Abstract

This paper addresses the numerical stability issue on the channelized Hotelling observer (CHO). The CHO is a well-known approach in the medical image quality assessment domain. Many researchers have found that the detection performance of the CHO does not increase with the number of channels, contrary to expectation. And to our knowledge, nobody in this domain has found the reason. We illustrated that this is due to the ill-posed problem of the scatter matrix and proposed a solution based on Tikhonov regularization. Although Tikhonov regularization has been used in many other domains, we show in this paper another important application of Tikhonov regularization. This is very important for researchers to continue the CHO (and other channelized model observer) investigation with a reliable detection performance calculation.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

L. Zhang, C. Cavaro-Ménard, P. L. Callet, and L. H. K. Cooper, “The effects of anatomical information and observer expertise on abnormality detection task,” Proc. SPIE 7966, 79661G (2011).
[CrossRef]

2010 (1)

B. Goossens, L. Platiša, E. Vansteenkiste, and W. Philips, “The use of steerable channels for detecting asymmetrical signals with random orientations,” Proc. SPIE 7627, 76270S (2010).
[CrossRef]

2009 (1)

S. Park, A. Badano, B. D. Gallas, and K. J. Myers, “Incorporating human contrast sensitivity in model observers for detection tasks,” IEEE Trans. Med. Imaging 28, 339–347 (2009).
[CrossRef]

2008 (1)

2006 (1)

S. Park, “Performance of a channelized-ideal observer using Laguerre–Gauss channels for detecting a Gaussian signal at a known location in different lumpy backgrounds,” Proc. SPIE 6146, 61460P (2006).
[CrossRef]

2003 (1)

2001 (1)

1999 (2)

H.-P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26, 2654–2668 (1999).
[CrossRef]

T. Narayan and G. Herman, “Prediction of human observer performance by numerical observers: an experimental study.” J. Opt. Soc. Am. A 16, 679–693 (1999).
[CrossRef]

1998 (1)

1997 (1)

1995 (1)

1992 (1)

1990 (1)

Abbey, C. K.

Badano, A.

S. Park, A. Badano, B. D. Gallas, and K. J. Myers, “Incorporating human contrast sensitivity in model observers for detection tasks,” IEEE Trans. Med. Imaging 28, 339–347 (2009).
[CrossRef]

Barrett, H. H.

Bochud, F.

Bruyant, P.

P. Bruyant, H. Gifford, G. Gindi, P. Pretorius, and M. King, “Human and numerical observer studies of lesion detection in Ga-67 images obtained with MAP-EM reconstructions and anatomical priors,” in Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4072–4075.

Callet, P. L.

L. Zhang, C. Cavaro-Ménard, P. L. Callet, and L. H. K. Cooper, “The effects of anatomical information and observer expertise on abnormality detection task,” Proc. SPIE 7966, 79661G (2011).
[CrossRef]

Castella, C.

Cavaro-Ménard, C.

L. Zhang, C. Cavaro-Ménard, P. L. Callet, and L. H. K. Cooper, “The effects of anatomical information and observer expertise on abnormality detection task,” Proc. SPIE 7966, 79661G (2011).
[CrossRef]

Chan, H.-P.

H.-P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26, 2654–2668 (1999).
[CrossRef]

Clarkson, E.

Cooper, L. H. K.

L. Zhang, C. Cavaro-Ménard, P. L. Callet, and L. H. K. Cooper, “The effects of anatomical information and observer expertise on abnormality detection task,” Proc. SPIE 7966, 79661G (2011).
[CrossRef]

Daly, S.

S. Daly, The Visible Differences Predictor: An Algorithm for the Assessment of Image Fidelity (Massachusetts Institute of Technology, 1993), Chap. 14, pp. 179–206.

Denny, J. L.

Descombes, F.

Eckstein, M.

Gallas, B. D.

