Ideal Observer Performance Research Articles

Ideal Observer Computation by Use of Markov-Chain Monte Carlo With Generative Adversarial Networks.

Medical imaging systems are often evaluated and optimized via objective, or task-specific, measures of image quality (IQ) that quantify the performance of an observer on a specific clinically-relevant task. The performance of the Bayesian Ideal Observer (IO) sets an upper limit among all observers, numerical or human, and has been advocated for use as a figure-of-merit (FOM) for evaluating and optimizing medical imaging systems. However, the IO test statistic corresponds to the likelihood ratio that is intractable to compute in the majority of cases. A sampling-based method that employs Markov-chain Monte Carlo (MCMC) techniques was previously proposed to estimate the IO performance. However, current applications of MCMC methods for IO approximation have been limited to a small number of situations where the considered distribution of to-be-imaged objects can be described by a relatively simple stochastic object model (SOM). As such, there remains an important need to extend the domain of applicability of MCMC methods to address a large variety of scenarios where IO-based assessments are needed but the associated SOMs have not been available. In this study, a novel MCMC method that employs a generative adversarial network (GAN)-based SOM, referred to as MCMC-GAN, is described and evaluated. The MCMC-GAN method was quantitatively validated by use of test-cases for which reference solutions were available. The results demonstrate that the MCMC-GAN method can extend the domain of applicability of MCMC methods for conducting IO analyses of medical imaging systems.

Impact of using sinogram domain data in the super-resolution of CT images on diagnostic information.

In recent times, deep-learning-based super-resolution (DL-SR) techniques for computed tomography (CT) images have shown outstanding results in terms of full-reference image quality (FR-IQ) metrics (e.g., root mean square error and structural similarity index metric), which assesses IQ by measuring its similarity to the high-resolution (HR) image. In addition, IQ can be evaluated via task-based IQ (Task-IQ) metrics that evaluate the ability to perform specific tasks. Ironically, most proposed image domain-based SR techniques are not possible to improve a Task-IQ metric, which assesses the amount of information related todiagnosis. In the case of CT imaging systems, sinogram domain data can be utilized for SR techniques. Therefore, this study aims to investigate the impact of utilizing sinogram domain data on diagnostic information restorationability. We evaluated three DL-SR techniques: using image domain data (Image-SR), using sinogram domain data (Sinogram-SR), and using sinogram as well as image domain data (Dual-SR). For Task-IQ evaluation, the Rayleigh discrimination task was used to evaluate diagnostic ability by focusing on the resolving power aspect, and an ideal observer (IO) can be used to perform the task. In this study, we used a convolutional neural network (CNN)-based IO that approximates the IO performance. We compared the IO performances of the SR techniques according to the data domain to evaluate the discriminative information restorationability. Overall, the low-resolution (LR) and SR exhibit lower IO performances compared with that of HR owing to their degraded discriminative information when detector binning is used. Next, between the SR techniques, Image-SR does not show superior IO performances compared to the LR image, but Sinogram-SR and Dual-SR show superior IO performances than the LR image. Furthermore, in Sinogram-SR, we confirm that FR-IQ and IO performance are positively correlated. These observations demonstrate that sinogram domain upsampling improves the representation ability for discriminative information in the image domain compared to the LR andImage-SR. Unlike Image-SR, Sinogram-SR can improve the amount of discriminative information present in the image domain. This demonstrates that to improve the amount of discriminative information on the resolving power aspect, it is necessary to employ sinogram domainprocessing.

Limitations of CNNs for Approximating the Ideal Observer Despite Quantity of Training Data or Depth of Network.

The performance of a convolutional neural network (CNN) on an image texture detection task as a function of linear image processing and the number of training images is investigated. Performance is quantified by the area under (AUC) the receiver operating characteristic (ROC) curve. The Ideal Observer (IO) maximizes AUC but depends on high-dimensional image likelihoods. In many cases, the CNN performance can approximate the IO performance. This work demonstrates counterexamples where a full-rank linear transform degrades the CNN performance below the IO in the limit of large quantities of training data and network layers. A subsequent linear transform changes the images' correlation structure, improves the AUC, and again demonstrates the CNN dependence on linear processing. Compression strictly decreases or maintains the IO detection performance while compression can increase the CNN performance especially for small quantities of training data. Results indicate an optimal compression ratio for the CNN based on task difficulty, compression method, and number of training images.

