Hotelling trace criterion as a figure of merit for the optimization of imaging systems

Smith, Warren E.; Barrett, Harrison H.

doi:10.1364/josaa.3.000717

Cited by 66 publications

(43 citation statements)

References 9 publications

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“…One notable omission from the following list of observers is that of the Hotelling or optimal linear observer ( [19] and [20]). Computation of the template w for this observer involves computing the pseudo-inverse of K f̂k +1, a 16,384 × 16,384 element matrix.…”

Section: Resultsmentioning

confidence: 99%

<title>Observer signal-to-noise ratios for the ML-EM algorithm</title>

Abbey

Barrett

Wilson

1996

Medical Imaging 1996: Image Perception

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We have used an approximate method developed by Barrett, Wilson, and Tsui for finding the ensemble statistics of the Maximum Likelihood-Expectation Maximization algorithm to compute task-dependent figures of merit as a function of stopping point. For comparison, human-observer performance was assessed through conventional psychophysics.The results of our studies show the dependence of the optimal stopping point of the algorithm on the detection task. Comparisons of human and various model observers show that a channelized Hotelling observer with overlapping channels is the best predictor of human performance.

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Section: Resultsmentioning

confidence: 99%

<title>Observer signal-to-noise ratios for the ML-EM algorithm</title>

Abbey

Barrett

Wilson

1996

Medical Imaging 1996: Image Perception

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“…The expression for t Hot (g | r p ) in Eq. (16), which requires the knowledge of the mean vectors and covariance matrix under the two hypotheses, is the socalled Hotelling observer [1,7,15,34,35] and is a linear function of g. As pointed out in [36], the Hotelling observer is still analytically tractable in realistic cases (for example, when the background can be described by a stationary random process), whereas computing the likelihood ratio in practical cases is, in general, a difficult problem. The derivation above shows that, if the data are normally distributed, the Hotelling observer is equivalent to the likelihood ratio, in the sense that they differ by an additive or positive multiplicative constant.…”

Section: Hotelling and Ideal Observers In Adaptive Opticsmentioning

confidence: 99%

Application of the Hotelling and ideal observers to detection and localization of exoplanets

et al. 2007

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The ideal linear discriminant or Hotelling observer is widely used for detection tasks and imagequality 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.

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“…A common recourse is then the ideal linear or Hotelling observer, [10][11][12] for which the test statistic is the linear discriminant that maximizes the SNR defined in (4.1). This optimal linear discriminant is given by (4.5) where the superscript t denotes transpose, the angle brackets denote averages over all sources of randomness (background object, signal to be detected, system and measurement noise) and Δ〈g〉 ≡ 〈g〉 1 − 〈g〉 0 is the difference between the mean data vectors under the two hypotheses.…”

Section: Ideal and Ideal-linear Observers For Binary Classificationmentioning

confidence: 99%

Statistical characterization of radiological images: basic principles and recent progress

Barrett

Myers

2007

SPIE Proceedings

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This paper surveys our current understanding of the statistical properties of radiological images and their effect on image quality. Attention is given to statistical descriptions needed to compute the performance of ideal or ideal-linear observers on detection and estimation tasks. The effects of measurement noise, random objects and random imaging system are analyzed by nested conditional averaging, leading to a three-term expansion of the data covariance matrix. Characteristic functionals are introduced to account for the object statistics, and it is shown how they can be used to compute the image statistics.

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Hotelling trace criterion as a figure of merit for the optimization of imaging systems

Cited by 66 publications

References 9 publications

<title>Observer signal-to-noise ratios for the ML-EM algorithm</title>

<title>Observer signal-to-noise ratios for the ML-EM algorithm</title>

Application of the Hotelling and ideal observers to detection and localization of exoplanets

Statistical characterization of radiological images: basic principles and recent progress

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