Abstract

Reference structure tomography (RST) uses multidimensional modulations to encode mappings between radiating objects and measurements. RST may be used to image source-density distributions, estimate source parameters, or classify sources. The RST paradigm permits scan-free multidimensional imaging, data-efficient and computation-efficient source analysis, and direct abstraction of physical features. We introduce the basic concepts of RST and illustrate the use of RST for multidimensional imaging based on a geometric radiation model.

© 2004 Optical Society of America

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    [CrossRef] [PubMed]
  36. U. Gopinathan, D. J. Brady, N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express 11, 2142–2152 (2003).
    [CrossRef] [PubMed]
  37. A. Sinha, D. J. Brady, “Size and shape recognition using measurement statistics and random 3D reference structures,” Opt. Express 11, 2606–2618 (2003).
    [CrossRef] [PubMed]
  38. R. Tsai, P. Burchard, L.-T. Cheng, S. Osher, G. Sapiro, “Dynamic visibility in a level set-based implicit frame work,” , UCLA Computational and Applied Mathematics Reports (University of California, Los Angeles, Los Angeles, Calif., 2002).

2003

2002

2001

2000

1999

R. W. Grosse-Kunstleve, A. T. Brunger, “A highly automated heavy-atom search procedure for macromolecular structures,” Acta Crystallogr. D 55, 1568–1577 (1999).
[CrossRef] [PubMed]

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284, 2164–2166 (1999).
[CrossRef] [PubMed]

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

G. Barbastathis, M. Balberg, D. J. Brady, “Confocal microscopy with a volume holographic filter,” Opt. Lett. 24, 811–813 (1999).
[CrossRef]

D. L. Marks, R. A. Stack, D. J. Brady, “Three-dimensional coherence imaging in the Fresnel domain,” Appl. Opt. 38, 1332–1342 (1999).
[CrossRef]

1998

1995

G. K. Skinner, T. J. Ponman, “Inverse problems in x-ray and gamma-ray astronomical imaging,” Inverse Probl. 11, 655–676 (1995).
[CrossRef]

M. Matsuoka, Y. Kohmura, “A new concept of x-ray microscopes with a coded-aperture imaging mask,” Jpn. J. Appl. Phys., Part 1 34, 372–373 (1995).
[CrossRef]

1992

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

1991

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

1990

W. Denk, J. H. Strickler, W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

1987

T. V. Ohalloran, S. J. Lippard, T. J. Richmond, A. Klug, “Multiple heavy-atom reagents for macromolecular x-ray structure determination—application to the nucleosome core particle,” J. Mol. Biol. 194, 705–712 (1987).
[CrossRef]

K. A. Nugent, “Coded-aperture imaging—a Fourier space analysis,” Appl. Opt. 26, 563–569 (1987).
[CrossRef] [PubMed]

1984

G. K. Skinner, “Imaging with coded-aperture masks,” Nucl. Instrum. Methods Phys. Res. Sect. A 221, 33–40 (1984).
[CrossRef]

1983

1982

G. Indebetouw, W. P. Shing, “Scanning optical reconstruction of coded aperture images,” Appl. Phys. B Photophys. Laser Chem. 27, 69–76 (1982).
[CrossRef]

1980

1978

Adleman, J. R.

Balberg, M.

Barbastathis, G.

Betzig, E.

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

Brady, D. J.

A. Sinha, D. J. Brady, “Size and shape recognition using measurement statistics and random 3D reference structures,” Opt. Express 11, 2606–2618 (2003).
[CrossRef] [PubMed]

P. Potuluri, U. Gopinathan, J. R. Adleman, D. J. Brady, “Lensless sensor system using a reference structure,” Opt. Express 11, 965–974 (2003).
[CrossRef] [PubMed]

U. Gopinathan, D. J. Brady, N. P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express 11, 2142–2152 (2003).
[CrossRef] [PubMed]

P. Potuluri, M. Xu, D. J. Brady, “Imaging with random 3D reference structures,” Opt. Express 11, 2134–2141 (2003).
[CrossRef] [PubMed]

