Model observer for assessing digital breast tomosynthesis for multi-lesion detection in the presence of anatomical noise.

Model observers are widely used in task-based assessments of medical image quality. The presence of multiple abnormalities in a single set of images, such as in multifocal multicentric breast cancer (MFMC), has an immense clinical impact on treatment planning and survival outcomes. Detecting multiple breast tumors is challenging as MFMC is relatively uncommon, and human observers do not know the number or locations of tumors a priori. Digital breast tomosynthesis (DBT), in which an x-ray beam sweeps over a limited angular range across the breast, has the potential to improve the detection of multiple tumors. However, prior studies of DBT image quality all focus on unifocal breast cancers. In this study, we extended our 2D multi-lesion (ML) channelized Hotelling observer (CHO) into a 3D ML-CHO that detects multiple lesions from volumetric imaging data. Then we employed the 3D ML-CHO to identify optimal DBT acquisition geometries for detection of MFMC. Digital breast phantoms with multiple embedded synthetic lesions were scanned by simulated DBT scanners of different geometries (wide/narrow angular span, different number of projections per scan) to simulate MFMC cases. With new implementations of 3D partial least squares (PLS) and modified Laguerre-Gauss (LG) channels, the 3D ML-CHO made detection decisions based upon the overall information from individual DBT slices and their correlations. Our evaluation results show that: (1) the 3D ML-CHO could achieve good detection performance with a small number of channels, and 3D PLS channels on average outperform the counterpart LG channels; (2) incorporating locally varying anatomical backgrounds and their correlations as in the 3D ML-CHO is essential for multi-lesion detection; (3) the most effective DBT geometry for detection of MFMC may vary when the task of clinical interest changes, and a given DBT geometry may not yield images that are equally informative for detecting MF, MC, and unifocal cancers.

Synthetic breast phantoms from patient based eigenbreasts.

PURPOSE: The limited number of 3D patient-based breast phantoms available could be augmented by synthetic breast phantoms in order to facilitate virtual clinical trials (VCTs) using model observers for breast imaging optimization and evaluation. METHODS: These synthetic breast phantoms were developed using Principal Component Analysis (PCA) to reduce the number of dimensions needed to describe a training set of images. PCA decomposed a training set of M breast CT volumes (with millions of voxels each) into an M-1-dimensional space of eigenvectors, which we call eigenbreasts. Each of the training breast phantoms was compactly represented by the mean image plus a weighted sum of eigenbreasts. The distribution of weights observed from training was then sampled to create new synthesized breast phantoms. RESULTS: The resulting synthesized breast phantoms demonstrated a high degree of realism, as supported by an observer study. Two out of three experienced physicist observers were unable to distinguish between the synthesized breast phantoms and the patient-based phantoms. The fibroglandular density and noise power law exponent of the synthesized breast phantoms agreed well with the training data. CONCLUSIONS: Our method extends our series of digital breast phantoms based on breast CT data, providing the capability to generate new, statistically varying ensembles consisting of tens of thousands of virtual subjects. This work represents an important step toward conducting future virtual trials for task-based assessment of breast imaging, where it is vital to have a large ensemble of realistic phantoms for statistical power as well as clinical relevance.

Model observer design for multi-signal detection in the presence of anatomical noise.

As psychophysical studies are resource-intensive to conduct, model observers are commonly used to assess and optimize medical imaging quality. Model observers are typically designed to detect at most one signal. However, in clinical practice, there may be multiple abnormalities in a single image set (e.g. multifocal multicentric (MFMC) breast cancer), which can impact treatment planning. Prevalence of signals can be different across anatomical regions, and human observers do not know the number or location of signals a priori. As new imaging techniques have the potential to improve multiple-signal detection (e.g. digital breast tomosynthesis may be more effective for diagnosis of MFMC than mammography), image quality assessment approaches addressing such tasks are needed. In this study, we present a model observer to detect multiple signals in an image dataset. A novel implementation of partial least squares (PLS) was developed to estimate different sets of efficient channels directly from the images. The PLS channels are adaptive to the characteristics of signals and the background, and they capture the interactions among signal locations. Corresponding linear decision templates are employed to generate both image-level and location-specific scores on the presence of signals. Our results show that: (1) the model observer can achieve high performance with a reasonably small number of channels; (2) the model observer with PLS channels outperforms that with benchmark modified Laguerre-Gauss channels, especially when realistic signal shapes and complex background statistics are involved; (3) the tasks of clinical interest, and other constraints such as sample size would alter the optimal design of the model observer.

