Image quality models for 2D and 3D x-ray imaging systems: A perspective vignette

Image quality models based on cascaded systems analysis and task-based imaging performance were an important aspect of the emergence of 2D and 3D digital x-ray systems over the last 25 years. This perspective vignette offers cursory review of such developments and personal insights that may not be obvious within previously published scientific literature. The vignette traces such models to the mid-1990s, when flat-panel x-ray detectors were emerging as a new base technology for digital radiography and benefited from the rigorous, objective characterization of imaging performance gained from such models. The connection of models for spatial resolution and noise to spatial-frequency-dependent descriptors of imaging task provided a useful framework for system optimization that helped to accelerate the development of new technologies to first clinical use. Extension of the models to new technologies and applications is also described, including dual-energy imaging, photon-counting detectors, phase contrast imaging, tomosynthesis, cone-beam CT, 3D image reconstruction, and image registration.

Standardization of histogram- and GLCM-based radiomics in the presence of blur and noise

Radiomics have been extensively investigated as quantitative biomarkers that can enhance the utility of imaging studies and aid the clinical decision making process. A major challenge to the clinical translation of radiomics is their variability as a result of different imaging and reconstruction protocols. In this work, we present a novel radiomics standardization framework capable of modeling and recovering the underlying radiomic feature in images that have been corrupted by the effects of spatial resolution and noise. We focus on two classes of radiomics based on pixel value distributions - i.e., histograms and gray-level co-occurrence matrices. We developed a model that predicts these distributions in the presence of system blur and noise, and used that model to invert these physical effects and recover the underlying distributions. Specifically, the effect of blur on histogram and GLCM is highly image-dependent, while additive noise convolves the histogram/GLCM of the noiseless image with those of the noise. The recovery method therefore consists of two deconvolution operations: the first in the image domain to remove the effect of system blur, the second in the histogram/GLCM domain to remove the effect of noise. The performance of the proposed recovery strategy was investigated using a set of texture phantoms and an emulated CT imaging chain with a range of realistic blur and noise levels. The proposed method was able to obtain histogram and GLCM estimates that closely resemble the ground truth. The method performed well across imaging conditions and significantly lowered the variability associated with different imaging protocols. This improvement also translated to better classification accuracy, where recovered radiomic values results in greater separation of radiomic clusters for two different texture phantoms as compared to values derived from the original blurred and noisy images. In summary, the novel radiomics standardization framework demonstrates high potential for mitigating radiomic variability as a result of the imaging system and can potentially be integrated as a preprocessing step towards more robust and reproducible radiomic models.

Statistical properties of cerebral CT perfusion imaging systems. Part II. Deconvolution-based systems

PURPOSE

The purpose of this work was to develop a theoretical framework to pinpoint the quantitative relationship between input parameters of deconvolution-based cerebral computed tomography perfusion (CTP) imaging systems and statistical properties of the output perfusion maps.

METHODS

Deconvolution-based CTP systems assume that the arterial input function, tissue enhancement curve, and flow-scaled residue function k(t) are related to each other through a convolution model, and thus by reversing the convolution operation, k(t) and the associated perfusion parameters can be estimated. The theoretical analysis started by deriving analytical formulas for the expected value and autocovariance of the residue function estimated using the singular value decomposition-based deconvolution method. Next, it analyzed statistical properties of the "max" and "arg max" operators, based on which the signal and noise properties of cerebral blood flow (CBF) and time-to-max ( t max ) are quantitatively related to the statistical model of the estimated residue function [ k * ( t ) ] and system parameters. To validate the theory, CTP images of a digital head phantom were simulated, from which signal and noise of each perfusion parameter were measured and compared with values calculated using the theoretical model. In addition, an in vivo canine experiment was performed to validate the noise model of cerebral blood volume (CBV).

