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We consider detection of a nodule signal profile in noisy images meant to roughly simulate the statistical properties of tomographic image reconstructions in nuclear medicine. The images have two sources of variability arising from quantum noise from the imaging process and anatomical variability in the ensemble of objects being imaged. Both of these sources of variability are simulated by a stationary Gaussian random process. Sample images from this process are generated by filtering white-noise images. Human-observer performance in several signal-known-exactly detection tasks is evaluated through psychophysical studies by using the two-alternative forced-choice method. The tasks considered investigate parameters of the images that influence both the signal profile and pixel-to-pixel correlations in the images. The effect of low-pass filtering is investigated as an approximation to regularization implemented by image-reconstruction algorithms. The relative magnitudes of the quantum and the anatomical variability are investigated as an approximation to the effects of exposure time. Finally, we study the effect of the anatomical correlations in the form of an anatomical slope as an approximation to the effects of different tissue types. Human-observer performance is compared with the performance of a number of model observers computed directly from the ensemble statistics of the images used in the experiments for the purpose of finding predictive models. The model observers investigated include a number of nonprewhitening observers, the Hotelling observer (which is equivalent to the ideal observer for these studies), and six implementations of channelized-Hotelling observers. The human observers demonstrate large effects across the experimental parameters investigated. In the regularization study, performance exhibits a mild peak at intermediate levels of regularization before degrading at higher levels. The exposure-time study shows that human observers are able to detect ever more subtle lesions at increased exposure times. The anatomical slope study shows that human-observer performance degrades as anatomical variability extends into higher spatial frequencies. Of the observers tested, the channelized-Hotelling observers best capture the features of the human data.

Image quality can be defined objectively in terms of the performance of some "observer" (either a human or a mathematical model) for some task of practical interest. If the end user of the image will be a human, model observers are used to predict the task performance of the human, as measured by psychophysical studies, and hence to serve as the basis for optimization of image quality. In this paper, we consider the task of detection of a weak signal in a noisy image. The mathematical observers considered include the ideal Bayesian, the nonprewhitening matched fiter, a model based on lineardiscriminant analysis and referred to as the Hotelling observer, and the Hotelling and Bayesian observers modified to account for the spatial-frequency-selective channels in the human visual system. The theory behind these observer models is briefly reviewed, and several psychophysical studies relating to the choice among them are summarized. Only the Hoteiling model with channels is mathematically tractable in all cases considered here and capable of accounting for all of these data. This model requires no adjustment of parameters to fit the data and is relatively insensitive to the details of the channel mechanism. We therefore suggest it as a useful model observer for the purpose of assessing and optimizing image quality with respect to simple detection tasks.Image quality, for scientific and medical purposes, can be defined in terms of how well desired information can be extracted from the image. In other words, image quality is measured by the performance of some "observer" on some specific task (1-3). The observer can be a human, such as a physician trying to make a diagnosis, or it can be a mathematical model or a computer algorithm. The tasks can be divided generically into classification and estimation tasks (4). In medical applications, an example of a classification task would be lesion detection, while an estimation task might be determination of the volume of blood expelled from the heart on each beat.For classification tasks performed by a human observer, psychophysical studies and receiver operating characteristic (ROC) analysis provide a reproducible, quantitative measure of image quality (2,3,5), but such studies are time consuming and require large numbers of images. Moreover, they do not provide an easy way to see how image quality is related to various parameters of the imaging system or processing algorithm. For these reasons, there is considerable interest, especially in the radiological literature (6-8), in mathematical model observers. If the ultimate observer will be a human rather than a machine, the objective of the model is to predict accurately the performance of the human. Then the model observer can be used for system evaluation and optimization with some assurance that the system that is best for the model is also best for a human. Model observers may also be usedThe publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby mark...

Several authors have measured the detection ability of human observers for objects in correlated (nonwhite) noise. These studies have shown that the human observer has approximately constant efficiency when compared with a nonprewhitening ideal observer. In this paper we add a frequency-selective mechanism to the ideal-observer model, similar to the channel mechanism that has been demonstrated through experiments that measure a subject's ability to detect grating stimuli. For a number of detection and discrimination tasks, the nonprewhitening ideal-observer model and the channelized ideal-observer model yield similar performance predictions. Thus both models seem equally capable of explaining a considerable body of psychophysical data, and it would be difficult to devise an experiment to determine which model is more nearly correct.

The expectation-maximization (EM) algorithm is an important tool for maximum-likelihood (ML) estimation and image reconstruction, especially in medical imaging. It is a non-linear iterative algorithm that attempts to find the ML estimate of the object that produced a data set. The convergence of the algorithm and other deterministic properties are well established, but relatively little is known about how noise in the data influences noise in the final reconstructed image. In this paper we present a detailed treatment of these statistical properties. The specific application we have in mind is image reconstruction in emission tomography, but the results are valid for any application of the EM algorithm in which the data set can be described by Poisson statistics. We show that the probability density function for the grey level at a pixel in the image is well approximated by a log-normal law. An expression is derived for the variance of the grey level and for pixel-to-pixel covariance. The variance increases rapidly with iteration number at first, but eventually saturates as the ML estimate is approached. Moreover, the variance at any iteration number has a factor proportional to the square of the mean image (though other factors may also depend on the mean image), so a map of the standard deviation resembles the object itself. Thus low-intensity regions of the image tend to have low noise. By contrast, linear reconstruction methods, such as filtered back-projection in tomography, show a much more global noise pattern, with high-intensity regions of the object contributing to noise at rather distant low-intensity regions. The theoretical results of this paper depend on two approximations, but in the second paper in this series we demonstrate through Monte Carlo simulation that the approximations are justified over a wide range of conditions in emission tomography. The theory can, therefore, be used as a basis for calculation of objective figures of merit for image quality.

A number of task-specific approaches to the assessment of image quality are treated. Both estimation and classification tasks are considered, but only linear estimators or classifiers are permitted. Performance on these tasks is limited by both quantum noise and object variability, and the effects of postprocessing or image-reconstruction algorithms are explicitly included. The results are expressed as signal-to-noise ratios (SNR's). The interrelationships among these SNR's are considered, and an SNR for a classification task is expressed as the SNR for a related estimation task times four factors. These factors show the effects of signal size and contrast, conspicuity of the signal, bias in the estimation task, and noise correlation. Ways of choosing and calculating appropriate SNR's for system evaluation and optimization are also discussed.

We analyze the effects of electrode size on performance of arrays of semiconductor gamma-ray detectors, especially when there is significant charge trapping. With large electrodes, motions of holes and electrons are of equal importance, but when the positive electrode is segmented into an array of small elements the contributions of holes to the output, and hence the effects of hole trapping, are much less significant. The implications of this analysis for the design of practical detector arrays are discussed, and some preliminary experimental verification of the theory is presented.