Effect of anatomical noise on the detectability of cone beam CT images with different slice direction, slice thickness, and volume glandular fraction.

We investigate the effect of anatomical noise on the detectability of cone beam CT (CBCT) images with different slice directions, slice thicknesses, and volume glandular fractions (VGFs). Anatomical noise is generated using a power law spectrum of breast anatomy, and spherical objects with diameters from 1mm to 11mm are used as breast masses. CBCT projection images are simulated and reconstructed using the FDK algorithm. A channelized Hotelling observer (CHO) with Laguerre-Gauss (LG) channels is used to evaluate detectability for the signal-known-exactly (SKE) binary detection task. Detectability is calculated for various slice thicknesses in the transverse and longitudinal planes for 15%, 30% and 60% VGFs. The optimal slice thicknesses that maximize the detectability of the objects are determined. The results show that the ß value increases as the slice thickness increases, but that thicker slices yield higher detectability in the transverse and longitudinal planes, except for the case of a 1mm diameter spherical object. It is also shown that the longitudinal plane with a 0.1mm slice thickness provides higher detectability than the transverse plane, despite its higher ß value. With optimal slice thicknesses, the longitudinal plane exhibits better detectability for all VGFs and spherical objects.

Investigation on slice direction dependent detectability of volumetric cone beam CT images.

We investigate the detection performance of transverse and longitudinal planes for various signal sizes (i.e., 1 mm to 8 mm diameter spheres) in cone beam computed tomography (CBCT) images. CBCT images are generated by computer simulation and images are reconstructed using an FDK algorithm. For each slice direction and signal size, a human observer study is conducted with a signal-known-exactly/background-known-exactly (SKE/BKE) binary detection task. The detection performance of human observers is compared with that of a channelized Hotelling observer (CHO). The detection performance of an ideal linear observer is also calculated using a CHO with Laguerre-Gauss (LG) channels. The detectability of high contrast small signals (i.e., up to 4-mm-diameter spheres) is higher in the longitudinal plane than the transverse plane. It is also shown that CHO performance correlates well with human observer performance in both transverse and longitudinal plane images.

Comparison of Channel Methods and Observer Models for the Task-Based Assessment of Multi-Projection Imaging in the Presence of Structured Anatomical Noise.

Although Laguerre-Gauss (LG) channels are often used for the task-based assessment of multi-projection imaging, LG channels may not be the most reliable in providing performance trends as a function of system or object parameters for all situations. Partial least squares (PLS) channels are more flexible in adapting to background and signal data statistics and were shown to be more efficient for detection tasks involving 2D non-Gaussian random backgrounds (Witten , 2010). In this work, we investigate ways of incorporating spatial correlations in the multi-projection data space using 2D LG channels and two implementations of PLS in the channelized version of the 3D projection Hotelling observer (Park , 2010) (3Dp CHO). Our task is to detect spherical and elliptical 3D signals in the angular projections of a structured breast phantom ensemble. The single PLS (sPLS) incorporates the spatial correlation within each projection, whereas the combined PLS (cPLS) incorporates the spatial correlations both within each of and across the projections. The 3Dp CHO-R indirectly incorporates the spatial correlation from the response space (R), whereas the 3Dp CHO-C from the channel space (C). The 3Dp CHO-R-sPLS has potential to be a good surrogate observer when either sample size is small or one training set is used for training both PLS channels and observer. So does the 3Dp CHO-C-cPLS when the sample size is large enough to have a good sized independent set for training PLS channels. Lastly a stack of 2D LG channels used as 3D channels in the CHO-C model showed the capability of incorporating the spatial correlation between the multiple angular projections.

