Abstract

Detection of signals in noisy images is necessary in many applications, including astronomy and medical imaging. The optimal linear observer for performing a detection task, called the Hotelling observer in the medical literature, can be regarded as a generalization of the familiar prewhitening matched filter. Performance on the detection task is limited by randomness in the image data, which stems from randomness in the object, randomness in the imaging system, and randomness in the detector outputs due to photon and readout noise, and the Hotelling observer accounts for all of these effects in an optimal way. If multiple temporal frames of images are acquired, the resulting data set is a spatio-temporal random process, and the Hotelling observer becomes a spatio-temporal linear operator. This paper discusses the theory of the spatio-temporal Hotelling observer and estimation of the required spatio-temporal covariance matrices. It also presents a parallel implementation of the observer on a cluster of Sony PLAYSTATION 3 gaming consoles. As an example, we consider the use of the spatio-temporal Hotelling observer for exoplanet detection.

© 2009 Optical Society of America

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2007 (5)

2006 (5)

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]

M. P. Fitzgerald and J. R. Graham, "Speckle Statistics in Adaptively Corrected Images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

B. D. Gallas, "One-shot estimate of MRMC Variance: AUC," Acad. Radiol. 13, 353-362 (2006).
[CrossRef] [PubMed]

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (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]

2005 (2)

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
[CrossRef]

2004 (1)

S. H. Park, J. M. Goo, and C.-H. Jo, "Receiver Operating Characteristic (ROC) Curve: Practical Review for Radiologists," Korean J. Radiol. 5, 11-18 (2004).
[CrossRef] [PubMed]

2003 (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]

2002 (1)

M. Tamura, "Extra-solar Planet Detection," Viva Origino 30, 157-161 (2002).

2001 (1)

1998 (1)

1996 (1)

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

1994 (1)

1986 (1)

D. J. Tylavsky and G. R. L. Sohie, "Generalization of the Matrix Inversion Lemma," Proc. IEEE 74, 1050-1052 (1986).
[CrossRef]

1985 (1)

1982 (1)

J. A. Hanley and B. J. McNeil, "The Meaning and use of the Area under a Receiver Operating Characteristic (ROC) Curve," Radiology 143, 29-36 (1982).
[PubMed]

1981 (1)

H. V. Henderson and S. R. Searle, "On Deriving the Inverse of a Sum of Matrices," SIAM Rev. 23, 53-60 (1981).
[CrossRef]

1979 (1)

D. W. Hughes, "Nonsolar Planets and Their Detection," Nature 279, 579 (1979).
[CrossRef]

1975 (1)

S. J. Starr, C. E. Metz, L. B. Lusted, and D. J. Goodenough, "Visual detection and localization of radiographic images," Radiology 116, 533-538 (1975).
[PubMed]

1965 (1)

D. L. Fried, "Statistics of a Geometric Representation of Wavefront Distortion," J. Opt. Soc. Am 55, 1427-1435 (1965).
[CrossRef]

1960 (1)

G. L. Turin, "An introduction to matched filters," IRE Trans. Inf. Theory 6, 311-329 (1960).
[CrossRef]

1953 (1)

H. W. Babcock, "The Possibility of Compensating Astronomical Seeing," Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[CrossRef]

1951 (1)

M. S. Bartlett, "An Inverse Matrix Adjustment Arising in Discriminant Analysis," Ann. Math. Stat. 22, 107-111 (1951).
[CrossRef]

1950 (1)

J. Sherman and W. J. Morrison, "Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix," Ann. Math. Stat. 21, 124-127 (1950).
[CrossRef]

1931 (1)

H. Hotelling, "The Generalization of Student’s Ratio," Ann. Math. Stat. 2, 360-378 (1931).
[CrossRef]

Abbey, C. K.

Agarwal, V.

D. A. Bader, V. Agarwal, K. Madduri, and S. Kang, "High performance combinatorial algorithm design on the Cell Broadband Engine processor," Parallel Comput. 33, 720-740 (2007).
[CrossRef]

Aipperspach, T.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Akbarpour, R.

