik, Tables of Integrals, Sums, Series and Products (Physics-Mathematician State Publishing House, Moscow, 1962), in Russian.

Schlag, P.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Shirokov, V. V.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

Stelling, C.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Tartakovsky, G. P.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

Thomsen, S. L.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Tittel, F. K.

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

Totkas, S.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Anal. Chem. (1)

A. Rosencwaig, “Photoacoustic spectroscopy,” Anal. Chem. 46, 592–602 (1975).
[CrossRef]

J. Biomed. Opt. (1)

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. Franceschini, M. Kaschke, P. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Med. Phys. (3)

R. A. Kruger, “Photoacoustic ultrasound,” Med. Phys. 21, 127–131 (1994).
[CrossRef] [PubMed]

R. A. Kruger, P. Liu, Y. R. Fang, C. R. Appledorn, “Photoacoustic ultrasound (PAUS)—reconstruction tomography,” Med. Phys. 22, 1605–1609 (1995).
[CrossRef] [PubMed]

R. A. Kruger, D. R. Reinecke, G. A. Kruger, “Thermoacoustic computed tomography,” Med. Phys. 26, 1832–1837 (1999).
[CrossRef] [PubMed]

Opt. Lett. (1)

Radiotekh. Elecktron. (1)

D. B. Ivashov, Y. V. Julina, “Potentials of the radioimage reconstruction algorithms,” Radiotekh. Elecktron. 41, 1–22 (1996), in Russian.

Other (5)

I. S. Gradstein, I. M. Ryshik, Tables of Integrals, Sums, Series and Products (Physics-Mathematician State Publishing House, Moscow, 1962), in Russian.

P. A. Bakut, I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P. Tartakovsky, V. V. Shirokov, Problems of the Statistical Theory of Radiolocation (Sovetskoye Radio, Moscow, 1963, 1964), in 2 vols, in Russian.

P. A. Bakut, Y. V. Julina, N. A. Ivanchuk, “Detection of mobile objects,” (Sovetskoye Radio, Moscow, 1980), in Russian.

P. Liu, “Image reconstruction from photoacoustic pressure signals,” in Laser–Tissue Interaction VII, S. L. Jacques, ed., Proc. SPIE2681, 285–296 (1996).
[CrossRef]

R. O. Esenaliev, F. K. Tittel, S. L. Thomsen, B. D. Fornage, C. Stelling, A. A. Karabutov, A. A. Oraevsky, “Laser optoacoustic imaging for breast cancer diagnostics: limit of detection and comparison with x-ray and ultrasound imaging,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 71–82 (1997).

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Figures (7)

Fig. 1
Fig. 1

True image of the three spheres.

Fig. 2
Fig. 2

Summing of signals from three spheres.

Fig. 3
Fig. 3

Result of optimal filtration.

Fig. 4
Fig. 4

Summing of signals from the sphere, placed in a gel.

Fig. 5
Fig. 5

Result of optimal filtration signals from the sphere in a gel.

Fig. 6
Fig. 6

Summing of real signals, obtained in vitro after the surgical operation.

Fig. 7
Fig. 7

Result of optimal filtration signals, obtained in vitro.

Equations (42)

Equations on this page are rendered with MathJax. Learn more.

ynt=Vexp-α|Rn-r||Rn-r| ut-1ν|Rn-r|Ord3r+nt, Rn.
exp-α|Rn-r||Rn-r|=exp-αtνtν.
ynt=exp-αtνtνV ut-1ν|Rn-r|Ord3r+nt, Rn.
xnt=yntνt expαtν.
xnt=V ut-1ν|Rn-r|Ord3r+mt, Rn,
LnP=-n=1N0Txnt-V ut-|Rn-r|/ν×Ord3r2dt.
δLnPδOr*=Zr*-V Cr*, rOrd3r=0.
δOrδOr*=δ3r-r*.
Zr=n=1N0T xntut-|Rn-r|/νdt,
Cr*, r=n=1N0T ut-|Rn-r*|/νut-|Rn-r|/νdt.
en=r*-Rn|r*-Rn| n=1,, N,
|Rn-r|  |Rn-r*| + en·r-r*,n=1,, N.
Zr*-S C2r*-rO2rd2r=0.
O2r=Z Ordz.
C2r-r*=n=1N0T utut-r-r*·endt,
FO2ω=FZω/FC2ω.
O2r=FO2-1ω.
FZω=ΦU|ω|νFZ0ω.
Z0r=n=1N xn|Rn-r|/ν.
ΦUΩ= utexpjΩtdt.
C2r=δ2r.
O2r=n=1N xn|Rn-r|/ν.
ut=exp-α2t2.
ΦUΩ=π/αexp-Ω2/4α2.
CΔ=- utut-Δdt=1απ21/2 exp-α2Δ2/2.
C2r=1α2π0πexp-α2|r|2|cosϕ|2/2ν2dϕ.
C2r=1απ21/2 exp-α|r|/2ν2I0α|r|/2ν2.
FC2ω2πν/α2|ω|.
FO2ω=FZ0ωHω,
Hω=|ω|exp-|ω|2ν2/4α2.
Hω=|ω|exp-|ω|σ2/|ωmax|2.
xt=2π 0Rad0π δt-τ+ρ cosϑ/νρ2dρ sinϑdθ.
xt=πRad2-|νt-τ|2,  if Rad2>|νt-τ|2),
xt=0,  if Rad2|νt-τ|2).
xnt=πRad2-νt-|Rn-Rcent|2,
MaxCorrel = maxrÕ2r1O2r+r1d2r1.
O˜2Rmax = maxrO˜2r.
EquivRad=J/π,
J=S Õ2rd2r.
J1= Õ2rd2r|r-Rmax|EquivRad,
J2= Õ2rd2rr-Rmax>EquivRadr-Rmax2 EquivRad.
Contrast=3J1/J2-1.

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