RESULTS

For the numerical study, the relative root mean squared error between the measured and theoretically calculated value is ≤0.21% for the autocovariance matrix of k * ( t ) , and is ≤0.13% for the expected form of k * ( t ) . A Bland-Altman analysis demonstrated no significant difference between measured and theoretical values for the mean or noise of each perfusion parameter. For the animal study, the theoretical CBV noise fell within the 25th and 75th percentiles of the experimental values. To provide an example of the theory's utility, an expansion of the CBV noise formula was performed to unveil the dominant role of the baseline image noise in deconvolution-based CBV. Correspondingly, data of the three canine subjects used in the Part I paper were retrospectively processed to confirm that preferentially partitioning dose to the baseline frames benefits both nondeconvolution- and deconvolution-based CBV maps.

CONCLUSIONS

Quantitative relationships between the statistical properties of deconvolution-based CTP maps, source image acquisition and reconstruction parameters, contrast injection protocol, and deconvolution parameters are established.

Statistical properties of cerebral CT perfusion imaging systems. Part I. Cerebral blood volume maps generated from nondeconvolution-based systems

PURPOSE

The development and clinical employment of a computed tomography (CT) imaging system benefit from a thorough understanding of the statistical properties of the output images; cerebral CT perfusion (CTP) imaging system is no exception. A series of articles will present statistical properties of CTP systems and the dependence of these properties on system parameters. This Part I paper focuses on the signal and noise properties of cerebral blood volume (CBV) maps calculated using a nondeconvolution-based method.

METHODS

The CBV imaging chain was decomposed into a cascade of subimaging stages, which facilitated the derivation of analytical models for the probability density function, mean value, and noise variance of CBV. These models directly take CTP source image acquisition, reconstruction, and postprocessing parameters as inputs. Both numerical simulations and in vivo canine experiments were performed to validate these models.

RESULTS

The noise variance of CBV is linearly related to the noise variance of source images and is strongly influenced by the noise variance of the baseline images. Uniformly partitioning the total radiation dose budget across all time frames was found to be suboptimal, and an optimal dose partition method was derived to minimize CBV noise. Results of the numerical simulation and animal studies validated the derived statistical properties of CBV.

CONCLUSIONS

The statistical properties of CBV imaging systems can be accurately modeled by extending the linear CT systems theory. Based on the statistical model, several key signal and noise characteristics of CBV were identified and an optimal dose partition method was developed to improve the image quality of CBV.

Cascaded systems analysis of shift-variant image quality in slit-scanning breast tomosynthesis

PURPOSE

Digital breast tomosynthesis (DBT) is becoming an important part of breast cancer screening and diagnosis. Compared to two-dimensional mammography, tomosynthesis introduces limited three-dimensional (3D) resolution, but maintains high in-plane resolution, low dose, and allows for similar clinical protocols. The scanning motion and oblique projections of tomosynthesis acquisitions introduce shift-variance to the image quality, in addition to effects such as source blurring and geometric magnification. Shift-variant detector response caused by oblique incidence has been extensively studied previously and is most easily mitigated by letting the source and detector move in sync. In addition, conical reconstruction grids, that is, a grid aligned with the central tomosynthesis projection, have been proposed to compensate for magnification effects. This paper introduces a shift-variant cascaded systems model for tomosynthesis and validates it against measurements. As an example, the model was used to investigate the shift-variance of a tomosynthesis system.

METHODS

The shift-variant cascaded systems model was validated on a slit-scanning photon-counting DBT system, with synchronous source-detector movement, using simple back-projection in a conical reconstruction volume. The modulation transfer function (MTF), normalized noise-power spectrum (NNPS), and detective quantum efficiency (DQE) were used as figures of merit. Simulations were performed for single points while measurements were done over a finite volume, assuming local shift invariance. To investigate the full extent of shift-variance, 80 locations across the volume were simulated, and the MTF and DQE at 2.5 lp/mm were calculated as a function of position.

RESULTS

The simulated metrics generally agreed well with their corresponding measurements. The frequency at 50% MTF along the scan direction showed a relatively small variation, ranging from 2.1 to 2.4 lp/mm for the different locations. The frequency at 50% MTF along the chest-mammilla direction showed a larger variation, ranging from 2.9 to 3.8 lp/mm. All points exhibited a similarly shaped NNPS but the noise magnitude varied with slice height. The zero-frequency DQE in reconstructed slices was lower than that of the projections, an effect likely caused by noise-aliasing increasing the zero-frequency noise.