P. Potuluri, M. R. Fetterman, D. J. Brady, “High-depth-of-field microscopic imaging using an interferometric camera,” Opt. Express 8, 624–630 (2001).
[CrossRef] [PubMed]

D. L. Marks, R. Stack, A. J. Johnson, D. J. Brady, D. C. Munson, “Cone-beam tomography with a digital camera,” Appl. Opt. 40, 1795–1805 (2001).
[CrossRef]

M. R. Fetterman, E. Tan, L. Ying, R. A. Stack, D. L. Marks, S. Feller, E. Cull, J. M. Sullivan, D. C. Munson, S. T. Thoroddsen, D. J. Brady, “Tomographic imaging of foam,” Opt. Express 7, 186–197 (2000).
[CrossRef] [PubMed]

G. Barbastathis, M. Balberg, D. J. Brady, “Confocal microscopy with a volume holographic filter,” Opt. Lett. 24, 811–813 (1999).
[CrossRef]

D. L. Marks, R. A. Stack, D. J. Brady, “Three-dimensional coherence imaging in the Fresnel domain,” Appl. Opt. 38, 1332–1342 (1999).
[CrossRef]

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284, 2164–2166 (1999).
[CrossRef] [PubMed]

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

D. L. Marks, D. J. Brady, “Three-dimensional source reconstruction with a scanned pinhole camera,” Opt. Lett. 23, 820–822 (1998).
[CrossRef]

Brady, R. B.

D. L. Marks, R. A. Stack, D. J. Brady, D. C. Munson, R. B. Brady, “Visible cone-beam tomography with a lensless interferometric camera,” Science 284, 2164–2166 (1999).
[CrossRef] [PubMed]

Bricogne, G.

E. de la Fortelle, G. Bricogne, “Maximum-likelihood, heavy-atom parameter refinement for multiple isomorphous replacement and multiwavelength anomalous diffraction methods,” in Macromolecular Crystallography, Part A, Vol. 276 of Methods in Enzymology, J. Abelson, ed. (Academic, San Diego, Calif., 1997), pp. 472–494.

Brown, D. G.

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

Brunger, A. T.

R. W. Grosse-Kunstleve, A. T. Brunger, “A highly automated heavy-atom search procedure for macromolecular structures,” Acta Crystallogr. D 55, 1568–1577 (1999).
[CrossRef] [PubMed]

Burchard, P.

R. Tsai, P. Burchard, L.-T. Cheng, S. Osher, G. Sapiro, “Dynamic visibility in a level set-based implicit frame work,” , UCLA Computational and Applied Mathematics Reports (University of California, Los Angeles, Los Angeles, Calif., 2002).

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Cheng, L.-T.

R. Tsai, P. Burchard, L.-T. Cheng, S. Osher, G. Sapiro, “Dynamic visibility in a level set-based implicit frame work,” , UCLA Computational and Applied Mathematics Reports (University of California, Los Angeles, Los Angeles, Calif., 2002).

Conn, P. M.

P. M. Conn, Confocal Microscopy, Vol. 307 of Methods in Enzymology, J. Abelson, ed. (Academic, San Diego, Calif., 1999).

Corle, T. R.

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, San Diego, Calif., 1996).

Cull, E.

de la Fortelle, E.

E. de la Fortelle, G. Bricogne, “Maximum-likelihood, heavy-atom parameter refinement for multiple isomorphous replacement and multiwavelength anomalous diffraction methods,” in Macromolecular Crystallography, Part A, Vol. 276 of Methods in Enzymology, J. Abelson, ed. (Academic, San Diego, Calif., 1997), pp. 472–494.

Denk, W.

W. Denk, J. H. Strickler, W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Feller, S.

Fenimore, E. E.

Fetterman, M. R.

Finn, P. L.

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gardner, R.

R. Gardner, Geometric Tomography (Cambridge U. Press, Cambridge, UK, 1995).

Gopinathan, U.

Gourlay, A. R.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Grosse-Kunstleve, R. W.

