Abstract

The ideal linear discriminant or Hotelling observer is widely used for detection tasks and image-quality assessment in medical imaging, but it has had little application in other imaging fields. We apply it to detection of planets outside of our solar system with long-exposure images obtained from ground-based or space-based telescopes. The statistical limitations in this problem include Poisson noise arising mainly from the host star, electronic noise in the image detector, randomness or uncertainty in the point-spread function (PSF) of the telescope, and possibly a random background. PSF randomness is reduced but not eliminated by the use of adaptive optics. We concentrate here on the effects of Poisson and electronic noise, but we also show how to extend the calculation to include a random PSF. For the case where the PSF is known exactly, we compare the Hotelling observer to other observers commonly used for planet detection; comparison is based on receiver operating characteristic (ROC) and localization ROC (LROC) curves.

© 2007 Optical Society of America

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  1. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley-Interscience, 2004).
  2. "The extrasolar planets encyclopaedia,"http://exoplanet.eu/.
  3. H. W. Babcock, "The possibility of compensating astronomical seeing," Publ. Astron. Soc. Pac. 65, 229-236 (1953).
    [CrossRef]
  4. R. K. Tyson, Principles of Adaptive Optics (Academic, 1998).
  5. B. A. Macintosh, J. Graham, L. Poyneer, G. Sommargren, J. Wilhelmsen, D. Gavel, S. Jones, P. Kalas, J. P. Lloyd, R. Makidon, S. Olivier, D. Palmer, J. Patience, M. Perrin, S. Severson, A. Sheinis, A. Sivaramakrishnan, M. Troy, and J. K. Wallace, "Extreme adaptive optics planet imager: XAOPI," Proc. SPIE 5170, 272-282 (2003).
    [CrossRef]
  6. J. R. P. Angel, "Ground-based imaging of extrasolar planets using adaptive optics," Nature 368, 203-207 (1994).
    [CrossRef]
  7. H. H. Barrett, K. J. Myers, N. Devaney, and J. C. Dainty, "Objective assessment of image quality. IV. Application to adaptive optics," J. Opt. Soc. Am. A 23, 3080-3105 (2006).
    [CrossRef]
  8. E. Thiébaut and L. Mugnier, "Maximum a posteriori planet detection and characterization with a nulling interferometer," in Direct Imaging of Exoplanets: Science and Techniques, C.Aime and F.Vakili, eds. (Cambridge U. Press, 2006), pp. 547-552.
  9. M. P. Hobson and C. McLachlan, "A Bayesian approach to discrete object detection in astronomical data sets," Mon. Not. R. Astron. Soc. 338, 765-784 (2003).
    [CrossRef]
  10. M. Postman, L. M. Lubin, J. E. Gunn, J. B. Oke, J. G. Hoessel, D. P. Schneider, and J. A. Christensen, "The Palomar distant clusters survey. I. The cluster catalog," Astron. J. 111, 615-641 (1996).
    [CrossRef]
  11. P. Schuecker and H. Böhringer, "Likelihood filter for cluster detection," Astron. Astrophys. 339, 315-326 (1998).
  12. C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. (Springer-Verlag, 2004).
  13. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman & Hall, 1998).
  14. N. J. Kasdin and I. Braems, "Linear and Bayesian planet detection algorithms for the Terrestrial Planet Finder," Astrophys. J. 646, 1260-1274 (2006).
    [CrossRef]
  15. H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990).
    [CrossRef]
  16. H. H. Barrett, J. L. Denny, R. F. Wagner, and K. J. Myers, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J. Opt. Soc. Am. A 12, 834-852 (1995).
    [CrossRef]
  17. H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions," J. Opt. Soc. Am. A 15, 1520-1535 (1998).
    [CrossRef]
  18. J.-P. Véran, F. Rigaut, H. Maître, and D. Rouan, "Estimation of the adaptive optics long-exposure point-spread function using control loop data," J. Opt. Soc. Am. A 14, 3057-3069 (1997).
    [CrossRef]
  19. C. Marois, D. Lafreniére, R. Doyon, B. Macintosh, and D. Nadeau, "Angular differential imaging: a powerful high-contrast imaging technique," Astrophys. J. 641, 556-564 (2006).
    [CrossRef]
  20. R. G. Swensson, "Unified measurement of observer performance in detecting and localizing target objects on images," Med. Phys. 23, 1709-1725 (1996).
    [CrossRef] [PubMed]
  21. E. W. Clarkson, "Estimation ROC curves and their corresponding ideal observers," Proc. SPIE 6515, 651504 (2007).
    [CrossRef]
  22. M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
    [CrossRef]
  23. E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, "Behavior of remnant speckles in an adaptively corrected imaging system," Astrophys. J. Lett. 558, 71-74 (2001).
    [CrossRef]