CONCLUSIONS

A shift-variant cascaded systems model has been developed for slit-scanning tomosynthesis using simple back-projection. The model was successfully validated against measurements. Even though the study was performed on a slit-scanning system, several parts of the framework can be applied and extended to other tomosynthesis geometries. The conical reconstruction grid has low variation in image quality in the scan direction where the 3D information is acquired, but source and geometric magnification still dominate in the slit direction, causing a larger variation in image quality. We conclude that image quality is close to shift-invariant in the scan direction, but not in the height and chest-mammilla directions, and we recommend that small measurement volumes are used when measuring image quality in these directions to minimize the effects of shift variance.

Impact of anti-charge sharing on the zero-frequency detective quantum efficiency of CdTe-based photon counting detector system: cascaded systems analysis and experimental validation

Inter-pixel communication and anti-charge sharing (ACS) technologies have been introduced to photon counting detector (PCD) systems to address the undesirable charge sharing problem. In addition to improving the energy resolution of PCD, ACS may also influence other aspects of PCD performance such as detector multiplicity (i.e. the number of pixels triggered by each interacted photon) and detective quantum efficiency (DQE). In this work, a theoretical model was developed to address how ACS impacts the multiplicity and zero-frequency DQE [DQE(0)] of PCD systems. The work focused on cadmium telluride (CdTe)-based PCD that often involves the generation and transport of K-fluorescence photons. Under the parallel cascaded systems analysis framework, the theory takes both photoelectric and scattering effects into account, and it also considers both the reabsorption and escape of photons. In a new theoretical treatment of ACS, it was considered as a modified version of the conventional single pixel (i.e. non-ACS) mode, but with reduced charge spreading distance and K-fluorescence travel distance. The proposed theoretical model does not require prior knowledge of the detailed ACS implementation method for each specific PCD, and its parameters can be experimentally determined using a radioisotope without invoking any Monte-Carlo simulation. After determining the model parameters, independent validation experiments were performed using a diagnostic x-ray tube and four different polychromatic beams (from 50 to 120 kVp). Both the theoretical and experimental results demonstrate that ACS increased the first and second moments of multiplicity for a majority of the x-ray energy and threshold levels tested, except when the threshold level was much lower than the x-ray energy level. However, ACS always improved DQE(0) at all energy and threshold levels tested.

Signal and noise characteristics of a CdTe-based photon counting detector: Cascaded systems analysis and experimental studies

Recent advances in single photon counting detectors (PCDs) are opening up new opportunities in medical imaging. However, the performance of PCDs is not flawless. Problems such as charge sharing may deteriorate the performance of PCD. This work studied the dependence of the signal and noise properties of a cadmium telluride (CdTe)-based PCD on the charge sharing effect and the anti-charge sharing (ACS) capability offered by the PCD. Through both serial and parallel cascaded systems analysis, a theoretical model was developed to trace the origin of charge sharing in CdTe-based PCD, which is primarily related to remote k-fluorescence re-absorption and spatial spreading of charge cloud. The ACS process was modeled as a sub-imaging state prior to the energy thresholding stage, and its impact on the noise power spectrum (NPS) of PCD can be qualitatively determined by the theoretical model. To validate the theoretical model, experimental studies with a CdTe-based PCD system (XC-FLITE X1, XCounter AB) was performed. Two x-ray radiation conditions, including an RQA-5 beam and a 40 kVp beam, were used for the NPS measurements. Both theoretical predictions and experimental results showed that ACS makes the NPS of the CdTe-based PCD flatter, which corresponds to reduced noise correlation length. The flatness of the NPS is further boosted by increasing the energy threshold or reducing the x-ray energy, both of which reduce the likelihood of registering multiple counts from the same incidenting x-ray photon.