Arnouts, S.

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

Babcock, H. W.

H. W. Babcock, "The Possibility of Compensating Astronomical Seeing," Publ. Astron. Soc. Pac. 65, 229-236 (1953).
[CrossRef]

Bader, D. A.

D. A. Bader, V. Agarwal, K. Madduri, and S. Kang, "High performance combinatorial algorithm design on the Cell Broadband Engine processor," Parallel Comput. 33, 720-740 (2007).
[CrossRef]

Barrett, H. H.

Bartlett, M. S.

M. S. Bartlett, "An Inverse Matrix Adjustment Arising in Discriminant Analysis," Ann. Math. Stat. 22, 107-111 (1951).
[CrossRef]

Bertin, E.

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

Bockenbach, O.

M. Kachelrieß, M. Knaup, and O. Bockenbach, "Hyperfast parallel-beam and cone-beam backprojection using the Cell general purpose hardware," Med. Phys. 34, 1474-1486 (2007).
[CrossRef] [PubMed]

Boerstler, D.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Bolliger, M.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Borgstrom, M. C.

Braems, I.

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

Caucci, L.

Chaudhry, R.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Clarkson, E.

Cox, D.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Cunningham, I. A.

Dainty, J. C.

Day, M. N.

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

Devaney, N.

Fitzgerald, M. P.

M. P. Fitzgerald and J. R. Graham, "Speckle Statistics in Adaptively Corrected Images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

Fried, D. L.

D. L. Fried, "Statistics of a Geometric Representation of Wavefront Distortion," J. Opt. Soc. Am 55, 1427-1435 (1965).
[CrossRef]

Friedman, S. N.

Gallas, B. D.

B. D. Gallas, "One-shot estimate of MRMC Variance: AUC," Acad. Radiol. 13, 353-362 (2006).
[CrossRef] [PubMed]

Goo, J. M.

S. H. Park, J. M. Goo, and C.-H. Jo, "Receiver Operating Characteristic (ROC) Curve: Practical Review for Radiologists," Korean J. Radiol. 5, 11-18 (2004).
[CrossRef] [PubMed]

Goodenough, D. J.

S. J. Starr, C. E. Metz, L. B. Lusted, and D. J. Goodenough, "Visual detection and localization of radiographic images," Radiology 116, 533-538 (1975).
[PubMed]

Graham, J. R.

M. P. Fitzgerald and J. R. Graham, "Speckle Statistics in Adaptively Corrected Images," Astrophys. J. 637, 541-547 (2006).
[CrossRef]

Hanley, J. A.

J. A. Hanley and B. J. McNeil, "The Meaning and use of the Area under a Receiver Operating Characteristic (ROC) Curve," Radiology 143, 29-36 (1982).
[PubMed]

Harvey, P.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Henderson, H. V.

H. V. Henderson and S. R. Searle, "On Deriving the Inverse of a Sum of Matrices," SIAM Rev. 23, 53-60 (1981).
[CrossRef]

Hobson, M. P.

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]

Hofstee, H.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Hofstee, H. P.

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

Hotelling, H.

H. Hotelling, "The Generalization of Student’s Ratio," Ann. Math. Stat. 2, 360-378 (1931).
[CrossRef]

Hughes, D. W.

D. W. Hughes, "Nonsolar Planets and Their Detection," Nature 279, 579 (1979).
[CrossRef]

Jo, C.-H.

S. H. Park, J. M. Goo, and C.-H. Jo, "Receiver Operating Characteristic (ROC) Curve: Practical Review for Radiologists," Korean J. Radiol. 5, 11-18 (2004).
[CrossRef] [PubMed]

Johns, C.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Johns, C. R.

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

Kachelrieß, M.

M. Kachelrieß, M. Knaup, and O. Bockenbach, "Hyperfast parallel-beam and cone-beam backprojection using the Cell general purpose hardware," Med. Phys. 34, 1474-1486 (2007).
[CrossRef] [PubMed]

Kahle, J.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Kahle, J. A.