  24. E. E. Bloemhof, "Suppression of speckle noise by speckle pinning in adaptive optics," Astrophys. J. Lett. 582, 59-62 (2003).
    [CrossRef]
  25. A. Sivaramakrishnan, J. P. Lloyd, P. E. Hodge, and B. A. Macintosh, "Speckle decorrelation and dynamic range in speckle noise-limited imaging," Astrophys. J. Lett. 581, 59-62 (2002).
    [CrossRef]
  26. M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, "The structure of high Strehl ratio point-spread functions," Astrophys. J. 596, 702-712 (2003).
    [CrossRef]
  27. C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. Lett. 612, 85-88 (2004).
    [CrossRef]
  28. R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
    [CrossRef]
  29. C. Marois, R. Doyon, R. Racine, and D. Nadeau, "Efficient speckle noise attenuation in faint companion imaging," Publ. Astron. Soc. Pac. 112, 91-96 (2000).
    [CrossRef]
  30. C. Marois, R. Racine, R. Doyon, D. Lafrenière, and D. Nadeau, "Differential imaging with a multicolor detector assembly: a new exoplanet finder concept," Astrophys. J. Lett. 615, 61-64 (2004).
    [CrossRef]
  31. O. Guyon, "Imaging faint sources within a speckle halo with synchronous interferometric speckle subtraction," Astrophys. J. 615, 562-572 (2004).
    [CrossRef]
  32. R. Lenzen, L. Close, W. Brandner, B. Biller, and M. Hartung, "A novel simultaneous differential imager for the direct imaging of giant planets," Proc. SPIE 5492, 970-977 (2004).
    [CrossRef]
  33. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).
  34. R. D. Fiete, H. H. Barrett, W. E. Smith, and K. J. Myers, "Hotelling trace criterion and its correlation with human-observer performance," J. Opt. Soc. Am. A 4, 945-953 (1987).
    [CrossRef] [PubMed]
  35. W. E. Smith and H. H. Barrett, "Hotelling trace criterion as a figure of merit for the optimization of imaging systems," J. Opt. Soc. Am. A 3, 717-725 (1986).
    [CrossRef]
  36. J. Yao and H. H. Barrett, "Predicting human performance by a channelized Hotelling observer model," Proc. SPIE 1768, 161-168 (1992).
    [CrossRef]
  37. P. Khurd and G. Gindi, "Decision strategies that maximize the area under the LROC curve," IEEE Trans. Med. Imaging 24, 1626-1636 (2005).
    [CrossRef] [PubMed]
  38. M. Freed, P. M. Hinz, M. R. Meyer, N. M. Milton, and M. Lloyd-Hart, "Clio: a 5-μm camera for the detection of giant exoplanets," Proc. SPIE 5492, 1561-1571 (2004).
    [CrossRef]
  39. M. Lloyd-Hart, F. P. Wildi, B. Martin, P. C. McGuire, M. A. Kenworthy, R. L. Johnson, B. C. Fitz-Patrick, G. Z. Angeli, S. M. Miller, III, and J. R. P. Angel, "Adaptive optics for the 6.5-m MMT," Proc. SPIE 4007, 167-174 (2000).
    [CrossRef]
  40. M. A. Kenworthy, P. M. Hinz, J. R. P. Angel, A. N. Heinze, and S. Sivanandam, "Whack-a-speckle: focal plane wavefront sensing in theory and practice with a deformable secondary mirror and 5-micron camera," Proc. SPIE 6272, 1074-1080 (2006).
  41. E. Bertin and S. Arnouts, "SEXTRACTOR: Software for source extraction," Astron. Astrophys., Suppl. Ser. 117, 393-404 (1996).
    [CrossRef]
  42. E. Bertin, "Terapix-SEXTRACTOR," http://terapix.iap.fr/soft/sextractor.
  43. K. Bundy, R. S. Ellis, C. J. Conselice, J. E. Taylor, M. C. Cooper, C. N. A. Willmer, B. J. Weiner, A. L. Coil, K. G. Noeske, and P. R. M. Eisenhardt, "The mass assembly history of field galaxies: detection of an evolving mass limit for star-forming galaxies," Astrophys. J. 651, 120-141 (2006).
    [CrossRef]
  44. N. Caldwell, "Color-magnitude diagrams of resolved stars in Virgo cluster dwarf galaxies," Astrophys. J. 651, 822-834 (2006).
    [CrossRef]
  45. B. E. Cobb, C. D. Bailyn, P. G. van Dokkum, and P. Natarajan, "Could GRB 060614 and its presumed host galaxy be a chance superposition?" Astrophys. J. Lett. 651, L85-L88 (2006).
    [CrossRef]
  46. S. J. Schmidt, A. J. Connolly, and A. M. Hopkins, "The DRaGONS survey: a search for high-redshift radio galaxies and heavily obscured active galactic nuclei," Astrophys. J. 1, 63-78 (2006).
    [CrossRef]
  47. T. Saito, K. Shimasaku, S. Okamura, M. Ouchi, M. Akiyama, and M. Yoshida, "Systematic survey of extended Lyα sources over z∼3-5," Astrophys. J. 648, 54-66 (2006).
    [CrossRef]
  48. R. J. Foley, D. A. Perley, D. Pooley, J. X. Prochaska, J. S. Bloom, W. Li, B. Cobb, H.-W. Chen, G. Aldering, C. Bailyn, C. H. Blake, E. E. Falco, P. J. Green, M. P. Kowalski, S. Perlmutter, K. Roth, and K. Volk, "GRB 050408: a bright gamma-ray burst probing an atypical galactic environment," Astrophys. J. 645, 450-463 (2006).
    [CrossRef]
  49. K. N. Allers, J. E. Kessler-Silacci, L. A. Cieza, and D. T. Jaffe, "Young, low-mass brown dwarfs with mid-infrared excesses," Astrophys. J. 644, 364-377 (2006).
    [CrossRef]