Task-driven image acquisition and reconstruction in cone-beam CT

This work introduces a task-driven imaging framework that incorporates a mathematical definition of the imaging task, a model of the imaging system, and a patient-specific anatomical model to prospectively design image acquisition and reconstruction techniques to optimize task performance. The framework is applied to joint optimization of tube current modulation, view-dependent reconstruction kernel, and orbital tilt in cone-beam CT. The system model considers a cone-beam CT system incorporating a flat-panel detector and 3D filtered backprojection and accurately describes the spatially varying noise and resolution over a wide range of imaging parameters in the presence of a realistic anatomical model. Task-based detectability index (d') is incorporated as the objective function in a task-driven optimization of image acquisition and reconstruction techniques. The orbital tilt was optimized through an exhaustive search across tilt angles ranging ± 30°. For each tilt angle, the view-dependent tube current and reconstruction kernel (i.e. the modulation profiles) that maximized detectability were identified via an alternating optimization. The task-driven approach was compared with conventional unmodulated and automatic exposure control (AEC) strategies for a variety of imaging tasks and anthropomorphic phantoms. The task-driven strategy outperformed the unmodulated and AEC cases for all tasks. For example, d' for a sphere detection task in a head phantom was improved by 30% compared to the unmodulated case by using smoother kernels for noisy views and distributing mAs across less noisy views (at fixed total mAs) in a manner that was beneficial to task performance. Similarly for detection of a line-pair pattern, the task-driven approach increased d' by 80% compared to no modulation by means of view-dependent mA and kernel selection that yields modulation transfer function and noise-power spectrum optimal to the task. Optimization of orbital tilt identified the tilt angle that reduced quantum noise in the region of the stimulus by avoiding highly attenuating anatomical structures. The task-driven imaging framework offers a potentially valuable paradigm for prospective definition of acquisition and reconstruction protocols that improve task performance without increase in dose.

Cascaded systems analysis of photon counting detectors

PURPOSE

Photon counting detectors (PCDs) are an emerging technology with applications in spectral and low-dose radiographic and tomographic imaging. This paper develops an analytical model of PCD imaging performance, including the system gain, modulation transfer function (MTF), noise-power spectrum (NPS), and detective quantum efficiency (DQE).

METHODS

A cascaded systems analysis model describing the propagation of quanta through the imaging chain was developed. The model was validated in comparison to the physical performance of a silicon-strip PCD implemented on an experimental imaging bench. The signal response, MTF, and NPS were measured and compared to theory as a function of exposure conditions (70 kVp, 1-7 mA), detector threshold, and readout mode (i.e., the option for coincidence detection). The model sheds new light on the dependence of spatial resolution, charge sharing, and additive noise effects on threshold selection and was used to investigate the factors governing PCD performance, including the fundamental advantages and limitations of PCDs in comparison to energy-integrating detectors (EIDs) in the linear regime for which pulse pileup can be ignored.

RESULTS

The detector exhibited highly linear mean signal response across the system operating range and agreed well with theoretical prediction, as did the system MTF and NPS. The DQE analyzed as a function of kilovolt (peak), exposure, detector threshold, and readout mode revealed important considerations for system optimization. The model also demonstrated the important implications of false counts from both additive electronic noise and charge sharing and highlighted the system design and operational parameters that most affect detector performance in the presence of such factors: for example, increasing the detector threshold from 0 to 100 (arbitrary units of pulse height threshold roughly equivalent to 0.5 and 6 keV energy threshold, respectively), increased the f50 (spatial-frequency at which the MTF falls to a value of 0.50) by ∼30% with corresponding improvement in DQE. The range in exposure and additive noise for which PCDs yield intrinsically higher DQE was quantified, showing performance advantages under conditions of very low-dose, high additive noise, and high fidelity rejection of coincident photons.

CONCLUSIONS

The model for PCD signal and noise performance agreed with measurements of detector signal, MTF, and NPS and provided a useful basis for understanding complex dependencies in PCD imaging performance and the potential advantages (and disadvantages) in comparison to EIDs as well as an important guide to task-based optimization in developing new PCD imaging systems.

Task-based detectability in CT image reconstruction by filtered backprojection and penalized likelihood estimation

PURPOSE

Nonstationarity is an important aspect of imaging performance in CT and cone-beam CT (CBCT), especially for systems employing iterative reconstruction. This work presents a theoretical framework for both filtered-backprojection (FBP) and penalized-likelihood (PL) reconstruction that includes explicit descriptions of nonstationary noise, spatial resolution, and task-based detectability index. Potential utility of the model was demonstrated in the optimal selection of regularization parameters in PL reconstruction.