S. Park, A. Badano, B. D. Gallas, and K. J. Myers, “Incorporating human contrast sensitivity in model observers for detection tasks,” IEEE Trans. Med. Imaging 28, 339–347 (2009).
[CrossRef]

B. D. Gallas and H. H. Barrett, “Validating the use of channels to estimate the ideal linear observer,” J. Opt. Soc. Am. A 20, 1725–1738 (2003).
[CrossRef]

Gifford, H.

P. Bruyant, H. Gifford, G. Gindi, P. Pretorius, and M. King, “Human and numerical observer studies of lesion detection in Ga-67 images obtained with MAP-EM reconstructions and anatomical priors,” in Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4072–4075.

Gindi, G.

P. Bruyant, H. Gifford, G. Gindi, P. Pretorius, and M. King, “Human and numerical observer studies of lesion detection in Ga-67 images obtained with MAP-EM reconstructions and anatomical priors,” in Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4072–4075.

Goossens, B.

B. Goossens, L. Platiša, E. Vansteenkiste, and W. Philips, “The use of steerable channels for detecting asymmetrical signals with random orientations,” Proc. SPIE 7627, 76270S (2010).
[CrossRef]

Herman, G.

King, M.

P. Bruyant, H. Gifford, G. Gindi, P. Pretorius, and M. King, “Human and numerical observer studies of lesion detection in Ga-67 images obtained with MAP-EM reconstructions and anatomical priors,” in Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4072–4075.

Kinkel, K.

Myers, K. J.

S. Park, A. Badano, B. D. Gallas, and K. J. Myers, “Incorporating human contrast sensitivity in model observers for detection tasks,” IEEE Trans. Med. Imaging 28, 339–347 (2009).
[CrossRef]

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]

Narayan, T.

Park, S.

S. Park, A. Badano, B. D. Gallas, and K. J. Myers, “Incorporating human contrast sensitivity in model observers for detection tasks,” IEEE Trans. Med. Imaging 28, 339–347 (2009).
[CrossRef]

S. Park, “Performance of a channelized-ideal observer using Laguerre–Gauss channels for detecting a Gaussian signal at a known location in different lumpy backgrounds,” Proc. SPIE 6146, 61460P (2006).
[CrossRef]

Petrick, N.

H.-P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26, 2654–2668 (1999).
[CrossRef]

Philips, W.

B. Goossens, L. Platiša, E. Vansteenkiste, and W. Philips, “The use of steerable channels for detecting asymmetrical signals with random orientations,” Proc. SPIE 7627, 76270S (2010).
[CrossRef]

Platiša, L.

B. Goossens, L. Platiša, E. Vansteenkiste, and W. Philips, “The use of steerable channels for detecting asymmetrical signals with random orientations,” Proc. SPIE 7627, 76270S (2010).
[CrossRef]

Pretorius, P.

P. Bruyant, H. Gifford, G. Gindi, P. Pretorius, and M. King, “Human and numerical observer studies of lesion detection in Ga-67 images obtained with MAP-EM reconstructions and anatomical priors,” in Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4072–4075.

Rolland, J. P.

Sahiner, B.

H.-P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26, 2654–2668 (1999).
[CrossRef]

Solomon, J.

Sottas, P.

Vansteenkiste, E.

B. Goossens, L. Platiša, E. Vansteenkiste, and W. Philips, “The use of steerable channels for detecting asymmetrical signals with random orientations,” Proc. SPIE 7627, 76270S (2010).
[CrossRef]

Verdun, F.

Wagner, R. F.

H.-P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26, 2654–2668 (1999).
[CrossRef]

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]

Watson, A.

Zhang, L.