2007 (1)

E. W. Clarkson, "Estimation ROC curves and their corresponding ideal observers," Proc. SPIE 6515, 651504 (2007).
[CrossRef]

2006 (12)

M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

N. J. Kasdin and I. Braems, "Linear and Bayesian planet detection algorithms for the Terrestrial Planet Finder," Astrophys. J. 646, 1260-1274 (2006).
[CrossRef]

C. Marois, D. Lafreniére, R. Doyon, B. Macintosh, and D. Nadeau, "Angular differential imaging: a powerful high-contrast imaging technique," Astrophys. J. 641, 556-564 (2006).
[CrossRef]

M. A. Kenworthy, P. M. Hinz, J. R. P. Angel, A. N. Heinze, and S. Sivanandam, "Whack-a-speckle: focal plane wavefront sensing in theory and practice with a deformable secondary mirror and 5-micron camera," Proc. SPIE 6272, 1074-1080 (2006).

K. Bundy, R. S. Ellis, C. J. Conselice, J. E. Taylor, M. C. Cooper, C. N. A. Willmer, B. J. Weiner, A. L. Coil, K. G. Noeske, and P. R. M. Eisenhardt, "The mass assembly history of field galaxies: detection of an evolving mass limit for star-forming galaxies," Astrophys. J. 651, 120-141 (2006).
[CrossRef]

N. Caldwell, "Color-magnitude diagrams of resolved stars in Virgo cluster dwarf galaxies," Astrophys. J. 651, 822-834 (2006).
[CrossRef]

B. E. Cobb, C. D. Bailyn, P. G. van Dokkum, and P. Natarajan, "Could GRB 060614 and its presumed host galaxy be a chance superposition?" Astrophys. J. Lett. 651, L85-L88 (2006).
[CrossRef]