Evaluating the sensitivity of the optimization of acquisition geometry to the choice of reconstruction algorithm in digital breast tomosynthesis through a simulation study.

Due to the limited number of views and limited angular span in digital breast tomosynthesis (DBT), the acquisition geometry design is an important factor that affects the image quality. Therefore, intensive studies have been conducted regarding the optimization of the acquisition geometry. However, different reconstruction algorithms were used in most of the reported studies. Because each type of reconstruction algorithm can provide images with its own image resolution, noise properties and artifact appearance, it is unclear whether the optimal geometries concluded for the DBT system in one study can be generalized to the DBT systems with a reconstruction algorithm different to the one applied in that study. Hence, we investigated the effect of the reconstruction algorithm on the optimization of acquisition geometry parameters through carefully designed simulation studies. Our results show that using various reconstruction algorithms, including the filtered back-projection, the simultaneous algebraic reconstruction technique, the maximum-likelihood method and the total-variation regularized least-square method, gave similar performance trends for the acquisition parameters for detecting lesions. The consistency of system ranking indicates that the choice of the reconstruction algorithm may not be critical for DBT system geometry optimization.

Model observers in medical imaging research.

Model observers play an important role in the optimization and assessment of imaging devices. In this review paper, we first discuss the basic concepts of model observers, which include the mathematical foundations and psychophysical considerations in designing both optimal observers for optimizing imaging systems and anthropomorphic observers for modeling human observers. Second, we survey a few state-of-the-art computational techniques for estimating model observers and the principles of implementing these techniques. Finally, we review a few applications of model observers in medical imaging research.

A virtual trial framework for quantifying the detectability of masses in breast tomosynthesis projection data.

PURPOSE: Digital breast tomosynthesis (DBT) is a promising breast cancer screening tool that has already begun making inroads into clinical practice. However, there is ongoing debate over how to quantitatively evaluate and optimize these systems, because different definitions of image quality can lead to different optimal design strategies. Powerful and accurate tools are desired to extend our understanding of DBT system optimization and validate published design principles. METHODS: The authors developed a virtual trial framework for task-specific DBT assessment that uses digital phantoms, open-source x-ray transport codes, and a projection-space, spatial-domain observer model for quantitative system evaluation. The authors considered evaluation of reconstruction algorithms as a separate problem and focused on the information content in the raw, unfiltered projection images. Specifically, the authors investigated the effects of scan angle and number of angular projections on detectability of a small (3 mm diameter) signal embedded in randomly-varying anatomical backgrounds. Detectability was measured by the area under the receiver-operating characteristic curve (AUC). Experiments were repeated for three test cases where the detectability-limiting factor was anatomical variability, quantum noise, or electronic noise. The authors also juxtaposed the virtual trial framework with other published studies to illustrate its advantages and disadvantages. RESULTS: The large number of variables in a virtual DBT study make it difficult to directly compare different authors' results, so each result must be interpreted within the context of the specific virtual trial framework. The following results apply to 25% density phantoms with 5.15 cm compressed thickness and 500 µm(3) voxels (larger 500 µm(2) detector pixels were used to avoid voxel-edge artifacts): 1. For raw, unfiltered projection images in the anatomical-variability-limited regime, AUC appeared to remain constant or increase slightly with scan angle. 2. In the same regime, when the authors fixed the scan angle, AUC increased asymptotically with the number of projections. The threshold number of projections for asymptotic AUC performance depended on the scan angle. In the quantum- and electronic-noise dominant regimes, AUC behaviors as a function of scan angle and number of projections sometimes differed from the anatomy-limited regime. For example, with a fixed scan angle, AUC generally decreased with the number of projections in the electronic-noise dominant regime. These results are intended to demonstrate the capabilities of the virtual trial framework, not to be used as optimization rules for DBT. CONCLUSIONS: The authors have demonstrated a novel simulation framework and tools for evaluating DBT systems in an objective, task-specific manner. This framework facilitates further investigation of image quality tradeoffs in DBT.