Approximating the Ideal Observer for Joint Signal Detection and Localization Tasks by use of Supervised Learning Methods.

Medical imaging systems are commonly assessed and optimized by use of objective measures of image quality (IQ). The Ideal Observer (IO) performance has been advocated to provide a figure-of-merit for use in assessing and optimizing imaging systems because the IO sets an upper performance limit among all observers. When joint signal detection and localization tasks are considered, the IO that employs a modified generalized likelihood ratio test maximizes observer performance as characterized by the localization receiver operating characteristic (LROC) curve. Computations of likelihood ratios are analytically intractable in the majority of cases. Therefore, sampling-based methods that employ Markov-Chain Monte Carlo (MCMC) techniques have been developed to approximate the likelihood ratios. However, the applications of MCMC methods have been limited to relatively simple object models. Supervised learning-based methods that employ convolutional neural networks have been recently developed to approximate the IO for binary signal detection tasks. In this paper, the ability of supervised learning-based methods to approximate the IO for joint signal detection and localization tasks is explored. Both background-known-exactly and background-known-statistically signal detection and localization tasks are considered. The considered object models include a lumpy object model and a clustered lumpy model, and the considered measurement noise models include Laplacian noise, Gaussian noise, and mixed Poisson-Gaussian noise. The LROC curves produced by the supervised learning-based method are compared to those produced by the MCMC approach or analytical computation when feasible. The potential utility of the proposed method for computing objective measures of IQ for optimizing imaging system performance is explored.

OEC-cnn: a simple method for over-exposure correction in photographs

This work reports on convolutional neural network (CNN) performance on an image texture classification task as a function of linear image processing and number of training images. Detection performance of single and multi-layer CNNs (sCNN/mCNN) are compared to optimal observers. Performance is quantified by the area under the receiver operating characteristic (ROC) curve, also known as the AUC. For perfect detection AUC = 1.0 and AUC = 0.5 for guessing. The Ideal Observer (IO) maximizes AUC but is prohibitive in practice because it depends on high-dimensional image likelihoods. The IO performance is invariant to any fullrank, invertible linear image processing. This work demonstrates the existence of full-rank, invertible linear transforms that can degrade both sCNN and mCNN even in the limit of large quantities of training data. A subsequent invertible linear transform changes the images’ correlation structure again and can improve this AUC. Stationary textures sampled from zero mean and unequal covariance Gaussian distributions allow closed-form analytic expressions for the IO and optimal linear compression. Linear compression is a mitigation technique for high-dimension low sample size (HDLSS) applications. By definition, compression strictly decreases or maintains IO detection performance. For small quantities of training data, linear image compression prior to the sCNN architecture can increase AUC from 0.56 to 0.93. Results indicate an optimal compression ratio for CNN based on task difficulty, compression method, and number of training images.

Analyzing thresholds and efficiency with hierarchical Bayesian logistic regression

Ideal observer analysis is a fundamental tool used widely in vision science for analyzing the efficiency with which a cognitive or perceptual system uses available information. The performance of an ideal observer provides a formal measure of the amount of information in a given experiment. The ratio of human to ideal performance is then used to compute efficiency, a construct that can be directly compared across experimental conditions while controlling for the differences due to the stimuli and/or task specific demands. In previous research using ideal observer analysis, the effects of varying experimental conditions on efficiency have been tested using ANOVAs and pairwise comparisons. In this work, we present a model that combines Bayesian estimates of psychometric functions with hierarchical logistic regression for inference about both unadjusted human performance metrics and efficiencies. Our approach improves upon the existing methods by constraining the statistical analysis using a standard model connecting stimulus intensity to human observer accuracy and by accounting for variability in the estimates of human and ideal observer performance scores. This allows for both individual and group level inferences.