S. J. Schmidt, A. J. Connolly, and A. M. Hopkins, "The DRaGONS survey: a search for high-redshift radio galaxies and heavily obscured active galactic nuclei," Astrophys. J. 1, 63-78 (2006).
[CrossRef]

T. Saito, K. Shimasaku, S. Okamura, M. Ouchi, M. Akiyama, and M. Yoshida, "Systematic survey of extended Lyα sources over z∼3-5," Astrophys. J. 648, 54-66 (2006).
[CrossRef]

R. J. Foley, D. A. Perley, D. Pooley, J. X. Prochaska, J. S. Bloom, W. Li, B. Cobb, H.-W. Chen, G. Aldering, C. Bailyn, C. H. Blake, E. E. Falco, P. J. Green, M. P. Kowalski, S. Perlmutter, K. Roth, and K. Volk, "GRB 050408: a bright gamma-ray burst probing an atypical galactic environment," Astrophys. J. 645, 450-463 (2006).
[CrossRef]

K. N. Allers, J. E. Kessler-Silacci, L. A. Cieza, and D. T. Jaffe, "Young, low-mass brown dwarfs with mid-infrared excesses," Astrophys. J. 644, 364-377 (2006).
[CrossRef]

H. H. Barrett, K. J. Myers, N. Devaney, and J. C. Dainty, "Objective assessment of image quality. IV. Application to adaptive optics," J. Opt. Soc. Am. A 23, 3080-3105 (2006).
[CrossRef]

2005 (1)

P. Khurd and G. Gindi, "Decision strategies that maximize the area under the LROC curve," IEEE Trans. Med. Imaging 24, 1626-1636 (2005).
[CrossRef] [PubMed]

2004 (5)

M. Freed, P. M. Hinz, M. R. Meyer, N. M. Milton, and M. Lloyd-Hart, "Clio: a 5-μm camera for the detection of giant exoplanets," Proc. SPIE 5492, 1561-1571 (2004).
[CrossRef]

C. Marois, R. Racine, R. Doyon, D. Lafrenière, and D. Nadeau, "Differential imaging with a multicolor detector assembly: a new exoplanet finder concept," Astrophys. J. Lett. 615, 61-64 (2004).
[CrossRef]

O. Guyon, "Imaging faint sources within a speckle halo with synchronous interferometric speckle subtraction," Astrophys. J. 615, 562-572 (2004).
[CrossRef]

R. Lenzen, L. Close, W. Brandner, B. Biller, and M. Hartung, "A novel simultaneous differential imager for the direct imaging of giant planets," Proc. SPIE 5492, 970-977 (2004).
[CrossRef]

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. Lett. 612, 85-88 (2004).
[CrossRef]

2003 (4)

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, "The structure of high Strehl ratio point-spread functions," Astrophys. J. 596, 702-712 (2003).
[CrossRef]

E. E. Bloemhof, "Suppression of speckle noise by speckle pinning in adaptive optics," Astrophys. J. Lett. 582, 59-62 (2003).
[CrossRef]

B. A. Macintosh, J. Graham, L. Poyneer, G. Sommargren, J. Wilhelmsen, D. Gavel, S. Jones, P. Kalas, J. P. Lloyd, R. Makidon, S. Olivier, D. Palmer, J. Patience, M. Perrin, S. Severson, A. Sheinis, A. Sivaramakrishnan, M. Troy, and J. K. Wallace, "Extreme adaptive optics planet imager: XAOPI," Proc. SPIE 5170, 272-282 (2003).
[CrossRef]

M. P. Hobson and C. McLachlan, "A Bayesian approach to discrete object detection in astronomical data sets," Mon. Not. R. Astron. Soc. 338, 765-784 (2003).
[CrossRef]

2002 (1)

A. Sivaramakrishnan, J. P. Lloyd, P. E. Hodge, and B. A. Macintosh, "Speckle decorrelation and dynamic range in speckle noise-limited imaging," Astrophys. J. Lett. 581, 59-62 (2002).
[CrossRef]

2001 (1)

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, "Behavior of remnant speckles in an adaptively corrected imaging system," Astrophys. J. Lett. 558, 71-74 (2001).
[CrossRef]

2000 (2)