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

Kameyama, A.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Kang, S.

D. A. Bader, V. Agarwal, K. Madduri, and S. Kang, "High performance combinatorial algorithm design on the Cell Broadband Engine processor," Parallel Comput. 33, 720-740 (2007).
[CrossRef]

Kasdin, N. J.

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

Keaty, J.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Knaup, M.

M. Kachelrieß, M. Knaup, and O. Bockenbach, "Hyperfast parallel-beam and cone-beam backprojection using the Cell general purpose hardware," Med. Phys. 34, 1474-1486 (2007).
[CrossRef] [PubMed]

Kupinski, M. A.

Lusted, L. B.

S. J. Starr, C. E. Metz, L. B. Lusted, and D. J. Goodenough, "Visual detection and localization of radiographic images," Radiology 116, 533-538 (1975).
[PubMed]

Madduri, K.

D. A. Bader, V. Agarwal, K. Madduri, and S. Kang, "High performance combinatorial algorithm design on the Cell Broadband Engine processor," Parallel Comput. 33, 720-740 (2007).
[CrossRef]

Maeurer, T. R.

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

Masubuchi, Y.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

McLachlan, C.

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]

McNeil, B. J.

J. A. Hanley and B. J. McNeil, "The Meaning and use of the Area under a Receiver Operating Characteristic (ROC) Curve," Radiology 143, 29-36 (1982).
[PubMed]

Metz, C. E.

S. J. Starr, C. E. Metz, L. B. Lusted, and D. J. Goodenough, "Visual detection and localization of radiographic images," Radiology 116, 533-538 (1975).
[PubMed]

Morrison, W. J.

J. Sherman and W. J. Morrison, "Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix," Ann. Math. Stat. 21, 124-127 (1950).
[CrossRef]

Myers, K. J.

Neary, J. D.

Parenti, R. R.

Park, S.

Park, S. H.

S. H. Park, J. M. Goo, and C.-H. Jo, "Receiver Operating Characteristic (ROC) Curve: Practical Review for Radiologists," Korean J. Radiol. 5, 11-18 (2004).
[CrossRef] [PubMed]

Patton, D. D.

Pham, D.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Pham, M.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Pille, J.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Posluszny, S.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Riley, M.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Rodr’iguez, J. J.

Sasiela, R. J.

Searle, S. R.

H. V. Henderson and S. R. Searle, "On Deriving the Inverse of a Sum of Matrices," SIAM Rev. 23, 53-60 (1981).
[CrossRef]

Seeley, G. W.

Sherman, J.

J. Sherman and W. J. Morrison, "Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix," Ann. Math. Stat. 21, 124-127 (1950).
[CrossRef]

Shippy, D.

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

Siewerdsen, J. H.

Sohie, G. R. L.

D. J. Tylavsky and G. R. L. Sohie, "Generalization of the Matrix Inversion Lemma," Proc. IEEE 74, 1050-1052 (1986).
[CrossRef]

Starr, S. J.

S. J. Starr, C. E. Metz, L. B. Lusted, and D. J. Goodenough, "Visual detection and localization of radiographic images," Radiology 116, 533-538 (1975).
[PubMed]

Stasiak, D.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Suzuoki, O.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Takahashi, M.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Tamura, M.

M. Tamura, "Extra-solar Planet Detection," Viva Origino 30, 157-161 (2002).

Turin, G. L.

G. L. Turin, "An introduction to matched filters," IRE Trans. Inf. Theory 6, 311-329 (1960).
[CrossRef]

Tylavsky, D. J.

D. J. Tylavsky and G. R. L. Sohie, "Generalization of the Matrix Inversion Lemma," Proc. IEEE 74, 1050-1052 (1986).
[CrossRef]

Warnock, J.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Weitzel, S.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Wendel, D.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

Yazawa, K.