METHODS

Analytical models for local modulation transfer function (MTF) and noise-power spectrum (NPS) were investigated for both FBP and PL reconstruction, including explicit dependence on the object and spatial location. For FBP, a cascaded systems analysis framework was adapted to account for nonstationarity by separately calculating fluence and system gains for each ray passing through any given voxel. For PL, the point-spread function and covariance were derived using the implicit function theorem and first-order Taylor expansion according to Fessler ["Mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Trans. Image Process. 5(3), 493-506 (1996)]. Detectability index was calculated for a variety of simple tasks. The model for PL was used in selecting the regularization strength parameter to optimize task-based performance, with both a constant and a spatially varying regularization map.

RESULTS

Theoretical models of FBP and PL were validated in 2D simulated fan-beam data and found to yield accurate predictions of local MTF and NPS as a function of the object and the spatial location. The NPS for both FBP and PL exhibit similar anisotropic nature depending on the pathlength (and therefore, the object and spatial location within the object) traversed by each ray, with the PL NPS experiencing greater smoothing along directions with higher noise. The MTF of FBP is isotropic and independent of location to a first order approximation, whereas the MTF of PL is anisotropic in a manner complementary to the NPS. Task-based detectability demonstrates dependence on the task, object, spatial location, and smoothing parameters. A spatially varying regularization "map" designed from locally optimal regularization can improve overall detectability beyond that achievable with the commonly used constant regularization parameter.

CONCLUSIONS

Analytical models for task-based FBP and PL reconstruction are predictive of nonstationary noise and resolution characteristics, providing a valuable framework for understanding and optimizing system performance in CT and CBCT.

Modeling and Control of Nonstationary Noise Characteristics in Filtered-Backprojection and Penalized Likelihood Image Reconstruction

Purpose

Nonstationarity of CT noise presents a major challenge to the assessment of image quality. This work presents models for imaging performance in both filtered backprojection (FBP) and penalized likelihood (PL) reconstruction that describe not only the dependence on the imaging chain but also the dependence on the object as well as the nonstationary characteristics of the signal and noise. The work furthermore demonstrates the ability to impart control over the imaging process by adjusting reconstruction parameters to exploit nonstationarity in a manner advantageous to a particular imaging task.

Methods

A cascaded systems analysis model was used to model the local noise-power spectrum (NPS) and modulation transfer function (MTF) for FBP reconstruction, with locality achieved by separate calculation of fluence and system gain for each view as a function of detector location. The covariance and impulse response function for PL reconstruction (quadratic penalty) were computed using the implicit function theorem and Taylor expansion. Detectability index was calculated under the assumption of local stationarity to show the variation in task-dependent image quality throughout the image for simple and complex, heterogeneous objects. Control of noise magnitude and correlation was achieved by applying a spatially varying roughness penalty in PL reconstruction in a manner that improved overall detectability.

Results

The models provide a foundation for task-based imaging performance assessment in FBP and PL image reconstruction. For both FBP and PL, noise is anisotropic and varies in a manner dependent on the path length of each view traversing the object. The anisotropy in turn affects task performance, where detectability is enhanced or diminished depending on the frequency content of the task relative to that of the NPS. Spatial variation of the roughness penalty can be exploited to control noise magnitude and correlation (and hence detectability).

Conclusions

Nonstationarity of image noise is a significant effect that can be modeled in both FBP and PL image reconstruction. Prevalent spatial-frequency-dependent metrics of spatial resolution and noise can be analyzed under assumptions of local stationarity, providing a means to analyze imaging performance as a function of location throughout the image. Knowledgeable selection of a spatially-varying roughness penalty in PL can potentially improve local noise and spatial resolution in a manner tuned to a particular imaging task.

