Data-driven modeling of noise time series with convolutional generative adversarial networks.

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing and data analysis tasks. Given the recent interest in generative adversarial networks (GANs) for data-driven modeling, it is important to determine to what extent GANs can faithfully reproduce noise in target data sets. In this paper, we present an empirical investigation that aims to shed light on this issue for time series. Namely, we assess two general-purpose GANs for time series that are based on the popular deep convolutional GAN architecture, a direct time-series model and an image-based model that uses a short-time Fourier transform data representation. The GAN models are trained and quantitatively evaluated using distributions of simulated noise time series with known ground-truth parameters. Target time series distributions include a broad range of noise types commonly encountered in physical measurements, electronics, and communication systems: band-limited thermal noise, power law noise, shot noise, and impulsive noise. We find that GANs are capable of learning many noise types, although they predictably struggle when the GAN architecture is not well suited to some aspects of the noise, e.g. impulsive time-series with extreme outliers. Our findings provide insights into the capabilities and potential limitations of current approaches to time-series GANs and highlight areas for further research. In addition, our battery of tests provides a useful benchmark to aid the development of deep generative models for time series.

Blind Measurement of Receiver System Noise.

Tightly packaged receivers pose a challenge for noise measurements. Their only outputs are often diagnostic or benchmark information-"user data" that result from unknown processing. These include data rate test results, signal-to-noise ratio estimated by the receiver, and so on. Some of these are important gauges of communication viability that may be enshrined in performance and conformance specifications. Engineers can estimate these parameters based on standards and simplified system models, but there are few means to validate against physical measurements. We propose here a set of measurement techniques to complement and support models of system noise. The approach is founded on a semiparametric model of the noise response of a full-stack receiver. We probe this response experimentally by systematically perturbing signals and excess noise levels at the receiver input. The resulting technique is blind to protocol and implementation details. We introduce the design and implementation of some novel test capabilities required for these tests: a precision programmable excess noise source and a highly directive programmable attenuator. We also introduce a regression procedure to estimate system noise (or NF) from the controlled input conditions and summary statistics of the user data output. We also estimate uncertainty in the measurement by combining traditional methods with a Monte Carlo method that propagates random errors through the regression. Case studies demonstrate the measurement with consumer wireless networking and geolocation equipment. These include verification by repeatability testing and cross-comparison against Y-factor measurements.

Deep Learning Classification of 3.5 GHz Band Spectrograms with Applications to Spectrum Sensing.

In the United States, the Federal Communications Commission has adopted rules permitting commercial wireless networks to share spectrum with federal incumbents in the 3.5 GHz Citizens Broadband Radio Service band. These rules require commercial systems to vacate the band when sensors detect radars operated by the U.S. military; a key example being the SPN-43 air traffic control radar. Such sensors require highly-accurate detection algorithms to meet their operating requirements. In this paper, using a library of over 14,000 3.5 GHz band spectrograms collected by a recent measurement campaign, we investigate the performance of thirteen methods for SPN-43 radar detection. Namely, we compare classical methods from signal detection theory and machine learning to several deep learning architectures. We demonstrate that machine learning algorithms appreciably outperform classical signal detection methods. Specifically, we find that a three-layer convolutional neural network offers a superior tradeoff between accuracy and computational complexity. Last, we apply this three-layer network to generate descriptive statistics for the full 3.5 GHz spectrogram library. Our findings highlight potential weaknesses of classical methods and strengths of modern machine learning algorithms for radar detection in the 3.5 GHz band.

A Utility/Cost Analysis of Breast Cancer Risk Prediction Algorithms.