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
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B. D. Gallas, "One-shot estimate of MRMC Variance: AUC," Acad. Radiol. 13, 353-362 (2006).
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Ann. Math. Stat. (3)

M. S. Bartlett, "An Inverse Matrix Adjustment Arising in Discriminant Analysis," Ann. Math. Stat. 22, 107-111 (1951).
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J. Sherman and W. J. Morrison, "Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix," Ann. Math. Stat. 21, 124-127 (1950).
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H. Hotelling, "The Generalization of Student’s Ratio," Ann. Math. Stat. 2, 360-378 (1931).
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Astron. Astrophys. Suppl. Ser. (1)

E. Bertin and S. Arnouts, "SEXTRACTOR: Software for source extraction," Astron. Astrophys. Suppl. Ser. 117, 393-404 (1996).
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Astrophys. J. (2)

M. P. Fitzgerald and J. R. Graham, "Speckle Statistics in Adaptively Corrected Images," Astrophys. J. 637, 541-547 (2006).
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N. J. Kasdin and I. Braems, "Linear and Bayesian Planet Detection Algorithms for the Terrestrial Planet Finder," Astrophys. J. 646, 1260-1274 (2006).
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IEEE J. Solid-State Circuits (1)

D. Pham, T. Aipperspach, D. Boerstler, M. Bolliger, R. Chaudhry, D. Cox, P. Harvey, P. Harvey, H. Hofstee, C. Johns, J. Kahle, A. Kameyama, J. Keaty, Y. Masubuchi, M. Pham, J. Pille, S. Posluszny, M. Riley, D. Stasiak, O. Suzuoki, M. Takahashi, J. Warnock, S. Weitzel, D. Wendel, and K. Yazawa, "Overview of the architecture, circuit design, and physical implementation of a first-generation Cell Processor," IEEE J. Solid-State Circuits 41, 179-196 (2006).
[CrossRef]

IMB J. Res. Dev. (1)

J. A. Kahle, M. N. Day, H. P. Hofstee, C. R. Johns, T. R. Maeurer, and D. Shippy, "Introduction to the Cell Multiprocessor," IMB J. Res. Dev. 49, 589-604 (2005).
[CrossRef]

IRE Trans. Inf. Theory (1)

G. L. Turin, "An introduction to matched filters," IRE Trans. Inf. Theory 6, 311-329 (1960).
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J. Opt. Soc. Am (1)

D. L. Fried, "Statistics of a Geometric Representation of Wavefront Distortion," J. Opt. Soc. Am 55, 1427-1435 (1965).
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J. Opt. Soc. Am. A (9)

R. R. Parenti and R. J. Sasiela, "Laser-guide-star systems for astronomical applications," J. Opt. Soc. Am. A 11, 288-309 (1994).
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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).
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K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, "Effect of Noise Correlation on Detectability of Disk Signals in Medical Imaging," J. Opt. Soc. Am. A 2, 1752-1759 (1985).
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C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-488 (2001).
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S. Park, E. Clarkson, M. A. Kupinski, and H. H. Barrett, "Efficiency of the human observer detecting random signals in random backgrounds," J. Opt. Soc. Am. A 22, 3-16 (2005).
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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).
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L. Caucci, H. H. Barrett, N. Devaney, and J. J. Rodr’ıguez, "Application of the Hotelling and ideal observers to detection and localization of exoplanets," J. Opt. Soc. Am. A 24, B13-B24 (2007).
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E. Clarkson, "Estimation receiver operating characteristic curve and ideal observers for combined detection/ estimation tasks," J. Opt. Soc. Am. A 24, B91-B98 (2007).
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R. Akbarpour, S. N. Friedman, J. H. Siewerdsen, J. D. Neary, and I. A. Cunningham, "Signal and noise transfer in spatiotemporal quantum-based imaging systems," J. Opt. Soc. Am. A 24, B151-B164 (2007).
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Korean J. Radiol. (1)

S. H. Park, J. M. Goo, and C.-H. Jo, "Receiver Operating Characteristic (ROC) Curve: Practical Review for Radiologists," Korean J. Radiol. 5, 11-18 (2004).
[CrossRef] [PubMed]