WE‐G‐204‐01: BEST IN PHYSICS (IMAGING): Effect of Image Processing Parameters On Nodule Detectability in Chest Radiography

Purpose:To investigate the effect of varying system image processing parameters on lung nodule detectability in digital radiography.Methods:An anthropomorphic chest phantom was imaged in the posterior‐anterior position using a GE Discovery XR656 digital radiography system. To simulate lung nodules, a polystyrene board with 6.35mm diameter PMMA spheres was placed adjacent to the phantom (into the x‐ray path). Due to magnification, the projected simulated nodules had a diameter in the radiographs of approximately 7.5 mm. The images were processed using one of GE's default chest settings (Factory3) and reprocessed by varying the “Edge” and “Tissue Contrast” processing parameters, which were the two user‐configurable parameters for a single edge and contrast enhancement algorithm. For each parameter setting, the nodule signals were calculated by subtracting the chest‐only image from the image with simulated nodules. Twenty nodule signals were averaged, Gaussian filtered, and radially averaged in order to generate an approximately noiseless signal. For each processing parameter setting, this noise‐free signal and 180 background samples from across the lung were used to estimate ideal observer performance in a signal‐known‐exactly detection task. Performance was estimated using a channelized Hotelling observer with 10 Laguerre‐Gauss channel functions.Results:The “Edge” and “Tissue Contrast” parameters each had an effect on the detectability as calculated by the model observer. The CHO‐estimated signal detectability ranged from 2.36 to 2.93 and was highest for “Edge” = 4 and “Tissue Contrast” = −0.15. In general, detectability tended to decrease as “Edge” was increased and as “Tissue Contrast” was increased. A human observer study should be performed to validate the relation to human detection performance.Conclusion:Image processing parameters can affect lung nodule detection performance in radiography. While validation with a human observer study is needed, model observer detectability for common tasks could provide a means for optimizing image processing parameters.

An ideal-observer framework to investigate signal detectability in diffuse optical imaging

With the emergence of diffuse optical tomography (DOT) as a non-invasive imaging modality, there is a requirement to evaluate the performance of the developed DOT systems on clinically relevant tasks. One such important task is the detection of high-absorption signals in the tissue. To investigate signal detectability in DOT systems for system optimization, an appropriate approach is to use the Bayesian ideal observer, but this observer is computationally very intensive. It has been shown that the Fisher information can be used as a surrogate figure of merit (SFoM) that approximates the ideal observer performance. In this paper, we present a theoretical framework to use the Fisher information for investigating signal detectability in DOT systems. The usage of Fisher information requires evaluating the gradient of the photon distribution function with respect to the absorption coefficients. We derive the expressions to compute the gradient of the photon distribution function with respect to the scattering and absorption coefficients. We find that computing these gradients simply requires executing the radiative transport equation with a different source term. We then demonstrate the application of the SFoM to investigate signal detectability in DOT by performing various simulation studies, which help to validate the proposed framework and also present some insights on signal detectability in DOT.

Perceiving sequential dependencies in auditory streams

This study examined the ability of human listeners to detect the presence and judge the strength of a statistical dependency among the elements comprising sequences of sounds. The statistical dependency was imposed by specifying transition matrices that determined the likelihood of occurrence of the sound elements. Markov chains were constructed from these transition matrices having states that were pure tones/noise bursts that varied along the stimulus dimensions of frequency and/or interaural time difference. Listeners reliably detected the presence of a statistical dependency in sequences of sounds varying along these stimulus dimensions. Furthermore, listeners were able to discriminate the relative strength of the dependency in pairs of successive sound sequences. Random variation along an irrelevant stimulus dimension had small but significant adverse effects on performance. A much greater decrement in performance was found when the sound sequences were concurrent. Likelihood ratios were computed based on the transition matrices to specify Ideal Observer performance for the experimental conditions. Preliminary modeling efforts were made based on degradations of Ideal Observer performance intended to represent human observer limitations. This experimental approach appears to be useful for examining auditory "stream" formation and maintenance over time based on the predictability of the constituent sound elements.