C. Marois, R. Doyon, R. Racine, and D. Nadeau, "Efficient speckle noise attenuation in faint companion imaging," Publ. Astron. Soc. Pac. 112, 91-96 (2000).
[CrossRef]

M. Lloyd-Hart, F. P. Wildi, B. Martin, P. C. McGuire, M. A. Kenworthy, R. L. Johnson, B. C. Fitz-Patrick, G. Z. Angeli, S. M. Miller, III, and J. R. P. Angel, "Adaptive optics for the 6.5-m MMT," Proc. SPIE 4007, 167-174 (2000).
[CrossRef]

1999 (1)

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

1998 (2)

1997 (1)

1996 (3)

E. Bertin and S. Arnouts, "SEXTRACTOR: Software for source extraction," Astron. Astrophys., Suppl. Ser. 117, 393-404 (1996).
[CrossRef]

R. G. Swensson, "Unified measurement of observer performance in detecting and localizing target objects on images," Med. Phys. 23, 1709-1725 (1996).
[CrossRef] [PubMed]

M. Postman, L. M. Lubin, J. E. Gunn, J. B. Oke, J. G. Hoessel, D. P. Schneider, and J. A. Christensen, "The Palomar distant clusters survey. I. The cluster catalog," Astron. J. 111, 615-641 (1996).
[CrossRef]

1995 (1)

1994 (1)

J. R. P. Angel, "Ground-based imaging of extrasolar planets using adaptive optics," Nature 368, 203-207 (1994).
[CrossRef]

1992 (1)

J. Yao and H. H. Barrett, "Predicting human performance by a channelized Hotelling observer model," Proc. SPIE 1768, 161-168 (1992).
[CrossRef]

1990 (1)

1987 (1)

1986 (1)

1953 (1)

H. W. Babcock, "The possibility of compensating astronomical seeing," Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[CrossRef]

Astron. Astrophys. (1)

P. Schuecker and H. Böhringer, "Likelihood filter for cluster detection," Astron. Astrophys. 339, 315-326 (1998).

Astron. Astrophys., Suppl. Ser. (1)

E. Bertin and S. Arnouts, "SEXTRACTOR: Software for source extraction," Astron. Astrophys., Suppl. Ser. 117, 393-404 (1996).
[CrossRef]

Astron. J. (1)

M. Postman, L. M. Lubin, J. E. Gunn, J. B. Oke, J. G. Hoessel, D. P. Schneider, and J. A. Christensen, "The Palomar distant clusters survey. I. The cluster catalog," Astron. J. 111, 615-641 (1996).
[CrossRef]

Astrophys. J. (11)

K. Bundy, R. S. Ellis, C. J. Conselice, J. E. Taylor, M. C. Cooper, C. N. A. Willmer, B. J. Weiner, A. L. Coil, K. G. Noeske, and P. R. M. Eisenhardt, "The mass assembly history of field galaxies: detection of an evolving mass limit for star-forming galaxies," Astrophys. J. 651, 120-141 (2006).
[CrossRef]

N. Caldwell, "Color-magnitude diagrams of resolved stars in Virgo cluster dwarf galaxies," Astrophys. J. 651, 822-834 (2006).
[CrossRef]

S. J. Schmidt, A. J. Connolly, and A. M. Hopkins, "The DRaGONS survey: a search for high-redshift radio galaxies and heavily obscured active galactic nuclei," Astrophys. J. 1, 63-78 (2006).
[CrossRef]

T. Saito, K. Shimasaku, S. Okamura, M. Ouchi, M. Akiyama, and M. Yoshida, "Systematic survey of extended Lyα sources over z∼3-5," Astrophys. J. 648, 54-66 (2006).
[CrossRef]

R. J. Foley, D. A. Perley, D. Pooley, J. X. Prochaska, J. S. Bloom, W. Li, B. Cobb, H.-W. Chen, G. Aldering, C. Bailyn, C. H. Blake, E. E. Falco, P. J. Green, M. P. Kowalski, S. Perlmutter, K. Roth, and K. Volk, "GRB 050408: a bright gamma-ray burst probing an atypical galactic environment," Astrophys. J. 645, 450-463 (2006).
[CrossRef]