Breast cancer risk prediction algorithms are used to identify subpopulations that are at increased risk for developing breast cancer. They can be based on many different sources of data such as demographics, relatives with cancer, gene expression, and various phenotypic features such as breast density. Women who are identified as high risk may undergo a more extensive (and expensive) screening process that includes MRI or ultrasound imaging in addition to the standard full-field digital mammography (FFDM) exam. Given that there are many ways that risk prediction may be accomplished, it is of interest to evaluate them in terms of expected cost, which includes the costs of diagnostic outcomes. In this work we perform an expected-cost analysis of risk prediction algorithms that is based on a published model that includes the costs associated with diagnostic outcomes (true-positive, false-positive, etc.). We assume the existence of a standard screening method and an enhanced screening method with higher scan cost, higher sensitivity, and lower specificity. We then assess expected cost of using a risk prediction algorithm to determine who gets the enhanced screening method under the strong assumption that risk and diagnostic performance are independent. We find that if risk prediction leads to a high enough positive predictive value, it will be cost-effective regardless of the size of the subpopulation. Furthermore, in terms of the hit-rate and false-alarm rate of the of the risk-prediction algorithm, iso-cost contours are lines with slope determined by properties of the available diagnostic systems for screening.

Optimal Joint Detection and Estimation That Maximizes ROC-Type Curves.

Combined detection-estimation tasks are frequently encountered in medical imaging. Optimal methods for joint detection and estimation are of interest because they provide upper bounds on observer performance, and can potentially be utilized for imaging system optimization, evaluation of observer efficiency, and development of image formation algorithms. We present a unified Bayesian framework for decision rules that maximize receiver operating characteristic (ROC)-type summary curves, including ROC, localization ROC (LROC), estimation ROC (EROC), free-response ROC (FROC), alternative free-response ROC (AFROC), and exponentially-transformed FROC (EFROC) curves, succinctly summarizing previous results. The approach relies on an interpretation of ROC-type summary curves as plots of an expected utility versus an expected disutility (or penalty) for signal-present decisions. We propose a general utility structure that is flexible enough to encompass many ROC variants and yet sufficiently constrained to allow derivation of a linear expected utility equation that is similar to that for simple binary detection. We illustrate our theory with an example comparing decision strategies for joint detection-estimation of a known signal with unknown amplitude. In addition, building on insights from our utility framework, we propose new ROC-type summary curves and associated optimal decision rules for joint detection-estimation tasks with an unknown, potentially-multiple, number of signals in each observation.

MRMC analysis of agreement studies.

The purpose of this work is to present and evaluate methods based on U-statistics to compare intra- or inter-reader agreement across different imaging modalities. We apply these methods to multi-reader multi-case (MRMC) studies. We measure reader-averaged agreement and estimate its variance accounting for the variability from readers and cases (an MRMC analysis). In our application, pathologists (readers) evaluate patient tissue mounted on glass slides (cases) in two ways. They evaluate the slides on a microscope (reference modality) and they evaluate digital scans of the slides on a computer display (new modality). In the current work, we consider concordance as the agreement measure, but many of the concepts outlined here apply to other agreement measures. Concordance is the probability that two readers rank two cases in the same order. Concordance can be estimated with a U-statistic and thus it has some nice properties: it is unbiased, asymptotically normal, and its variance is given by an explicit formula. Another property of a U-statistic is that it is symmetric in its inputs; it doesn't matter which reader is listed first or which case is listed first, the result is the same. Using this property and a few tricks while building the U-statistic kernel for concordance, we get a mathematically tractable problem and efficient software. Simulations show that our variance and covariance estimates are unbiased.

Seamless Insertion of Pulmonary Nodules in Chest CT Images.

The availability of large medical image datasets is critical in many applications, such as training and testing of computer-aided diagnosis systems, evaluation of segmentation algorithms, and conducting perceptual studies. However, collection of data and establishment of ground truth for medical images are both costly and difficult. To address this problem, we are developing an image blending tool that allows users to modify or supplement existing datasets by seamlessly inserting a lesion extracted from a source image into a target image. In this study, we focus on the application of this tool to pulmonary nodules in chest CT exams. We minimize the impact of user skill on the perceived quality of the composite image by limiting user involvement to two simple steps: the user first draws a casual boundary around a nodule in the source, and, then, selects the center of desired insertion area in the target. We demonstrate the performance of our system on clinical samples, and report the results of a reader study evaluating the realism of inserted nodules compared to clinical nodules. We further evaluate our image blending techniques using phantoms simulated under different noise levels and reconstruction filters. Specifically, we compute the area under the ROC curve of the Hotelling observer (HO) and noise power spectrum of regions of interest enclosing native and inserted nodules, and compare the detectability, noise texture, and noise magnitude of inserted and native nodules. Our results indicate the viability of our approach for insertion of pulmonary nodules in clinical CT images.