Optimization of energy window for 90Y bremsstrahlung SPECT imaging for detection tasks using the ideal observer with model‐mismatch

In yttrium-90 ((90)Y) microsphere brachytherapy (radioembolization) of unresectable liver cancer, posttherapy (90)Y bremsstrahlung single photon emission computed tomography (SPECT) has been used to document the distribution of microspheres in the patient and to help predict potential side effects. The energy window used during projection acquisition can have a significant effect on image quality. Thus, using an optimal energy window is desirable. However, there has been great variability in the choice of energy window due to the continuous and broad energy distribution of (90)Y bremsstrahlung photons. The area under the receiver operating characteristic curve (AUC) for the ideal observer (IO) is a widely used figure of merit (FOM) for optimizing the imaging system for detection tasks. The IO implicitly assumes a perfect model of the image formation process. However, for (90)Y bremsstrahlung SPECT there can be substantial model-mismatch (i.e., difference between the actual image formation process and the model of it assumed in reconstruction), and the amount of the model-mismatch depends on the energy window. It is thus important to account for the degradation of the observer performance due to model-mismatch in the optimization of the energy window. The purpose of this paper is to optimize the energy window for (90)Y bremsstrahlung SPECT for a detection task while taking into account the effects of the model-mismatch. An observer, termed the ideal observer with model-mismatch (IO-MM), has been proposed previously to account for the effects of the model-mismatch on IO performance. In this work, the AUC for the IO-MM was used as the FOM for the optimization. To provide a clinically realistic object model and imaging simulation, the authors used a background-known-statistically and signal-known-statistically task. The background was modeled as multiple compartments in the liver with activity parameters independently following a Gaussian distribution; the signal was modeled as a tumor with a Gaussian-distributed activity parameter located randomly with equal probability at one of three positions. The IO test statistics (i.e., likelihood ratios) were estimated using Markov-chain Monte Carlo methods. The authors realistically modeled human anatomy using a digital phantom code, and realistically simulated (90)Y bremsstrahlung SPECT imaging with a clinical SPECT system and typical imaging parameters using a previously validated Monte Carlo bremsstrahlung simulation method. Model-mismatch was included by modeling image formation process in the calculation of IO test statistics using an analytic modeling method previously developed for quantitative (90)Y bremsstrahlung SPECT. To demonstrate the effects of the model-mismatch on the detection task, the authors optimized the energy window both with and without model-mismatch included in the IO. For all the energy windows, the AUC values for the IO-MM were smaller than that for the IO. The optimal windows for the IO-MM and the IO were 80-180 and 60-400 keV, respectively. The authors have demonstrated the degradation of the ideal performance due to model-mismatch and optimized the energy window for (90)Y bremsstrahlung SPECT for detection tasks by accounting for the effects of the model-mismatch. The obtained optimal window was much narrower when taking into account the model-mismatch and similar to that obtained previously for estimation tasks.

Asymptotic ideal observers and surrogate figures of merit for signal detection with list-mode data

The asymptotic form for the likelihood ratio is derived for list-mode data generated by an imaging system viewing a possible signal in a randomly generated background. This calculation provides an approximation to the likelihood ratio that is valid in the limit of large number of list entries, i.e., a large number of photons. These results are then used to derive surrogate figures of merit, quantities that are correlated with ideal-observer performance on detection tasks, as measured by the area under the receiver operating characteristic curve, but are easier to compute. A key component of these derivations is the determination of asymptotic forms for the Fisher information for the signal amplitude in the limit of a large number of counts or a long exposure time. This quantity is useful in its own right as a figure of merit (FOM) for the task of estimating the signal amplitude. The use of the Fisher information in detection tasks is based on the fact that it provides an approximation for ideal-observer detectability when the signal is weak. For both the fixed-count and fixed-time cases, four surrogate figures of merit are derived. Two are based on maximum likelihood reconstructions; one uses the characteristic functional of the random backgrounds. The fourth surrogate FOM is identical in the two cases and involves an integral over attribute space for each of a randomly generated sequence of backgrounds.