K. N. Allers, J. E. Kessler-Silacci, L. A. Cieza, and D. T. Jaffe, "Young, low-mass brown dwarfs with mid-infrared excesses," Astrophys. J. 644, 364-377 (2006).
[CrossRef]

N. J. Kasdin and I. Braems, "Linear and Bayesian planet detection algorithms for the Terrestrial Planet Finder," Astrophys. J. 646, 1260-1274 (2006).
[CrossRef]

M. P. Fitzgerald and J. R. Graham, "Speckle statistics in adaptively corrected images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

M. D. Perrin, A. Sivaramakrishnan, R. B. Makidon, B. R. Oppenheimer, and J. R. Graham, "The structure of high Strehl ratio point-spread functions," Astrophys. J. 596, 702-712 (2003).
[CrossRef]

O. Guyon, "Imaging faint sources within a speckle halo with synchronous interferometric speckle subtraction," Astrophys. J. 615, 562-572 (2004).
[CrossRef]

C. Marois, D. Lafreniére, R. Doyon, B. Macintosh, and D. Nadeau, "Angular differential imaging: a powerful high-contrast imaging technique," Astrophys. J. 641, 556-564 (2006).
[CrossRef]

Astrophys. J. Lett. (6)

C. Marois, R. Racine, R. Doyon, D. Lafrenière, and D. Nadeau, "Differential imaging with a multicolor detector assembly: a new exoplanet finder concept," Astrophys. J. Lett. 615, 61-64 (2004).
[CrossRef]

C. Aime and R. Soummer, "The usefulness and limits of coronagraphy in the presence of pinned speckles," Astrophys. J. Lett. 612, 85-88 (2004).
[CrossRef]

E. E. Bloemhof, R. G. Dekany, M. Troy, and B. R. Oppenheimer, "Behavior of remnant speckles in an adaptively corrected imaging system," Astrophys. J. Lett. 558, 71-74 (2001).
[CrossRef]

E. E. Bloemhof, "Suppression of speckle noise by speckle pinning in adaptive optics," Astrophys. J. Lett. 582, 59-62 (2003).
[CrossRef]

A. Sivaramakrishnan, J. P. Lloyd, P. E. Hodge, and B. A. Macintosh, "Speckle decorrelation and dynamic range in speckle noise-limited imaging," Astrophys. J. Lett. 581, 59-62 (2002).
[CrossRef]

B. E. Cobb, C. D. Bailyn, P. G. van Dokkum, and P. Natarajan, "Could GRB 060614 and its presumed host galaxy be a chance superposition?" Astrophys. J. Lett. 651, L85-L88 (2006).
[CrossRef]

IEEE Trans. Med. Imaging (1)

P. Khurd and G. Gindi, "Decision strategies that maximize the area under the LROC curve," IEEE Trans. Med. Imaging 24, 1626-1636 (2005).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (7)

Med. Phys. (1)

R. G. Swensson, "Unified measurement of observer performance in detecting and localizing target objects on images," Med. Phys. 23, 1709-1725 (1996).
[CrossRef] [PubMed]

Mon. Not. R. Astron. Soc. (1)

M. P. Hobson and C. McLachlan, "A Bayesian approach to discrete object detection in astronomical data sets," Mon. Not. R. Astron. Soc. 338, 765-784 (2003).
[CrossRef]

Nature (1)

J. R. P. Angel, "Ground-based imaging of extrasolar planets using adaptive optics," Nature 368, 203-207 (1994).
[CrossRef]

Proc. SPIE (7)

B. A. Macintosh, J. Graham, L. Poyneer, G. Sommargren, J. Wilhelmsen, D. Gavel, S. Jones, P. Kalas, J. P. Lloyd, R. Makidon, S. Olivier, D. Palmer, J. Patience, M. Perrin, S. Severson, A. Sheinis, A. Sivaramakrishnan, M. Troy, and J. K. Wallace, "Extreme adaptive optics planet imager: XAOPI," Proc. SPIE 5170, 272-282 (2003).
[CrossRef]

E. W. Clarkson, "Estimation ROC curves and their corresponding ideal observers," Proc. SPIE 6515, 651504 (2007).
[CrossRef]

R. Lenzen, L. Close, W. Brandner, B. Biller, and M. Hartung, "A novel simultaneous differential imager for the direct imaging of giant planets," Proc. SPIE 5492, 970-977 (2004).
[CrossRef]

