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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., (© 2019 American Association of Physicists in Medicine.)

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., (© 2019 American Association of Physicists in Medicine.)

Computed tomography (CT) is widely used in medical diagnosis and non-destructive detection. Image reconstruction in CT aims to accurately recover pixel values from measured line integrals, i.e., the summed pixel values along straight lines. Provided that the acquired data satisfy the data sufficiency condition as well as other conditions regarding the view angle sampling interval and the severity of transverse data truncation, researchers have discovered many solutions to accurately reconstruct the image. However, if these conditions are violated, accurate image reconstruction from line integrals remains an intellectual challenge. In this paper, a deep learning method with a common network architecture, termed iCT-Net, was developed and trained to accurately reconstruct images for previously solved and unsolved CT reconstruction problems with high quantitative accuracy. Particularly, accurate reconstructions were achieved for the case when the sparse view reconstruction problem (i.e., compressed sensing problem) is entangled with the classical interior tomographic problems.

While CTA is an established clinical gold standard for imaging large cerebral arteries and veins, an important challenge that currently remains for CTA is its limited performance in imaging small perforating arteries with diameters below 0.5 mm. The purpose of this work was to theoretically and experimentally study the potential benefits of using photon counting detector (PCD)-based CT (PCCT) to improve the performance of CTA in imaging these small arteries. In particular, the study focused on an important component of the CTA image package known as the maximum intensity projection (MIP) image. To help understand how the physical properties of a detector quantitatively influence the MIP image quality, a theoretical model on the statistical properties of MIP images was developed. After validating this model, it was used to explore the individual and joint contribution of the following detector properties to the MIP signal-to-noise ratio (SNR): inter-slice noise covariance, spatial resolution along the z direction, and native pixel pitch along z. The model demonstrated that superior slice sensitivity, reduced inter-slice noise correlation, and smaller native pixel pitch along z provided by PCDs lead to improved vessel SNR in MIP images. Finally, experiments were performed by scanning an anthropomorphic cerebral angiographic phantom using a benchtop PCCT system and a commercial MDCT system. The experimental MIP results consistently demonstrated that compared with MDCT, PCCT provides superior vessel conspicuity and reduced artifactual stenosis.

Current computed tomography (CT) image reconstruction methods generally assume that a complete and consistent data set was acquired during data acquisition. In practice, however, the acquired data are often not consistent from one view angle to another. In this case, the application of a well-developed image reconstruction algorithm to an inconsistent data set still generates artifacts in the reconstructed images. Therefore, it is highly desirable to develop a simple method to classify the acquired data set into several consistency classes and to incorporate the data consistency information into an image reconstruction framework to simultaneously reconstruct several sub-images of the same image object according to the data consistency level of the acquired data set. In this paper, an empirical data inconsistency metric (DIM) was introduced to characterize the inconsistency level of the acquired cone beam CT projection data at each view angle caused by the polychromatic X-ray spectrum and the use of tube potential modulation. The entire acquired data set is then sorted into several subsets of view angles based upon the value of the DIM at each view angle. After data classification, the previously published algorithm, synchronized multiartifact reduction with tomographic reconstruction, was applied to simultaneously reconstruct images for these sub-images in different spectral consistency classes. Each sub-image is consistent with the subset of the projection view angles for a given range of DIM values. To validate the method, numerical simulation studies from an anthropomorphic numerical phantom, a hybrid phantom of known truth with human anatomy, and in vivo human subject data were conducted to demonstrate the practical utility of the proposed method.

In a recently published paper by Li et al (2018 Phys. Med. Biol. 63 075001), reconstruction parameters were optimized for the so-called synchronized multiArtifact reduction with tomographic reconstruction (SMART-RECON) method to enable time-resolved Cone beam computed tomography angiography (TR-CBCTA) from a single short-scan CBCT data set. However, the paper did not quantitatively address how much temporal resolution can be improved by using the SMART-RECON algorithm in TR-CBCTA. The purpose of this note was to present a method to quantify this temporal resolution improvement factor and to use that method to quantify the improvement in temporal resolution using SMART-RECON and optimized reconstruction parameters. In the method proposed in this note, the potential temporal blurring caused by SMART-RECON was modeled as a convolution between a temporal Gaussian blurring kernel and the ground truth temporal enhancement curve. The width parameter of the resulting Gaussian blurring kernel was used as a surrogate metric for temporal resolution to quantify the achievable temporal resolution for the conventional filtered backprojection (FBP) and SMART-RECON methods. The ratio of the surrogate temporal resolutions for the two reconstruction methods was calculated to quantify the factor of temporal resolution improvement. The quantitative results show that the temporal resolution is improved by a factor of 4.5 using SMART-RECON compared with FBP.

Given that the computed tomography (CT) reconstruction algorithm based on compressed sensing (CS) results in blurred edges, we propose a modified Canny operator that assists the CS algorithm to accurately capture an object's edge, to preserve and further enhance the contrasts in the reconstructed image, thereby improving image quality. We modified two procedures of the traditional Canny operator, namely non-maximum suppression and edge tracking by hysteresis according to the characteristics of low-dose CT reconstruction, and proposed two major modifications: double-response edge detection and directional edge tracking. The newly modified Canny operator was combined with the CS reconstruction algorithm to become an edge-enhanced CS (EECS). Both a 2D Shepp-Logan phantom and a 3D dental phantom were used to conduct reconstruction testing. Root-mean-square error, peak signal-to-noise ratio, and universal quality index were employed to verify the reconstruction results. Qualitative and quantitative results of EECS reconstruction showed its superiority over conventional CS or CS combined with different edge detection techniques, such as Laplacian, Prewitt, Sobel operators, etc. The experiments verified that the proposed modified Canny operator is able to effectively detect the edge location of an object during low-dose reconstruction, enabling EECS to reconstruct images with better quality than those produced by other algorithms.