Channelized Hotelling observers for the assessment of volumetric imaging data sets.

Current clinical practice is rapidly moving in the direction of volumetric imaging. For two-dimensional (2D) images, task-based medical image quality is often assessed using numerical model observers. For three-dimensional (3D) images, however, these models have been little explored so far. In this work, first, two novel designs of a multislice channelized Hotelling observer (CHO) are proposed for the task of detecting 3D signals in 3D images. The novel designs are then compared and evaluated in a simulation study with five different CHO designs: a single-slice model, three multislice models, and a volumetric model. Four different random background statistics are considered, both gaussian (noncorrelated and correlated gaussian noise) and non-gaussian (lumpy and clustered lumpy backgrounds). Overall, the results show that the volumetric model outperforms the others, while the disparity between the models decreases for greater complexity of the detection task. Among the multislice models, the second proposed CHO could most closely approach the volumetric model, whereas the first new CHO seems to be least affected by the number of training samples.

A fast, angle-dependent, analytical model of CsI detector response for optimization of 3D x-ray breast imaging systems.

PURPOSE: Accurate models of detector blur are crucial for performing meaningful optimizations of three-dimensional (3D) x-ray breast imaging systems as well as for developing reconstruction algorithms that faithfully reproduce the imaged object anatomy. So far, x-ray detector blur has either been ignored or modeled as a shift-invariant symmetric function for these applications. The recent development of a Monte Carlo simulation package called MANTIS has allowed detailed modeling of these detector blur functions and demonstrated the magnitude of the anisotropy for both tomosynthesis and breast CT imaging systems. Despite the detailed results that MANTIS produces, the long simulation times required make inclusion of these results impractical in rigorous optimization and reconstruction algorithms. As a result, there is a need for detector blur models that can be rapidly generated. METHODS: In this study, the authors have derived an analytical model for deterministic detector blur functions, referred to here as point response functions (PRFs), of columnar CsI phosphor screens. The analytical model is x-ray energy and incidence angle dependent and draws on results from MANTIS to indirectly include complicated interactions that are not explicitly included in the mathematical model. Once the mathematical expression is derived, values of the coefficients are determined by a two-dimensional (2D) fit to MANTIS-generated results based on a figure-of-merit (FOM) that measures the normalized differences between the MANTIS and analytical model results averaged over a region of interest. A smaller FOM indicates a better fit. This analysis was performed for a monochromatic x-ray energy of 25 keV, a CsI scintillator thickness of 150 microm, and four incidence angles (0 degrees, 15 degrees, 30 degrees, and 45 degrees). RESULTS: The FOMs comparing the analytical model to MANTIS for these parameters were 0.1951 +/- 0.0011, 0.1915 +/- 0.0014, 0.2266 +/- 0.0021, and 0.2416 +/- 0.0074 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. As a comparison, the same FOMs comparing MANTIS to 2D symmetric Gaussian fits to the zero-angle PRF were 0.6234 +/- 0.0020, 0.9058 +/- 0.0029, 1.491 +/- 0.012, and 2.757 +/- 0.039 for the same set of incidence angles. Therefore, the analytical model matches MANTIS results much better than a 2D symmetric Gaussian function. A comparison was also made against experimental data for a 170 microm thick CsI screen and an x-ray energy of 25.6 keV. The corresponding FOMs were 0.3457 +/- 0.0036, 0.3281 +/- 0.0057, 0.3422 +/- 0.0023, and 0.3677 +/- 0.0041 for 0 degrees, 15 degrees, 30 degrees, and 45 degrees, respectively. In a previous study, FOMs comparing the same experimental data to MANTIS PRFs were found to be 0.2944 +/- 0.0027, 0.2387 +/- 0.0039, 0.2816 +/- 0.0025, and 0.2665 +/- 0.0032 for the same set of incidence angles. CONCLUSIONS: The two sets of derived FOMs, comparing MANTIS-generated PRFs and experimental data to the analytical model, demonstrate that the analytical model is able to reproduce experimental data with a FOM of less than two times that comparing MANTIs and experimental data. This performance is achieved in less than one millionth the computation time required to generate a comparable PRF with MANTIS. Such small computation times will allow for the inclusion of detailed detector physics in rigorous optimization and reconstruction algorithms for 3D x-ray breast imaging systems.