M. Freed, P. M. Hinz, M. R. Meyer, N. M. Milton, and M. Lloyd-Hart, "Clio: a 5-μm camera for the detection of giant exoplanets," Proc. SPIE 5492, 1561-1571 (2004).
[CrossRef]

M. Lloyd-Hart, F. P. Wildi, B. Martin, P. C. McGuire, M. A. Kenworthy, R. L. Johnson, B. C. Fitz-Patrick, G. Z. Angeli, S. M. Miller, III, and J. R. P. Angel, "Adaptive optics for the 6.5-m MMT," Proc. SPIE 4007, 167-174 (2000).
[CrossRef]

M. A. Kenworthy, P. M. Hinz, J. R. P. Angel, A. N. Heinze, and S. Sivanandam, "Whack-a-speckle: focal plane wavefront sensing in theory and practice with a deformable secondary mirror and 5-micron camera," Proc. SPIE 6272, 1074-1080 (2006).

J. Yao and H. H. Barrett, "Predicting human performance by a channelized Hotelling observer model," Proc. SPIE 1768, 161-168 (1992).
[CrossRef]

Publ. Astron. Soc. Pac. (3)

R. Racine, G. A. H. Walker, D. Nadeau, R. Doyon, and C. Marois, "Speckle noise and the detection of faint companions," Publ. Astron. Soc. Pac. 111, 587-594 (1999).
[CrossRef]

C. Marois, R. Doyon, R. Racine, and D. Nadeau, "Efficient speckle noise attenuation in faint companion imaging," Publ. Astron. Soc. Pac. 112, 91-96 (2000).
[CrossRef]

H. W. Babcock, "The possibility of compensating astronomical seeing," Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[CrossRef]

Other (8)

R. K. Tyson, Principles of Adaptive Optics (Academic, 1998).

A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th ed. (McGraw-Hill, 2002).

E. Thiébaut and L. Mugnier, "Maximum a posteriori planet detection and characterization with a nulling interferometer," in Direct Imaging of Exoplanets: Science and Techniques, C.Aime and F.Vakili, eds. (Cambridge U. Press, 2006), pp. 547-552.

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd ed. (Springer-Verlag, 2004).

W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, Markov Chain Monte Carlo in Practice (Chapman & Hall, 1998).

E. Bertin, "Terapix-SEXTRACTOR," http://terapix.iap.fr/soft/sextractor.

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley-Interscience, 2004).

"The extrasolar planets encyclopaedia,"http://exoplanet.eu/.

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Figures (7)

Fig. 1
Fig. 1

Configuration of an adaptive optics telescope.

Fig. 2
Fig. 2

Log-scale simulation of (a) image g ¯ 0 of the star and (b) image g ¯ 1 of the star and the planet. The intensity of the planet was set to a = 10 6 e only in this figure and to make the planet location visible.

Fig. 3
Fig. 3

ROC curves for the simulated data.

Fig. 4
Fig. 4

Images used for the simulated data case and unknown r p : (a) locations of the planets for the test with the simulated image (Airy disk) and (b) test locations.

Fig. 5
Fig. 5

LROC curves for simulated data ( A = 10 7 e , a = 20 e , b m = 100 e , σ m = 10 e ).

Fig. 6
Fig. 6

Images used for the real data case and unknown r p : (a) real image g ¯ 0 of the star (plotted on logarithmic scale), (b) locations of the planets, (c) test locations.

Fig. 7
Fig. 7

LROC curves for real data ( A = 3,066,000 e , a = 1533 e , b m = 250,680 e , σ m = 700 e ).