Exact confidence intervals for channelized Hotelling observer performance in image quality studies.

Task-based assessments of image quality constitute a rigorous, principled approach to the evaluation of imaging system performance. To conduct such assessments, it has been recognized that mathematical model observers are very useful, particularly for purposes of imaging system development and optimization. One type of model observer that has been widely applied in the medical imaging community is the channelized Hotelling observer (CHO), which is well-suited to known-location discrimination tasks. In the present work, we address the need for reliable confidence interval estimators of CHO performance. Specifically, we show that the bias associated with point estimates of CHO performance can be overcome by using confidence intervals proposed by Reiser for the Mahalanobis distance. In addition, we find that these intervals are well-defined with theoretically-exact coverage probabilities, which is a new result not proved by Reiser. The confidence intervals are tested with Monte Carlo simulation and demonstrated with two examples comparing X-ray CT reconstruction strategies. Moreover, commonly-used training/testing approaches are discussed and compared to the exact confidence intervals. MATLAB software implementing the estimators described in this work is publicly available at http://code.google.com/p/iqmodelo/.

Nonparametric estimation receiver operating characteristic analysis for performance evaluation on combined detection and estimation tasks.

In an effort to generalize task-based assessment beyond traditional signal detection, there is a growing interest in performance evaluation for combined detection and estimation tasks, in which signal parameters, such as size, orientation, and contrast are unknown and must be estimated. One motivation for studying such tasks is their rich complexity, which offers potential advantages for imaging system optimization. To evaluate observer performance on combined detection and estimation tasks, Clarkson introduced the estimation receiver operating characteristic (EROC) curve and the area under the EROC curve as a summary figure of merit. This work provides practical tools for EROC analysis of experimental data. In particular, we propose nonparametric estimators for the EROC curve, the area under the EROC curve, and for the variance/covariance matrix of a vector of correlated EROC area estimates. In addition, we show that reliable confidence intervals can be obtained for EROC area, and we validate these intervals with Monte Carlo simulation. Application of our methodology is illustrated with an example comparing magnetic resonance imaging [Formula: see text]-space sampling trajectories. MATLAB® software implementing the EROC analysis estimators described in this work is publicly available at http://code.google.com/p/iqmodelo/.

Multireader multicase reader studies with binary agreement data: simulation, analysis, validation, and sizing.

We treat multireader multicase (MRMC) reader studies for which a reader's diagnostic assessment is converted to binary agreement (1: agree with the truth state, 0: disagree with the truth state). We present a mathematical model for simulating binary MRMC data with a desired correlation structure across readers, cases, and two modalities, assuming the expected probability of agreement is equal for the two modalities ([Formula: see text]). This model can be used to validate the coverage probabilities of 95% confidence intervals (of [Formula: see text], [Formula: see text], or [Formula: see text] when [Formula: see text]), validate the type I error of a superiority hypothesis test, and size a noninferiority hypothesis test (which assumes [Formula: see text]). To illustrate the utility of our simulation model, we adapt the Obuchowski-Rockette-Hillis (ORH) method for the analysis of MRMC binary agreement data. Moreover, we use our simulation model to validate the ORH method for binary data and to illustrate sizing in a noninferiority setting. Our software package is publicly available on the Google code project hosting site for use in simulation, analysis, validation, and sizing of MRMC reader studies with binary agreement data.

eeDAP: An Evaluation Environment for Digital and Analog Pathology.