R. W. Grosse-Kunstleve, A. T. Brunger, “A highly automated heavy-atom search procedure for macromolecular structures,” Acta Crystallogr. D 55, 1568–1577 (1999).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Heinemann, U.

U. Heinemann, G. Illing, H. Oschkinat, “High-throughput three-dimensional protein structure determination,” Curr. Opin. Biotechnol. 12, 348–354 (2001).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Illing, G.

U. Heinemann, G. Illing, H. Oschkinat, “High-throughput three-dimensional protein structure determination,” Curr. Opin. Biotechnol. 12, 348–354 (2001).
[CrossRef] [PubMed]

Indebetouw, G.

G. Indebetouw, W. P. Shing, “Scanning optical reconstruction of coded aperture images,” Appl. Phys. B Photophys. Laser Chem. 27, 69–76 (1982).
[CrossRef]

Johnson, A. J.

Kak, A. C.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, Piscataway, N.J., 1988).

Kino, G. S.

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, San Diego, Calif., 1996).

Klug, A.

T. V. Ohalloran, S. J. Lippard, T. J. Richmond, A. Klug, “Multiple heavy-atom reagents for macromolecular x-ray structure determination—application to the nucleosome core particle,” J. Mol. Biol. 194, 705–712 (1987).
[CrossRef]

Kohmura, Y.

M. Matsuoka, Y. Kohmura, “A new concept of x-ray microscopes with a coded-aperture imaging mask,” Jpn. J. Appl. Phys., Part 1 34, 372–373 (1995).
[CrossRef]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Lippard, S. J.

T. V. Ohalloran, S. J. Lippard, T. J. Richmond, A. Klug, “Multiple heavy-atom reagents for macromolecular x-ray structure determination—application to the nucleosome core particle,” J. Mol. Biol. 194, 705–712 (1987).
[CrossRef]

Liu, W. H.

Marks, D. L.

Matsuoka, M.

M. Matsuoka, Y. Kohmura, “A new concept of x-ray microscopes with a coded-aperture imaging mask,” Jpn. J. Appl. Phys., Part 1 34, 372–373 (1995).
[CrossRef]

Metz, C. E.

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

Munson, D. C.

Nugent, K. A.

Ohalloran, T. V.

T. V. Ohalloran, S. J. Lippard, T. J. Richmond, A. Klug, “Multiple heavy-atom reagents for macromolecular x-ray structure determination—application to the nucleosome core particle,” J. Mol. Biol. 194, 705–712 (1987).
[CrossRef]

Oschkinat, H.

U. Heinemann, G. Illing, H. Oschkinat, “High-throughput three-dimensional protein structure determination,” Curr. Opin. Biotechnol. 12, 348–354 (2001).
[CrossRef] [PubMed]

Osher, S.

R. Tsai, P. Burchard, L.-T. Cheng, S. Osher, G. Sapiro, “Dynamic visibility in a level set-based implicit frame work,” , UCLA Computational and Applied Mathematics Reports (University of California, Los Angeles, Los Angeles, Calif., 2002).

Pitsianis, N. P.

Ponman, T. J.

G. K. Skinner, T. J. Ponman, “Inverse problems in x-ray and gamma-ray astronomical imaging,” Inverse Probl. 11, 655–676 (1995).
[CrossRef]

Potuluri, P.

Psaltis, D.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Richmond, T. J.

T. V. Ohalloran, S. J. Lippard, T. J. Richmond, A. Klug, “Multiple heavy-atom reagents for macromolecular x-ray structure determination—application to the nucleosome core particle,” J. Mol. Biol. 194, 705–712 (1987).
[CrossRef]

Sapiro, G.

R. Tsai, P. Burchard, L.-T. Cheng, S. Osher, G. Sapiro, “Dynamic visibility in a level set-based implicit frame work,” , UCLA Computational and Applied Mathematics Reports (University of California, Los Angeles, Los Angeles, Calif., 2002).

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Seltzer, S. M.

Sheppard, C.