Theoretical Framework for the Dual-Energy Cone-Beam CT Noise-Power Spectrum, NEQ, and Tasked-Based Detectability Index

The optimization of dual-energy computed tomography (DE-CT) is challenged by the lack of a theoretical foundation for image quality. This work reports a cascaded systems analysis model that was used to derive signal and noise propagation in DE-CBCT in prevalent Fourier metrics such as the noise-power spectrum (NPS) and noise-equivalent quanta (NEQ). The model was validated in comparison to measurements of the 3D NPS and NEQ in DE-CBCT images acquired using an experimental imaging bench. Task-based detectability index was derived using DE-NPS and NEQ as an objective function in optimizing DE imaging parameters such as the dose allocation factor (D_A) and kVp pair. The resulting dose allocation optimization is in agreement with the practice of assigning more dose to the high-energy image (D_A < 0.5), and the model provides a quantitative basis for examining the optimal dose allocation as a function of total dose, kVp pair, the presence of electronics noise, and the imaging task. An example optimization is shown for a breast tumor detection task. Using DE decomposition to cancel fibroglandular tissue (rendering a DE-CBCT image of breast tumor against an adipose tissue background) and assuming a total dose of 15mGy, the optimal kVp pair is identified at [45, 105]kVp with D_A=0.46. The model is sufficiently general for applications beyond this example, demonstrating utility in the optimization in a broad range of imaging parameters. The model provides a new, valuable framework for understanding the theoretical limits of DE-CBCT imaging performance and maximizing image quality while minimizing radiation dose.

Task-based modeling and optimization of a cone-beam CT scanner for musculoskeletal imaging

PURPOSE

This work applies a cascaded systems model for cone-beam CT imaging performance to the design and optimization of a system for musculoskeletal extremity imaging. The model provides a quantitative guide to the selection of system geometry, source and detector components, acquisition techniques, and reconstruction parameters.

METHODS

The model is based on cascaded systems analysis of the 3D noise-power spectrum (NPS) and noise-equivalent quanta (NEQ) combined with factors of system geometry (magnification, focal spot size, and scatter-to-primary ratio) and anatomical background clutter. The model was extended to task-based analysis of detectability index (d') for tasks ranging in contrast and frequency content, and d' was computed as a function of system magnification, detector pixel size, focal spot size, kVp, dose, electronic noise, voxel size, and reconstruction filter to examine trade-offs and optima among such factors in multivariate analysis. The model was tested quantitatively versus the measured NPS and qualitatively in cadaver images as a function of kVp, dose, pixel size, and reconstruction filter under conditions corresponding to the proposed scanner.

RESULTS

The analysis quantified trade-offs among factors of spatial resolution, noise, and dose. System magnification (M) was a critical design parameter with strong effect on spatial resolution, dose, and x-ray scatter, and a fairly robust optimum was identified at M ∼ 1.3 for the imaging tasks considered. The results suggested kVp selection in the range of ∼65-90 kVp, the lower end (65 kVp) maximizing subject contrast and the upper end maximizing NEQ (90 kVp). The analysis quantified fairly intuitive results-e.g., ∼0.1-0.2 mm pixel size (and a sharp reconstruction filter) optimal for high-frequency tasks (bone detail) compared to ∼0.4 mm pixel size (and a smooth reconstruction filter) for low-frequency (soft-tissue) tasks. This result suggests a specific protocol for 1 × 1 (full-resolution) projection data acquisition followed by full-resolution reconstruction with a sharp filter for high-frequency tasks along with 2 × 2 binning reconstruction with a smooth filter for low-frequency tasks. The analysis guided selection of specific source and detector components implemented on the proposed scanner. The analysis also quantified the potential benefits and points of diminishing return in focal spot size, reduced electronic noise, finer detector pixels, and low-dose limits of detectability. Theoretical results agreed quantitatively with the measured NPS and qualitatively with evaluation of cadaver images by a musculoskeletal radiologist.

CONCLUSIONS

A fairly comprehensive model for 3D imaging performance in cone-beam CT combines factors of quantum noise, system geometry, anatomical background, and imaging task. The analysis provided a valuable, quantitative guide to design, optimization, and technique selection for a musculoskeletal extremities imaging system under development.

Anatomical background and generalized detectability in tomosynthesis and cone-beam CT

PURPOSE

Anatomical background presents a major impediment to detectability in 2D radiography as well as 3D tomosynthesis and cone-beam CT (CBCT). This article incorporates theoretical and experimental analysis of anatomical background "noise" in cascaded systems analysis of 2D and 3D imaging performance to yield "generalized" metrics of noise-equivalent quanta (NEQ) and detectability index as a function of the orbital extent of the (circular arc) source-detector orbit.