Fisher information and surrogate figures of merit for the task-based assessment of image quality

Fisher information can be used as a surrogate for task-based measures of image quality based on ideal observer performance. A new and improved derivation of the Fisher information approximation for ideal-observer detectability is provided. This approximation depends only on the presence of a weak signal and does not depend on Gaussian statistical assumptions. This is also not an asymptotic result and therefore applies to imaging, where there is typically only one dataset, albeit a large one. Applications to statistical mixture models for image data are presented. For Gaussian and Poisson mixture models the results are used to connect reconstruction error with ideal-observer detection performance. When the task is the estimation of signal parameters of a weak signal, the ensemble mean squared error of the posterior mean estimator can also be expanded in powers of the signal amplitude. There is no linear term in this expansion, and it is shown that the quadratic term involves a Fisher information kernel that generalizes the standard Fisher information. Applications to imaging mixture models reveal a close connection between ideal performance on these estimation tasks and detection tasks for the same signals. Finally, for tasks that combine detection and estimation, we may also define a detectability that measures performance on this combined task and an ideal observer that maximizes this detectability. This detectability may also be expanded in powers of the signal amplitude, and the quadratic term again involves the Fisher information kernel. Applications of this approximation to imaging mixture models show a relation with the pure detection and pure estimation tasks for the same signals.

Contour grouping: Ecological statistics, generative models and ideal observers

While the Gestalt laws of perceptual grouping were originally conceived as qualitative principles, the contemporary view is quantitative, treating perceptual organization as a problem of statistical inference. Here we consider the problem of contour grouping within this modern framework. In particular, we use a contour tracing technique to study the statistics of proximity, good continuation and similarity cues for contour grouping in natural images. Statistical modeling of the proximity cue indicates that it is by far the most powerful of the three cues, and follows a scale-invariant power law in close agreement with prior psychophysics. The approximate independence of the three cues leads to a simple Bayesian model for contour inference which, when combined with global cues and priors, can be used for the inference of bounding contours from natural images. This generative model of contour grouping also allows naturalistic contours to be synthesized and used as stimuli in controlled psychophysical experiments. We employ the methodology of Field et al. (1993), in which human observers are presented with images containing random fields of oriented elements. The observer's task is to detect a stochastic sequence of elements generated by the natural contour model. Interpreting human performance is difficult without an ideal observer model, i.e. a benchmark that reflects the inherent difficulty of the task. Unfortunately, the computational complexity of the problem precludes a direct simulation of the ideal observer. Here we describe an alternative method that uses two sub-optimal machine observers to derive bounds on ideal observer performance. Using this technique, we find human efficiency to be in the 25–50% range, declining as a function of the number of elements on the contour. The proximity cue appears to be more efficiently exploited than good continuation cues, consistent with our finding that proximity provides more information in the natural environment. ElderJ.H.KrupnikA.JohnstonL.A.(2003). Contour grouping with prior models, IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(25), 661–674. ElderJ.H.GoldbergR. M.(2002). Ecological statistics of Gestalt laws for the perceptual organization of contours. Journal of Vision, 2(4), 324–353, http://journalofvision.org/2/4/5/, DOI 10.1167/2.4.5. FieldD. J.HayesA.HessR. F.(1993). Contour integration by the human visual system: Evidence for a local “association field.” Vision Research, 33, 173–193.