C. Sheppard, D. Shotton, “Confocal Laser Scanning Microscopy,” No. 38 of Royal Microscopical Society Microscopy Handbooks Series (Oxford BIOS Scientific, New York, 1997).

Shing, W. P.

G. Indebetouw, W. P. Shing, “Scanning optical reconstruction of coded aperture images,” Appl. Phys. B Photophys. Laser Chem. 27, 69–76 (1982).
[CrossRef]

Shotton, D.

C. Sheppard, D. Shotton, “Confocal Laser Scanning Microscopy,” No. 38 of Royal Microscopical Society Microscopy Handbooks Series (Oxford BIOS Scientific, New York, 1997).

Sinha, A.

Skinner, G. K.

G. K. Skinner, T. J. Ponman, “Inverse problems in x-ray and gamma-ray astronomical imaging,” Inverse Probl. 11, 655–676 (1995).
[CrossRef]

G. K. Skinner, “Imaging with coded-aperture masks,” Nucl. Instrum. Methods Phys. Res. Sect. A 221, 33–40 (1984).
[CrossRef]

Slaney, M.

A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, Piscataway, N.J., 1988).

Stack, R.

Stack, R. A.

Stephen, J. B.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Strickler, J. H.

W. Denk, J. H. Strickler, W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Sullivan, J. M.

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef] [PubMed]

Tan, E.

Thoroddsen, S. T.

Trombka, J. I.

Tsai, R.

R. Tsai, P. Burchard, L.-T. Cheng, S. Osher, G. Sapiro, “Dynamic visibility in a level set-based implicit frame work,” , UCLA Computational and Applied Mathematics Reports (University of California, Los Angeles, Los Angeles, Calif., 2002).

Wagner, R. F.

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

Webb, W. W.

W. Denk, J. H. Strickler, W. W. Webb, “2-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Weiner, J. S.

E. Betzig, P. L. Finn, J. S. Weiner, “Combined shear force and near-field scanning optical microscopy,” Appl. Phys. Lett. 60, 2484–2486 (1992).
[CrossRef]

Wilson, T.

T. Wilson, Confocal Microscopy (Academic, New York, 1990).

Xu, M.

Yin, L. I.

Ying, L.

Acta Crystallogr. D

R. W. Grosse-Kunstleve, A. T. Brunger, “A highly automated heavy-atom search procedure for macromolecular structures,” Acta Crystallogr. D 55, 1568–1577 (1999).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. B Photophys. Laser Chem.

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Figures (6)

Fig. 1
Fig. 1

Visibility modulated by an opaque geometric reference structure, Φ(r).

Fig. 2
Fig. 2

Object domain, signature-cell segmentation by an opaque geometric reference structure.

Fig. 3
Fig. 3

Sample two-dimensional object domain partition induced by a reference structure.

Fig. 4
Fig. 4

Pictorial representation of the two-dimensional cubic Daubechies wavelet basis of cardinality 64. The intensity of each image has been enhanced to utilize the full gray scale and is not consistent from image to image.

Fig. 5
Fig. 5

Simulated band-limited object-density function used in our reconstruction; on the left is the original, in the middle is the representation in the Daubechies cubic wavelet basis, and the resulting reconstruction is on the right.

Fig. 6
Fig. 6

Detail from the clown image used in our reconstruction; on the left is the original, in the middle is the representation in the Daubechies cubic wavelet basis, and the resulting reconstruction is on the right.

Equations (10)

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

v(r1, r2)=exp-r1r2Φ(r)dr.
m(ri)=R3v(ri, r)f(r)dr,
mi=S2ds0v(ri, ri+αs)f(ri+αs)α2dα,
mi=jχijvjfj,
fj=1vjCjf(r)dr
m=XDwf,
m=XDwBc,
mi=Ωhi(r)f(r)dr=Ωhi(r)j=1ncjBj(r)dr=j=1ncjΩhi(r)Bj(r)dr,
0DwBceTm.
(1-τ)mXDwBc(1+τ)m,

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