Tables (4)

Tables Icon

Table 1 Comparison between t Hot ( g r p ) and t sub ( k ) ( g r p ) for Simulated Data and Known r p

Tables Icon

Table 2 Comparison between t Hot ( g ) and t sub ( k ) ( g ) for Simulated Data and Unknown r p

Tables Icon

Table 3 SEXTRACTOR Parameters

Tables Icon

Table 4 Comparison between t Hot ( g ) , t sub ( k ) ( g ) , and SEXTRACTOR for Real Data and Unknown r p

Equations (32)

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K G = K ̿ G noise + K ¯ G ¯ PSF + K G ̿ obj ,
K ̿ G noise = [ G G ¯ ] [ G G ¯ ] T G P , F P F F ,
K ¯ G ¯ PSF = [ G ¯ G ̿ ] [ G ¯ G ̿ ] T P F F ,
K G ̿ obj = [ G ̿ G ] [ G ̿ G ] T F ,
H 0 : g = g ¯ 0 + n ,
g ¯ 0 , m = A h m ( r ) + b m ,
g ¯ 1 , m = A h m ( r ) + a h m ( r p ) + b m ,
pr ( g H 0 ) = [ 1 ( 2 π ) M det ( K g ) ] 1 / 2 exp [ 1 2 ( g g ¯ 0 ) T K g 1 ( g g ¯ 0 ) ] ,
pr ( g H 1 , r p ) = [ 1 ( 2 π ) M det ( K g ) ] 1 / 2 exp [ 1 2 ( g g ¯ 0 s r p ) T K g 1 ( g g ¯ 0 s r p ) ] ,
[ K g ] m , m = [ A h m ( r ) + b m + σ m 2 ] δ m , m ,
λ ( g r p ) = ln [ Λ ( g r p ) ]
= 1 2 ( g g ¯ 0 ) T K g 1 ( g g ¯ 0 ) 1 2 ( g g ¯ 0 s r p ) T K g 1 ( g g ¯ 0 s r p ) .
λ ( g r p ) = 1 2 [ g T K g 1 s r p + g 0 ¯ T K g 1 s r p s r p T K g 1 g + s r p T K g 1 g ¯ 0 + s r p T K g 1 s r p T ]
= 1 2 [ 2 s r p T K g 1 g ¯ 0 2 s r p T K g 1 g + s r p T K g 1 s r p T ] .
λ ( g r p ) = t Hot ( g r p ) = w T g ,
w = K g 1 s r p
t Hot ( g r p ) = m = 1 M w m g m = m = 1 M a h m ( r p ) A h m ( r ) + b m + σ m 2 g m .
Λ ( g ) = max r p T Λ ( g r p ) = max r p T pr ( g H 1 , r p ) pr ( g H 0 ) ,
r ̂ p = arg max r p T Λ ( g r p ) .
λ ( g ) = ln [ Λ ( g ) ]
= max r p T [ 1 2 ( g g ¯ 0 ) T K g 1 ( g g ¯ 0 ) 1 2 ( g g ¯ 0 s r p ) T K g 1 ( g g ¯ 0 s r p ) ] .
λ ( g ) g ¯ = max r p T [ 1 2 ( g T K g 1 s r p + g 0 ¯ T K g 1 s r p s r p T K g 1 g + s r p T K g 1 g ¯ 0 + s r p T K g 1 s r p T ) ]
= max r p T [ 1 2 ( 2 s r p T K g 1 g ¯ 0 2 s r p T K g 1 g + s r p T K g 1 s r p T ) ] .
t Hot ( g ) = max r p T m = 1 M a h m ( r p ) A h m ( r ) + b m + σ m 2 [ g m g ¯ 0 , m 1 2 a h m ( r p ) ] ;
r ̂ p = arg max r p T m = 1 M a h m ( r p ) A h m ( r ) + b m + σ m 2 [ g m g ¯ 0 , m 1 2 a h m ( r p ) ] .
FPF ( τ ) = { i such that t 0 , i > τ , i = 1 , , 10,000 } 10,000 ,
TPF ( τ ) = { i such that t 1 , i > τ , i = 1 , , 10,000 } 10,000 ,
t sub ( k ) ( g r p ) = m N ( r p , k ) [ g m b m A h m ( r ) ] .
d A ( t 0 , t 1 ) = t 1 , i i t 0 , i i 1 2 σ t 0 , i 2 + 1 2 σ t 1 , i 2 ,
d A ( AUC ) = 2 erf 1 ( 2 AUC 1 ) ,
t sub ( k ) ( g ) = max r p T m N ( r p , k ) [ g m b m A h m ( r ) ] ,
r ̂ p = arg max r p T m N ( r p , k ) [ g m b m A h m ( r ) ] .

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