Visual search: Gaze contingent displays and optimal search strategies

Although generic visual search in the real world involves integrating information over multiple fixations, most research has focused on single-fixation tasks where stimuli are presented briefly. At least two factors have held back progress in understanding visual processing in more natural search tasks: (1) the difficulty of precisely controlling and manipulating the stimulus on the retina and (2) the lack of a Bayesian ideal-observer theory for multiple-fixation (extended) visual search. To enable precise stimulus control in extended search tasks, we developed “gaze-contingent” software (see http://svi.cps.utexas.edu/) that allows real-time control of the content of video displays relative to the observer's current gaze direction (measured with an eye tracker). In our first experiment, we measured search time and eye movements while subjects searched for Gabor targets in 1/f noise. We varied parametrically: target spatial frequency, noise contrast, and rate of fall-off in display resolution from the point of fixation. This experiment provides quantitative data on how much information can be removed from the periphery (how much foveation can be tolerated) without affecting search time or the pattern of eye movements. We find that the shape of the function describing search time versus degree of foveation is dependent upon target spatial frequency, but is (interestingly) independent of noise contrast. To provide an appropriate benchmark against which to evaluate search performance, and to provide a starting point for developing models of search performance, we derived the ideal observer for visual search in broadband noise, where the ideal searcher is constrained by an arbitrary function describing sensitivity across the retina and by some level of internal noise. We compare the eye movements and performance of ideal and real observers. More detailsR of the ideal visual searcher are given in another presentation (Najemnik et al. VSS 2003).

Efficient estimation of ideal-observer performance in classification tasks involving high-dimensional complex backgrounds

The Bayesian ideal observer is optimal among all observers and sets an absolute upper bound for the performance of any observer in classification tasks [Van Trees, Detection, Estimation, and Modulation Theory, Part I (Academic, 1968).]. Therefore, the ideal observer should be used for objective image quality assessment whenever possible. However, computation of ideal-observer performance is difficult in practice because this observer requires the full description of unknown, statistical properties of high-dimensional, complex data arising in real life problems. Previously, Markov-chain Monte Carlo (MCMC) methods were developed by Kupinski et al. [J. Opt. Soc. Am. A 20, 430(2003) ] and by Park et al. [J. Opt. Soc. Am. A 24, B136 (2007) and IEEE Trans. Med. Imaging 28, 657 (2009) ] to estimate the performance of the ideal observer and the channelized ideal observer (CIO), respectively, in classification tasks involving non-Gaussian random backgrounds. However, both algorithms had the disadvantage of long computation times. We propose a fast MCMC for real-time estimation of the likelihood ratio for the CIO. Our simulation results show that our method has the potential to speed up ideal-observer performance in tasks involving complex data when efficient channels are used for the CIO.

The efficiency of the human observer for lesion detection and localization in emission tomography

For the medically relevant task of joint detection and localization of a signal (lesion) in an emission computed tomographic (ECT) image, it is of interest to measure the efficiency, defined as the relative task performance of a human observer versus that of an ideal observer. Efficiency studies can be used in system optimization, improving postprocessing (e.g., reconstruction) algorithms, deriving human-emulating model observers and computer-aided detection methods. Calculation of ideal observer performance for ECT is highly computationally complex. We can, however, compute ideal observer performance exactly using a simplified ‘filtered-noise’ model of ECT. This model results in images whose correlation structure, due to quantum noise, background variability and regularization, is similar to that of real ECT reconstructed images. A two-alternative forced choice test is used to obtain the performance of the human observers. We compare the efficiency of our joint detection–localization task with that of a corresponding signal-known-exactly (SKE) detection task. For the joint task, efficiency is low when the search tolerance is stringent. Efficiency for the joint task rises with signal intensity but is flat for the SKE task. For both tasks, efficiency peaks at a mid-range level of regularization corresponding to a particular noise-resolution tradeoff.

Singular Vectors of a Linear Imaging System as Efficient Channels for the Bayesian Ideal Observer

The Bayesian ideal observer provides an absolute upper bound for diagnostic performance of an imaging system and hence should be used for the assessment of image quality whenever possible. However, computation of ideal-observer performance in clinical tasks is difficult since the probability density functions of the data required for this observer are often unknown in tasks involving realistic, complex backgrounds. Moreover, the high dimensionality of the integrals that need to be calculated for the observer makes the computation more difficult. The ideal observer constrained to a set of channels, which we call a channelized-ideal observer (CIO), can reduce the dimensionality of the problem. These channels are called efficient if the CIO can approximate ideal-observer performance. In this paper, we propose a method to choose efficient channels for the ideal observer based on a singular value decomposition of a linear imaging system. As a demonstration, we test our method on detection tasks using non-Gaussian lumpy backgrounds and signals of Gaussian and elliptical profiles. Our simulation results show that singular vectors associated with either the background or the signal are highly efficient for the ideal observer for detecting both types of signals. In addition, this CIO outperforms a channelized-Hotelling observer with the same channels.