PURPOSE: The purpose of this work is to present a platform for designing and executing studies that compare pathologists interpreting histopathology of whole slide images (WSI) on a computer display to pathologists interpreting glass slides on an optical microscope. METHODS: Here we present eeDAP, an evaluation environment for digital and analog pathology. The key element in eeDAP is the registration of the WSI to the glass slide. Registration is accomplished through computer control of the microscope stage and a camera mounted on the microscope that acquires images of the real time microscope view. Registration allows for the evaluation of the same regions of interest (ROIs) in both domains. This can reduce or eliminate disagreements that arise from pathologists interpreting different areas and focuses the comparison on image quality. RESULTS: We reduced the pathologist interpretation area from an entire glass slide (≈10-30 mm)2 to small ROIs <(50 um)2. We also made possible the evaluation of individual cells. CONCLUSIONS: We summarize eeDAP's software and hardware and provide calculations and corresponding images of the microscope field of view and the ROIs extracted from the WSIs. These calculations help provide a sense of eeDAP's functionality and operating principles, while the images provide a sense of the look and feel of studies that can be conducted in the digital and analog domains. The eeDAP software can be downloaded from code.google.com (project: eeDAP) as Matlab source or as a precompiled stand-alone license-free application.

Utility as a rationale for choosing observer performance assessment paradigms for detection tasks in medical imaging.

PURPOSE: Studies of lesion detectability are often carried out to evaluate medical imaging technology. For such studies, several approaches have been proposed to measure observer performance, such as the receiver operating characteristic (ROC), the localization ROC (LROC), the free-response ROC (FROC), the alternative free-response ROC (AFROC), and the exponentially transformed FROC (EFROC) paradigms. Therefore, an experimenter seeking to carry out such a study is confronted with an array of choices. Traditionally, arguments for different approaches have been made on the basis of practical considerations (statistical power, etc.) or the gross level of analysis (case-level or lesion-level). This article contends that a careful consideration of utility should form the rationale for matching the assessment paradigm to the clinical task of interest. METHODS: In utility theory, task performance is commonly evaluated with total expected utility, which integrates the various event utilities against the probability of each event. To formalize the relationship between expected utility and the summary curve associated with each assessment paradigm, the concept of a "natural" utility structure is proposed. A natural utility structure is defined for a summary curve when the variables associated with the summary curve axes are sufficient for computing total expected utility, assuming that the disease prevalence is known. RESULTS: Natural utility structures for ROC, LROC, FROC, AFROC, and EFROC curves are introduced, clarifying how the utilities of correct and incorrect decisions are aggregated by summary curves. Further, conditions are given under which general utility structures for localization-based methodologies reduce to case-based assessment. CONCLUSIONS: Overall, the findings reveal how summary curves correspond to natural utility structures of diagnostic tasks, suggesting utility as a motivating principle for choosing an assessment paradigm.

New Theoretical Results on Channelized Hotelling Observer Performance Estimation with Known Difference of Class Means.

Task-based assessments of image quality constitute a rigorous, principled approach to the evaluation of imaging system performance. To conduct such assessments, it has been recognized that mathematical model observers are very useful, particularly for purposes of imaging system development and optimization. One type of model observer that has been widely applied in the medical imaging community is the channelized Hotelling observer (CHO). Since estimates of CHO performance typically include statistical variability, it is important to control and limit this variability to maximize the statistical power of image-quality studies. In a previous paper, we demonstrated that by including prior knowledge of the image class means, a large decrease in the bias and variance of CHO performance estimates can be realized. The purpose of the present work is to present refinements and extensions of the estimation theory given in our previous paper, which was limited to point estimation with equal numbers of images from each class. Specifically, we present and characterize minimum-variance unbiased point estimators for observer signal-to-noise ratio (SNR) that allow for unequal numbers of lesion-absent and lesion-present images. Building on this SNR point estimation theory, we then show that confidence intervals with exactly-known coverage probabilities can be constructed for commonly-used CHO performance measures. Moreover, we propose simple, approximate confidence intervals for CHO performance, and we show that they are well-behaved in most scenarios of interest.

A nonparametric procedure for comparing the areas under correlated LROC curves.