Med. Phys. (1)

M. Kachelrieß, M. Knaup, and O. Bockenbach, "Hyperfast parallel-beam and cone-beam backprojection using the Cell general purpose hardware," Med. Phys. 34, 1474-1486 (2007).
[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)

D. W. Hughes, "Nonsolar Planets and Their Detection," Nature 279, 579 (1979).
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Parallel Comput. (1)

D. A. Bader, V. Agarwal, K. Madduri, and S. Kang, "High performance combinatorial algorithm design on the Cell Broadband Engine processor," Parallel Comput. 33, 720-740 (2007).
[CrossRef]

Proc. IEEE (1)

D. J. Tylavsky and G. R. L. Sohie, "Generalization of the Matrix Inversion Lemma," Proc. IEEE 74, 1050-1052 (1986).
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H. W. Babcock, "The Possibility of Compensating Astronomical Seeing," Publ. Astron. Soc. Pac. 65, 229-236 (1953).
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Radiology (2)

S. J. Starr, C. E. Metz, L. B. Lusted, and D. J. Goodenough, "Visual detection and localization of radiographic images," Radiology 116, 533-538 (1975).
[PubMed]

J. A. Hanley and B. J. McNeil, "The Meaning and use of the Area under a Receiver Operating Characteristic (ROC) Curve," Radiology 143, 29-36 (1982).
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SIAM Rev. (1)

H. V. Henderson and S. R. Searle, "On Deriving the Inverse of a Sum of Matrices," SIAM Rev. 23, 53-60 (1981).
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Viva Origino (1)

M. Tamura, "Extra-solar Planet Detection," Viva Origino 30, 157-161 (2002).

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R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, 2nd ed. (John Wiley and Sons, Inc., New York, NY, 2001).

J. L. Melsa and D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, NY, 1978).

R. N. McDonough and A. D. Whalen, Detection of Signal in Noise (Academic Press, San Diego, CA, 1995).

R. K. Tyson, Adaptive Optics Engineering Handbook (Marcel Dekker, New York, NY, 2000).

D. M. Green and J. A. Swets, Signal Detection Theory and Psychophysics (JohnWiley and Sons, Inc., New York, NY, 1966).

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Figures (1)

Fig. 1.
Fig. 1.

Plots of the ROC for the observers tHot(G), tHot(g), and tmat(g).

Tables (2)

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Table 1. Possible Outcomes of a Binary Discrimination Problem

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Table 2. Values of the AUC, σ, and the SNR for the Observers t Hot( G ), t Hot( g ), and t mat( g )

Equations (13)

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TPF(τ)=τpr(tH1)dt, FPF (τ) = τpr (tH0) d t ,
SNRt(G)=t(G)GH1t(G)GH012Var{t(G)H1}+12Var{t(G)H0},
WHot=[KG]1S,
KG=K̿Gnoise+KˉGˉPSF+KG̿object,
WHot=[K̿Gnoise+KˉGˉPSF+KG̿object]1S.
KG=[GG][GG]TGP,fPff,
[KGnoise]m,m(j,j)= {σm2+gm(j)ifm=mandj=j,0otherwise,
[Kˉ̂GˉPSF]m,m(j,j)=1L11Σ1=1L1[ΔGˉ0(1)]m(j)[ΔGˉ0(1)]m(j),
[ΔGˉ0(1)]m(j)=[Gˉ0(1)]m(j)1L1Σ1=1L1[Gˉ0(1)]m(j).
ŴHot=[K̂G]1Ŝ=[K̿̂Gnoise+Kˉ̂GˉPSF+K̂G̿object]1Ŝ.
ŴHot=[K̂G]1Ŝ=[K̿̂Gnoise+Kˉ̂GˉPSF]1Ŝ.
[K̿̂Gnoise+Kˉ̂GˉPSF]1=[K̿̂Gnoise]1{IMJRQ1R[K̿̂Gnoise]1},
Cn2(h)=8.161054h10eh/1000+3.021017eh/1500+1.901015eh/100

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