Foundations of Image Science

Barrett, Harrison H.; Myers, Kyle J.; Rathee, S

doi:10.1118/1.1677252

Cited by 792 publications

(1,057 citation statements)

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“…The resulting standard deviation using the Bootstrap method after 1000 iterations was 0.181 ( Fig. 5), which is in the same order as the one obtained using (8). However, the algorithm for obtaining standard deviation using (8) took approximately eight days.…”

Section: Methodssupporting

confidence: 48%

“…Note that E(U ijk U mnl ) is the probability that both U ijk and U mnl are 1. Expanding (7), as described in [13] results in the following formula for variance of the VUS (8) Note that the elements in each expectation in (8) have at least one identical subscript, e.g., the two elements in E(U ijk U IJk ) have subscripts ijk and IJk, respectively. E(U ijk U IJk ) is de fined as (9) Other expectations in (8) have analogous definitions.…”

Section: B Estimation Of the Variance Of The Vus Valuementioning

confidence: 99%

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The Meaning and Use of the Volume Under a Three-Class ROC Surface (VUS)

Frey²

2008

IEEE Trans. Med. Imaging

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Previously, we have proposed a method for three-class receiver operating characteristic (ROC) analysis based on decision theory. In this method, the volume under a three-class ROC surface (VUS) serves as a figure-of-merit (FOM) and measures three-class task performance. The proposed three-class ROC analysis method was demonstrated to be optimal under decision theory according to several decision criteria. Further, an optimal three-class linear observer was proposed to simultaneously maximize the signal-to-noise ratio (SNR) between the test statistics of each pair of the classes provided certain data linearity condition. Applicability of this three-class ROC analysis method would be further enhanced by the development of an intuitive meaning of the VUS and a more general method to calculate the VUS that provides an estimate of its standard error. In this paper, we investigated the general meaning and usage of VUS as a FOM for threeclass classification task performance. We showed that the VUS value, which is obtained from a rating procedure, equals the percent correct in a corresponding categorization procedure for continuous rating data. The significance of this relationship goes beyond providing another theoretical basis for three-class ROC analysis-it enables statistical analysis of the VUS value. Based on this relationship, we developed and tested algorithms for calculating the VUS and its variance. Finally, we reviewed the current status of the proposed three-class ROC analysis methodology, and concluded that it extends and unifies decision theoretic, linear discriminant analysis, and psychophysical foundations of binary ROC analysis in a three-class paradigm.

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Section: Methodssupporting

confidence: 48%

Section: B Estimation Of the Variance Of The Vus Valuementioning

confidence: 99%

The Meaning and Use of the Volume Under a Three-Class ROC Surface (VUS)

Frey²

2008

IEEE Trans. Med. Imaging

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“…However, both approaches (3) and (4) yield the same result in correspondence with Burgess variance theorem applied for random amplification process with Poisson input as, for example, discussed in [11].…”

Section: General Considerationmentioning

confidence: 83%

Analytical models of probability distribution and excess noise factor of solid state photomultiplier signals with crosstalk

Vinogradov

2012

Nuclear Instruments and Methods in Physics Research Section A:

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Silicon Photomultipliers (SiPM), also so-called Solid State Photomultipliers (SSPM), are based on Geiger mode avalanche breakdown limited by strong negative feedback. SSPM can detect and resolve single photons due to high gain and ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and afterpulsing processes associated with the high gain introduce specific excess noise and deteriorate photon number resolution of the SSPM. Probabilistic features of these processes are widely studied because of its high importance for the SSPM design, characterization, optimization and application, but the process modeling is mostly based on Monte Carlo simulations and numerical methods. In this study, crosstalk is considered to be a branching Poisson process, and analytical models of probability distribution and excess noise factor (ENF) of SSPM signals based on the Borel distribution as an advance on the geometric distribution models are presented and discussed. The models are found to be in a good agreement with the experimental probability distributions for dark counts and a few photon spectrums in a wide range of fired pixels number as well as with observed super-linear behavior of crosstalk ENF.

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“…1 In the case of a signal detection task, the hypotheses H 0 and H 1 will represent a signal-absent and signal-present case (see Sec. II.B).…”

Section: Iic 2afc Studymentioning

confidence: 99%

“…(8) is the basis for much active research. For instance, approximate inversions of the image covariance in data space either by efficient channels 1,5,10,11 or assumptions of stationarity in the image covariance are sometimes made to ease the computational burden. In the present case, 1024 view angles and 256 detector bins are used, implying that g and K g have dimensions 262, 144 × 1 and 262, 144 × 262, 144, respectively.…”

Section: Iid Hotelling Observermentioning

confidence: 99%

Comparison of human and Hotelling observer performance for a fan‐beam CT signal detection task

et al. 2013

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Purpose: A human observer study was performed for a signal detection task for the case of fan-beam x-ray computed tomography. Hotelling observer (HO) performance was calculated for the same detection task without the use of efficient channels. By considering the full image covariance produced by the filtered backprojection (FBP) algorithm and avoiding the use of channels in the computation of HO performance, the authors establish an absolute upper bound on signal detectability. Therefore, this study serves as a baseline for relating human and ideal observer performance in the case of fan-beam CT. Methods: Eight human observers participated in a two-alternative forced choice experiment where the signal of interest was a small simulated ellipsoid in the presence of independent, identically distributed Gaussian detector noise. Theoretical performance of the HO, which is equivalent to the ideal observer in this case (see Sec. 13.2.12 in Barrett and Myers [Foundations of Image Science (Wiley, Hoboken, NJ, 2004)], was also computed and compared to the performance of the human observers. In addition to a reference FBP implementation, two FBP implementations with inherent loss of HO signal detectability (e.g., by apodizing the ramp filter) were also investigated. Each of these latter two implementations takes the form of a discrete-to-discrete linear operator (i.e., a matrix), which has a nontrivial null-space resulting in the loss of detectability. Results: Estimated observer detectability index (d A ) values for the human observers and SNR values for the HO were obtained. While Hanning filtering in the FBP implementation with a cutoff frequency of 1/4 of the Nyquist frequency reduces HO SNR (due to the reconstruction matrix's nontrivial nullspace), this filtering was shown to consistently improve human observer performance. By contrast, increasing the image pixel size was seen to have a comparable effect on both the HO and the human observers, degrading performance. Conclusions: These results, which characterize HO and human observer performance for a signal detection task in fan-beam FBP noise, form a basis for applying model observer metrics to fanbeam CT when knowledge of the full image-domain noise statistics is important. Further, by calculating HO performance without relying on channels, these results are particularly relevant when an information theoretic approach is considered, e.g., in optimization of the image reconstruction algorithm with respect to preservation of signal detectability. Finally, the HO (which is here equivalent to the ideal observer) provides an absolute upper bound on detection performance, and our results therefore provide insight into the performance of human observers relative to the optimum for two different cases wherein ideal observer performance is compromised through degradation of the data quality. In one case (regularization), human performance is improved to practically ideal performance, and in the other (larger pixel size), ideal and human observer performance are approximate...

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Foundations of Image Science

Cited by 792 publications

References 0 publications

The Meaning and Use of the Volume Under a Three-Class ROC Surface (VUS)

The Meaning and Use of the Volume Under a Three-Class ROC Surface (VUS)

Analytical models of probability distribution and excess noise factor of solid state photomultiplier signals with crosstalk

Comparison of human and Hotelling observer performance for a fan‐beam CT signal detection task

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