In contrast to the receiver operating characteristic (ROC) assessment paradigm, localization ROC (LROC) analysis provides a means to jointly assess the accuracy of localization and detection in an observer study. In a typical multireader, multicase (MRMC) evaluation, the data sets are paired so that correlations arise in observer performance both between readers and across the imaging conditions (e.g., reconstruction methods or scanning parameters) being compared. Therefore, MRMC evaluations motivate the need for a statistical methodology to compare correlated LROC curves. In this work, we suggest a nonparametric strategy for this purpose. Specifically, we find that seminal work of Sen on U-statistics can be applied to estimate the covariance matrix for a vector of LROC area estimates. The resulting covariance estimator is the LROC analog of the covariance estimator given by DeLong et al. for ROC analysis. Once the covariance matrix is estimated, it can be used to construct confidence intervals and/or confidence regions for purposes of comparing observer performance across imaging conditions. In addition, given the results of a small-scale pilot study, the covariance estimator may be used to estimate the number of images and observers needed to achieve a desired confidence interval size in a full-scale observer study. The utility of our methodology is illustrated with a human-observer LROC evaluation of three image reconstruction strategies for fan-beam x-ray computed tomography (CT).

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom.

Mathematical phantoms are essential for the development and early stage evaluation of image reconstruction algorithms in x-ray computed tomography (CT). This note offers tools for computer simulations using a two-dimensional (2D) phantom that models the central axial slice through the FORBILD head phantom. Introduced in 1999, in response to a need for a more robust test, the FORBILD head phantom is now seen by many as the gold standard. However, the simple Shepp-Logan phantom is still heavily used by researchers working on 2D image reconstruction. Universal acceptance of the FORBILD head phantom may have been prevented by its significantly higher complexity: software that allows computer simulations with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom. The tools offered here address this problem. They are designed for use with Matlab®, as well as open-source variants, such as FreeMat and Octave, which are all widely used in both academia and industry. To get started, the interested user can simply copy and paste the codes from this PDF document into Matlab® M-files.

On Efficient Assessment of Image-Quality Metrics Based on Linear Model Observers.

This paper is motivated by the problem of image-quality assessment using model observers for the purpose of development and optimization of medical imaging systems. Specifically, we present a study regarding the estimation of the receiver operating characteristic (ROC) curve for the observer and associated summary measures. This study evaluates the statistical advantage that may be gained in ROC estimates of observer performance by assuming that the difference of the class means for the observer ratings is known. Such knowledge is frequently available in image-quality studies employing known-location lesion detection tasks together with linear model observers. The study is carried out by introducing parametric point and confidence interval estimators that incorporate a known difference of class means. An evaluation of the new estimators for the area under the ROC curve establishes that a large reduction in statistical variability can be achieved through incorporation of knowledge of the difference of class means. Namely, the mean 95% AUC confidence interval length can be as much as seven times smaller in some cases. We also examine how knowledge of the difference of class means can be advantageously used to compare the areas under two correlated ROC curves, and observe similar gains.

Confidence intervals for performance assessment of linear observers.

PURPOSE: This work seeks to develop exact confidence interval estimators for figures of merit that describe the performance of linear observers, and to demonstrate how these estimators can be used in the context of x-ray computed tomography (CT). The figures of merit are the receiver operating characteristic (ROC) curve and associated summary measures, such as the area under the ROC curve. Linear computerized observers are valuable for optimization of parameters associated with image reconstruction algorithms and data acquisition geometries. They provide a means to perform assessment of image quality with metrics that account not only for shift-variant resolution and nonstationary noise but that are also task-based. METHODS: We suppose that a linear observer with fixed template has been defined and focus on the problem of assessing the performance of this observer for the task of deciding if an unknown lesion is present at a specific location. We introduce a point estimator for the observer signal-to-noise ratio (SNR) and identify its sampling distribution. Then, we show that exact confidence intervals can be constructed from this distribution. The sampling distribution of our SNR estimator is identified under the following hypotheses: (i) the observer ratings are normally distributed for each class of images and (ii) the variance of the observer ratings is the same for each class of images. These assumptions are, for example, appropriate in CT for ratings produced by linear observers applied to low-contrast lesion detection tasks. RESULTS: Unlike existing approaches to the estimation of ROC confidence intervals, the new confidence intervals presented here have exactly known coverage probabilities when our data assumptions are satisfied. Furthermore, they are applicable to the most commonly used ROC summary measures, and they may be easily computed (a computer routine is supplied along with this article on the Medical Physics Website). The utility of our exact interval estimators is demonstrated through an image quality evaluation example using real x-ray CT images. Also, strong robustness is shown to potential deviations from the assumption that the ratings for the two classes of images have equal variance. Another aspect of our interval estimators is the fact that we can calculate their mean length exactly for fixed parameter values, which enables precise investigations of sampling effects. We demonstrate this aspect by exploring the potential reduction in statistical variability that can be gained by using additional images from one class, if such images are readily available. We find that when additional images from one class are used for an ROC study, the mean AUC confidence interval length for our estimator can decrease by as much as 35%. CONCLUSIONS: We have shown that exact confidence intervals can be constructed for ROC curves and for ROC summary measures associated with fixed linear computerized observers applied to binary discrimination tasks at a known location. Although our intervals only apply under specific conditions, we believe that they form a valuable tool for the important problem of optimizing parameters associated with image reconstruction algorithms and data acquisition geometries, particularly in x-ray CT.

