Subok Park

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.

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 150μm, and four incidence angles (0°, 15°, 30°, and 45°). 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°, 15°, 30°, and 45°, 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 170μm 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°, 15°, 30°, and 45°, 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.

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 observers 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 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.

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.

Ideal-observer performance under signal and background uncertainty.

We use the performance of the Bayesian ideal observer as a figure of merit for hardware optimization because this observer makes optimal use of signal-detection information. Due to the high dimensionality of certain integrals that need to be evaluated, it is difficult to compute the ideal observer test statistic, the likelihood ratio, when background variability is taken into account. Methods have been developed in our laboratory for performing this computation for fixed signals in random backgrounds. In this work, we extend these computational methods to compute the likelihood ratio in the case where both the backgrounds and the signals are random with known statistical properties. We are able to write the likelihood ratio as an integral over possible backgrounds and signals, and we have developed Markov-chain Monte Carlo (MCMC) techniques to estimate these high-dimensional integrals. We can use these results to quantify the degradation of the ideal-observer performance when signal uncertainties are present in addition to the randomness of the backgrounds. For background uncertainty, we use lumpy backgrounds. We present the performance of the ideal observer under various signal-uncertainty paradigms with different parameters of simulated parallel-hole collimator imaging systems. We are interested in any change in the rankings between different imaging systems under signal and background uncertainty compared to the background-uncertainty case. We also compare psychophysical studies to the performance of the ideal observer.

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.

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.

Estimating breast tomosynthesis performance in detection tasks with variable-background phantoms

Digital breast tomosynthesis (DBT) shows potential for improving breast cancer detection. However, this technique has not yet been fully characterized with consideration of the various uncertainties in the imaging chain and optimized with respect to system acquisition parameters. To obtain maximum diagnostic information in DBT, system optimization needs to be performed across a range of patients and acquisition parameters to quantify their impact on tumor detection performance. In addition, a balance must be achieved between x-ray dose and image quality to minimize risk to the patient while maximizing the systems detection performance. To date, researchers have applied a task-based approach to the optimization of DBT with use of mathematical observers for tasks in the signal-known-exactly background-known-exactly (SKE/BKE) and signal-known-exactly background-known statistically (SKE/BKS) paradigms1-3. However, previous observer models provided insufficient treatment of the spatial correlations between multi-angle DBT projections, so we incorporated this correlation information into the modeling methodology. We developed a computational approach that includes three-dimensional variable background phantoms for incorporating background variability, accurate ray-tracing and Poisson distributions for generating noise-free and noisy projections of the phantoms, and a channelized-Hotelling observer4 (CHO) for estimating performance in DBT. We demonstrated our method for a DBT acquisition geometry and calculated the performance of the CHO with Laguerre-Gauss channels as a function of the angular span of the system. Preliminary results indicate that the implementation of a CHO model that incorporates correlations between multi-angle projections gives different performance predictions than a CHO model that ignores multi-angle correlations. With improvement of the observer design, we anticipate more accurate investigations into the impact of multi-angle correlations and background variability on the performance of DBT.

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.

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.