Partial least squares: a method to estimate efficient channels for the ideal observers.

We advocate a task-based approach to the assessment of image quality using the Bayesian ideal observer. The Bayesian ideal observer provides an absolute upper bound for performance estimates. However, using the full images as inputs to the observer is often infeasible due to their high dimensionality. A practical alternative is to reduce the dimensionality of the images by applying channels, while approximating the ideal observer by an observer constrained to the channels. Laguerre-Gauss (LG) channels and those derived from the singular value decomposition (SVD) of the system operator have previously been used with the Bayesian ideal observer. However, the channelized observer with LG and SVD channels was only applicable in situations with a rotationally symmetric signal or known system operator, respectively. We investigate a method using partial least squares (PLS) to compute efficient channels directly from the images, without prior knowledge of the background, signal, or system operator. Results show that the channelized ideal observer with PLS channels approximates the nonchannelized observer, and does so with fewer channels than the observer with either LG or SVD channels. The images are reduced from 4096 pixel values to 20 channel outputs, yet preserve the salient information. Furthermore, PLS reveals that the background image statistics provide important information necessary in signal-detection tasks. Overall, PLS is shown to be a viable channel generation method and may be applicable to real-life situations.

A statistical, task-based evaluation method for three-dimensional x-ray breast imaging systems using variable-background phantoms.

PURPOSE: For the last few years, development and optimization of three-dimensional (3D) x-ray breast imaging systems, such as digital breast tomosynthesis (DBT) and computed tomography, have drawn much attention from the medical imaging community, either academia or industry. However, there is still much room for understanding how to best optimize and evaluate the devices over a large space of many different system parameters and geometries. Current evaluation methods, which work well for 2D systems, do not incorporate the depth information from the 3D imaging systems. Therefore, it is critical to develop a statistically sound evaluation method to investigate the usefulness of inclusion of depth and background-variability information into the assessment and optimization of the 3D systems. METHODS: In this paper, we present a mathematical framework for a statistical assessment of planar and 3D x-ray breast imaging systems. Our method is based on statistical decision theory, in particular, making use of the ideal linear observer called the Hotelling observer. We also present a physical phantom that consists of spheres of different sizes and materials for producing an ensemble of randomly varying backgrounds to be imaged for a given patient class. Lastly, we demonstrate our evaluation method in comparing laboratory mammography and three-angle DBT systems for signal detection tasks using the phantom's projection data. We compare the variable phantom case to that of a phantom of the same dimensions filled with water, which we call the uniform phantom, based on the performance of the Hotelling observer as a function of signal size and intensity. RESULTS: Detectability trends calculated using the variable and uniform phantom methods are different from each other for both mammography and DBT systems. CONCLUSIONS: Our results indicate that measuring the system's detection performance with consideration of background variability may lead to differences in system performance estimates and comparisons. For the assessment of 3D systems, to accurately determine trade offs between image quality and radiation dose, it is critical to incorporate randomness arising from the imaging chain including background variability into system performance calculations.

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.

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.

Incorporating human contrast sensitivity in model observers for detection tasks.