Line plus arc source trajectories and their R-line coverage for long-object cone-beam imaging with a C-arm system.

Cone-beam imaging with C-arm systems has become a valuable tool in interventional radiology. Currently, a simple circular trajectory is used, but future applications should use more sophisticated source trajectories, not only to avoid cone-beam artifacts but also to allow extended volume imaging. One attractive strategy to achieve these two goals is to use a source trajectory that consists of two parallel circular arcs connected by a line segment, possibly with repetition. In this work, we address the question of R-line coverage for such a trajectory. More specifically, we examine to what extent R-lines for such a trajectory cover a central cylindrical region of interest (ROI). An R-line is a line segment connecting any two points on the source trajectory. Knowledge of R-line coverage is crucial because a general theory for theoretically exact and stable image reconstruction from axially truncated data is only known for the points in the scanned object that lie on R-lines. Our analysis starts by examining the R-line coverage for the elemental trajectories consisting of (i) two parallel circular arcs and (ii) a circular arc connected orthogonally to a line segment. Next, we utilize our understanding of the R-lines for the aforementioned elemental trajectories to determine the R-line coverage for the trajectory consisting of two parallel circular arcs connected by a tightly fit line segment. For this trajectory, we find that the R-line coverage is insufficient to completely cover any central ROI. Because extension of the line segment beyond the circular arcs helps to increase the R-line coverage, we subsequently propose a trajectory composed of two parallel circular arcs connected by an extended line. We show that the R-lines for this trajectory can fully cover a central ROI if the line extension is long enough. Our presentation includes a formula for the minimum line extension needed to achieve full R-line coverage of an ROI with a specified size, and also includes a preliminary study on the required detector size, showing that the R-lines added by the line extension are not constraining.

Band-restricted estimation of noise variance in filtered backprojection reconstructions using repeated scans.

We introduce a new estimator for noise variance in tomographic images reconstructed using algorithms of the filtered backprojection type. The new estimator operates on data acquired from repeated scans of the object under examination, is unbiased, and is shown to have significantly lower variance than the conventional unbiased estimator for many scenarios of practical interest. We provide an extensive theoretical analysis of this estimator, highlighting the circumstances under which it is most effective. This analysis includes both general and specific data-correlation patterns. Moreover, we have applied our estimator to real X-ray computed tomography data and present preliminary results that support the theory and provide experimental evidence of the new estimator's efficacy.

Estimation of channelized hotelling observer performance with known class means or known difference of class means.

This paper concerns task-based image quality assessment for the task of discriminating between two classes of images. We address the problem of estimating two widely-used detection performance measures, SNR and AUC, from a finite number of images, assuming that the class discrimination is performed with a channelized Hotelling observer. In particular, we investigate the advantage that can be gained when either 1) the means of the signal-absent and signal-present classes are both known, or 2) when the difference of class means is known. For these two scenarios, we propose uniformly minimum variance unbiased estimators of SNR(2), derive the corresponding sampling distributions and provide variance expressions. In addition, we demonstrate how the bias and variance for the related AUC estimators may be calculated numerically by using the sampling distributions for the SNR(2) estimators. We find that for both SNR(2) and AUC, the new estimators have significantly lower bias and mean-square error than the traditional estimator, which assumes that the class means, and their difference, are unknown.