What limits performance in the amblyopic visual system: Seeing signals in noise with an amblyopic brain

Amblyopia results in a loss of visual acuity, contrast sensitivity, and position acuity. However, the nature of the neural losses is not yet fully understood. Here we report the results of experiments using noise to try to better understand the losses in amblyopia. Specifically, in one experiment we compared the performance of normal, amblyopic, and ideal observers for detecting a localized signal (a discrete frequency pattern or DFP) in fixed contrast white noise. In a second experiment, we used visibility-scaled noise and varied both the visibility of the noise (from 2 to 20 times the noise detection threshold) and the spatial frequency of the signal. Our results show a loss of efficiency for detection of known signals in noise that increases with the spatial frequency of the signal in observers with amblyopia. To determine whether the loss of efficiency was a consequence of a mismatched template, we derived classification images. We found that although the amblyopic observers' template was shifted to lower spatial frequencies, the shift was insufficient to account for their threshold elevation. Reduced efficiency in the amblyopic visual system may reflect a high level of internal noise, a poorly matched position template, or both. To analyze the type of internal noise we used an "N-pass" technique, in which observers performed the identical experiment N times (where N = 3 or 4). The amount of disagreement between the repeated trials enables us to parse the internal noise into random noise and consistent noise beyond that due to the poorly matched template. Our results show that the amblyopes' reduced efficiency for detecting signals in noise is explained in part by reduced template efficiency but to a greater extent by increased random internal noise. This loss is more or less independent of external noise contrast over a log unit range of external noise.

Channelized-ideal observer using Laguerre-Gauss channels in detection tasks involving non-Gaussian distributed lumpy backgrounds and a Gaussian signal

We investigate a channelized-ideal observer (CIO) with Laguerre-Gauss (LG) channels to approximate ideal-observer performance in detection tasks involving non-Gaussian distributed lumpy backgrounds and a Gaussian signal. A Markov-chain Monte Carlo approach is employed to determine the performance of both the ideal observer and the CIO using a large number of LG channels. Our results indicate that the CIO with LG channels can approximate ideal-observer performance within error bars, depending on the imaging system, object, and channel parameters. The CIO also outperforms a channelized-Hotelling observer using the same channels. In addition, an alternative approach for estimating the CIO is investigated. This approach makes use of the characteristic functions of channelized data and employs an approximation method to the area under the receiver operating characteristic curve. The alternative approach provides good estimates of the performance of the CIO with five LG channels. However, for large channel cases, more efficient computational methods need to be developed for the CIO to become useful in practice.

Using Fisher information to approximate ideal-observer performance on detection tasks for lumpy-background images

When building an imaging system for detection tasks in medical imaging, we need to evaluate how well the system performs before we can optimize it. One way to do the evaluation is to calculate the performance of the Bayesian ideal observer. The ideal-observer performance is often computationally expensive, and it is very useful to have an approximation to it. We use a parameterized probability density function to represent the corresponding densities of data under the signal-absent and the signal-present hypotheses. We develop approximations to the ideal-observer detectability as a function of signal parameters involving the Fisher information matrix, which is normally used in parameter estimation problems. The accuracy of the approximation is illustrated in analytical examples and lumpy-background simulations. We are able to predict the slope of the detectability as a function of the signal parameter. This capability suggests that the Fisher information matrix itself evaluated at the null parameter value can be used as the figure of merit in imaging system evaluation. We are also able to provide a theoretical foundation for the connection between detection tasks and estimation tasks.