Contrast sensitivity of the human visual system is a characteristic that can adversely affect human performance in detection tasks. In this paper, we propose a method for incorporating human contrast sensitivity in anthropomorphic model observers. In our method, we model human contrast sensitivity using the Barten model with the mean luminance of a region of interest centered at the signal location. In addition, one free parameter is varied to control the effect of the contrast sensitivity on the model observer's performance. We investigate our model of human contrast sensitivity in a channelized-Hotelling observer (CHO) with difference-of-Gaussian channels. We call the CHO incorporating the contrast sensitivity a contrast-sensitive CHO (CS-CHO). The human data from a psychophysical study by Park et al. [1] are used for comparing the performance of the CS-CHO to human performance. That study used Gaussian signals with six different signal intensities in non-Gaussian lumpy backgrounds. A value of the free parameter is chosen to match the performance of the CS-CHO to the mean human performance only at the strongest signal. Results show that the CS-CHO with the chosen value of the free parameter predicts the mean human performance at the five lower signal intensities. Our results show that the CS-CHO predicts human performance well as a function of signal intensity.

Image browsing in slow medical liquid crystal displays.

RATIONALE AND OBJECTIVES: Statistics show that radiologists are reading more studies than ever before, creating the challenge of interpreting an increasing number of images without compromising diagnostic performance. Stack-mode image display has the potential to allow radiologists to browse large three-dimensional (3D) datasets at refresh rates as high as 30 images/second. In this framework, the slow temporal response of liquid crystal displays (LCDs) can compromise the image quality when the images are browsed in a fast sequence. MATERIALS AND METHODS: In this article, we report on the effect of the LCD response time at different image browsing speeds based on the performance of a contrast-sensitive channelized-hoteling observer. A stack of simulated 3D clustered lumpy background images with a designer nodule to be detected is used. The effect of different browsing speeds is calculated with LCD temporal response measurements from our previous work. The image set is then analyzed by the model observer, which has been shown to predict human detection performance in Gaussian and non-Gaussian lumpy backgrounds. This methodology allows us to quantify the effect of slow temporal response of medical liquid crystal displays on the performance of the anthropomorphic observers. RESULTS: We find that the slow temporal response of the display device greatly affects lesion contrast and observer performance. A detectability decrease of more than 40% could be caused by the slow response of the display. CONCLUSIONS: After validation with human observers, this methodology can be applied to more realistic background data with the goal of providing recommendations for the browsing speed of large volumetric image datasets (from computed tomography, magnetic resonance, or tomosynthesis) when read in stack-mode.

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.

Efficiency of the human observer for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds.

A previous study [J. Opt. Soc. Am. A22, 3 (2005)] has shown that human efficiency for detecting a Gaussian signal at a known location in non-Gaussian distributed lumpy backgrounds is approximately 4%. This human efficiency is much less than the reported 40% efficiency that has been documented for Gaussian-distributed lumpy backgrounds [J. Opt. Soc. Am. A16, 694 (1999) and J. Opt. Soc. Am. A18, 473 (2001)]. We conducted a psychophysical study with a number of changes, specifically in display-device calibration and data scaling, from the design of the aforementioned study. Human efficiency relative to the ideal observer was found again to be approximately 5%. Our variance analysis indicates that neither scaling nor display made a statistically significant difference in human performance for the task. We conclude that the non-Gaussian distributed lumpy background is a major factor in our low human-efficiency results.

Efficiency of the human observer detecting random signals in random backgrounds.

The efficiencies of the human observer and the channelized-Hotelling observer relative to the ideal observer for signal-detection tasks are discussed. Both signal-known-exactly (SKE) tasks and signal-known-statistically (SKS) tasks are considered. Signal location is uncertain for the SKS tasks, and lumpy backgrounds are used for background uncertainty in both cases. Markov chain Monte Carlo methods are employed to determine ideal-observer performance on the detection tasks. Psychophysical studies are conducted to compute human-observer performance on the same tasks. Efficiency is computed as the squared ratio of the detectabilities of the observer of interest to the ideal observer. Human efficiencies are approximately 2.1% and 24%, respectively, for the SKE and SKS tasks. The results imply that human observers are not affected as much as the ideal observer by signal-location uncertainty even though the ideal observer outperforms the human observer for both tasks. Three different simplified pinhole imaging systems are simulated, and the humans and the model observers rank the systems in the same order for both the SKE and the SKS tasks.