L. Zhang, C. Cavaro-Ménard, P. L. Callet, and L. H. K. Cooper, “The effects of anatomical information and observer expertise on abnormality detection task,” Proc. SPIE 7966, 79661G (2011).
[CrossRef]

IEEE Trans. Med. Imaging (1)

S. Park, A. Badano, B. D. Gallas, and K. J. Myers, “Incorporating human contrast sensitivity in model observers for detection tasks,” IEEE Trans. Med. Imaging 28, 339–347 (2009).
[CrossRef]

J. Opt. Soc. Am. A (8)

Med. Phys. (1)

H.-P. Chan, B. Sahiner, R. F. Wagner, and N. Petrick, “Classifier design for computer-aided diagnosis: effects of finite sample size on the mean performance of classical and neural network classifiers,” Med. Phys. 26, 2654–2668 (1999).
[CrossRef]

Opt. Express (1)

Proc. SPIE (3)

L. Zhang, C. Cavaro-Ménard, P. L. Callet, and L. H. K. Cooper, “The effects of anatomical information and observer expertise on abnormality detection task,” Proc. SPIE 7966, 79661G (2011).
[CrossRef]

B. Goossens, L. Platiša, E. Vansteenkiste, and W. Philips, “The use of steerable channels for detecting asymmetrical signals with random orientations,” Proc. SPIE 7627, 76270S (2010).
[CrossRef]

S. Park, “Performance of a channelized-ideal observer using Laguerre–Gauss channels for detecting a Gaussian signal at a known location in different lumpy backgrounds,” Proc. SPIE 6146, 61460P (2006).
[CrossRef]

Other (2)

S. Daly, The Visible Differences Predictor: An Algorithm for the Assessment of Image Fidelity (Massachusetts Institute of Technology, 1993), Chap. 14, pp. 179–206.

P. Bruyant, H. Gifford, G. Gindi, P. Pretorius, and M. King, “Human and numerical observer studies of lesion detection in Ga-67 images obtained with MAP-EM reconstructions and anatomical priors,” in Nuclear Science Symposium Conference Record (IEEE, 2004), pp. 4072–4075.

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Figures (5)

Fig. 1.
Fig. 1.

Simulated test images (128×128) with Gaussian lesion profile in the center of different backgrounds: (a) white Gaussian, (b) correlated Gaussian, (c) lumpy, and (d) clustered lumpy.

Fig. 2.
Fig. 2.

LG functions for aU=5,10,20,40 (column) and the order of channel = 0, 3, 9, 17 (line). The grayscale is normalized by the factor of 2/aU for each column.

Fig. 3.
Fig. 3.

LG CHO detection performances (SNR) using different LG channel numbers with direct inverse (by Gaussian elimination) of the scatter covariance matrix S^. Four backgrounds are tested, each with 2000 training image inputs and 2000 testing images. LG spread parameters au [cf. Eq. (9)] and the y axis ranges are adjusted for each case. The channel numbers all range from 2 to 40.

Fig. 4.
Fig. 4.

Example of the condition number of the matrix S^ with increasing dimension p for the five classes of LG channels (au=[15102040]). The test is realized on a lumpy background identical to the lower panel (signal profile σ=5) of Fig. 3(c).

Fig. 5.
Fig. 5.

SNR with proposed Tikhonov regularization for all backgrounds with simulation data identical to Fig. 3. The y axis ranges are adjusted for each case given specific backgrounds and signal sizes.

Equations (15)

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Hh:g=hx+b,h=0,1,
[x]p=aexp(12(pq)tD1(pq)),
g=Utg
wCHO=S^1x^
x^=g¯1g¯0,
S^=12(Var(g1)+Var(g0)).
λCHO=wCHOtg.
SNR=(λ¯0λ¯1)2(Var(λ0)+Var(λ1))/2,
un(r|aU)=2aUexp(πr2aU2)Ln(2πr2aU2),
y(r)=n=0αnun(r|aU)
αn=aU2y(r)un(r|aU)dr.
S^=VDVt,
S^·w=x^,
min{12S^·wx^2+12ηw2},η>0
S=(S^tS^+ηI)1S^t=V[d1η+d12dpη+dp2]Vt,

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