METHODS

A physical phantom was designed based on principles of fractal self-similarity to exhibit power-law spectral density (kappa/Fbeta) comparable to various anatomical sites (e.g., breast and lung). Background power spectra [S(B)(F)] were computed as a function of source-detector orbital extent, including tomosynthesis (approximately 10 degrees -180 degrees) and CBCT (180 degrees + fan to 360 degrees) under two acquisition schemes: (1) Constant angular separation between projections (variable dose) and (2) constant total number of projections (constant dose). The resulting S(B) was incorporated in the generalized NEQ, and detectability index was computed from 3D cascaded systems analysis for a variety of imaging tasks.

RESULTS

The phantom yielded power-law spectra within the expected spatial frequency range, quantifying the dependence of clutter magnitude (kappa) and correlation (beta) with increasing tomosynthesis angle. Incorporation of S(B) in the 3D NEQ provided a useful framework for analyzing the tradeoffs among anatomical, quantum, and electronic noise with dose and orbital extent. Distinct implications are posed for breast and chest tomosynthesis imaging system design-applications varying significantly in kappa and beta, and imaging task and, therefore, in optimal selection of orbital extent, number of projections, and dose. For example, low-frequency tasks (e.g., soft-tissue masses or nodules) tend to benefit from larger orbital extent and more fully 3D tomographic imaging, whereas high-frequency tasks (e.g., microcalcifications) require careful, application-specific selection of orbital extent and number of projections to minimize negative effects of quantum and electronic noise.

CONCLUSIONS

The complex tradeoffs among anatomical background, quantum noise, and electronic noise in projection imaging, tomosynthesis, and CBCT can be described by generalized cascaded systems analysis, providing a useful framework for system design and optimization.

The Generalized NEQ and Detectability Index for Tomosynthesis and Cone-Beam CT: From Cascaded Systems Analysis to Human Observers

PURPOSE

In the early development of new imaging modalities - such as tomosynthesis and cone-beam CT (CBCT) - an accurate predictive model for imaging performance is particularly valuable in identifying the physical factors that govern image quality and guiding system optimization. In this work, a task-based cascaded systems model for detectability index is proposed that describes not only the signal and noise propagation in the 2D (projection) and 3D (reconstruction) imaging chain but also the influence of background anatomical noise. The extent to which generalized detectability index provides a valid metric for imaging performance was assessed through direct comparison to human observer experiments.

METHODS

Detectability index (d') was generalized to include anatomical background noise in the same manner as the generalized noise-equivalent quanta (NEQ) proposed by Barrett et al. (Proc. SPIE Med. Imaging, Vol. 1090, 1989). Anatomical background noise was measured from a custom phantom designed to present power-law spectral density comparable to various anatomical sites (e.g., breast and lung). Theoretical calculations of d' as a function of the source-detector orbital extent (θtot) was obtained from a 3D cascaded systems analysis model for tomosynthesis and cone-beam CT (CBCT). Four model observers were considered in the calculation of d': prewhitening (PW), non-prewhitening (NPW), prewhitening with eye filter and internal noise (PWE), and non-prewhitening with eye filter and internal noise (NPWE). Human observer performance was measured from 9AFC tests for a variety of idealized imaging tasks presented within a clutter phantom. Theoretical results (d') were converted to area under the ROC curve (Az ) and compared directly to human observer performance as a function of imaging task and orbital extent.

RESULTS

Theoretical results demonstrated reasonable correspondence with human observer response for all tasks across the continuum in θtot ranging from low-angle tomosynthesis (θtot ~10°) to CBCT (θtot ~180°). Both theoretical and experimental Az were found to increase with acquisition angle, consistent with increased rejection of out-of-plane clutter for larger tomosynthesis angle. Of the four theoretical model observers considered, the prewhitening models tended to overestimate real observer performance, while the non-prewhitening models demonstrated reasonable agreement.

CONCLUSIONS

Generalized detectability index was shown to provide a meaningful metric for imaging performance, helping to bridge the gap between real observer performance and prevalent Fourier-based metrics based in first principles of spatial-frequency-dependent NEQ and imaging task.