Purpose: Digital breast tomosynthesis (DBT) has been shown to somewhat alleviate the breast tissue overlapping issues of two-dimensional (2D) mammography. However, the improvement in current DBT systems over mammography is still limited. Statistical image reconstruction (SIR) methods have the potential to reduce through-plane artifacts in DBT, and thus may be used to further reduce anatomical clutter. The purpose of this work was to study the impact of SIR on anatomical clutter in the reconstructed DBT image volumes., Methods: An SIR with a slice-wise total variation (TV) regularizer was implemented to reconstruct DBT images which were compared with the clinical reconstruction method (filtered backprojection). The artifact spread function (ASF) was measured to quantify the reduction of the through-plane artifacts level in phantom studies and microcalcifications in clinical cases. The anatomical clutter was quantified by the anatomical noise power spectrum with a power law fitting model: NPS a ( f) = α f -β . The β values were measured from the reconstructed image slices when the two reconstruction methods were applied to a cohort of clinical breast exams (N = 101) acquired using Hologic Selenia Dimensions DBT systems., Results: The full width half maximum (FWHM) of the measured ASF was reduced from 8.7 ± 0.1 mm for clinical reconstruction to 6.5 ± 0.1 mm for SIR which yields a 25% reduction in FWHM in phantom studies and the same amount of ASF reduction was also found in clinical measurements from microcalcifications. The measured β values for the two reconstruction methods were 3.17 ± 0.36 and 2.14 ± 0.39 for the clinical reconstruction method and the SIR method, respectively. This difference was statistically significant (P << 0.001). The dependence of β on slice location using either method was negligible., Conclusions: Statistical image reconstruction enabled a significant reduction of both the through-plane artifacts level and anatomical clutter in the DBT reconstructions. The β value was found to be β≈2.14 with the SIR method. This value stays in the middle between the β≈1.8 for cone beam CT and β≈3.2 for mammography. In contrast, the measured β value in the clinical reconstructions (β≈3.17) remains close to that of mammography., (© 2018 American Association of Physicists in Medicine.)

Purpose: Different low-signal correction (LSC) methods have been shown to efficiently reduce noise streaks and noise level in CT to provide acceptable images at low-radiation dose levels. These methods usually result in CT images with highly shift-variant and anisotropic spatial resolution and noise, which makes the parameter optimization process highly nontrivial. The purpose of this work was to develop a local task-based parameter optimization framework for LSC methods., Methods: Two well-known LSC methods, the adaptive trimmed mean (ATM) filter and the anisotropic diffusion (AD) filter, were used as examples to demonstrate how to use the task-based framework to optimize filter parameter selection. Two parameters, denoted by the set P, for each LSC method were included in the optimization problem. For the ATM filter, these parameters are the low- and high-signal threshold levels p l and p h ; for the AD filter, the parameters are the exponents δ and γ in the brightness gradient function. The detectability index d' under the non-prewhitening (NPW) mathematical observer model was selected as the metric for parameter optimization. The optimization problem was formulated as an unconstrained optimization problem that consisted of maximizing an objective function d'(P), where i and j correspond to the i-th imaging task and j-th spatial location, respectively. Since there is no explicit mathematical function to describe the dependence of d' on the set of parameters P for each LSC method, the optimization problem was solved via an experimentally measured d' map over a densely sampled parameter space. In this work, three high-contrast-high-frequency discrimination imaging tasks were defined to explore the parameter space of each of the LSC methods: a vertical bar pattern (task I), a horizontal bar pattern (task II), and a multidirectional feature (task III). Two spatial locations were considered for the analysis, a posterior region-of-interest (ROI) located within the noise streaks region and an anterior ROI, located further from the noise streaks region. Optimal results derived from the task-based detectability index metric were compared to other operating points in the parameter space with different noise and spatial resolution trade-offs., Results: The optimal operating points determined through the d' metric depended on the interplay between the major spatial frequency components of each imaging task and the highly shift-variant and anisotropic noise and spatial resolution properties associated with each operating point in the LSC parameter space. This interplay influenced imaging performance the most when the major spatial frequency component of a given imaging task coincided with the direction of spatial resolution loss or with the dominant noise spatial frequency component; this was the case of imaging task II. The performance of imaging tasks I and III was influenced by this interplay in a smaller scale than imaging task II, since the major frequency component of task I was perpendicular to imaging task II, and because imaging task III did not have strong directional dependence. For both LSC methods, there was a strong dependence of the overall d' magnitude and shape of the contours on the spatial location within the phantom, particularly for imaging tasks II and III. The d' value obtained at the optimal operating point for each spatial location and imaging task was similar when comparing the LSC methods studied in this work., Conclusions: A local task-based detectability framework to optimize the selection of parameters for LSC methods was developed. The framework takes into account the potential shift-variant and anisotropic spatial resolution and noise properties to maximize the imaging performance of the CT system. Optimal parameters for a given LSC method depend strongly on the spatial location within the image object., (© 2018 American Association of Physicists in Medicine.)

Purpose: Low-signal correction (LSC) in the raw counts domain has been shown to effectively reduce noise streaks in CT because the data inconsistency associated with photon-starved regions may be mitigated prior to the log transformation step. However, a systematic study of the performance of these raw data correction methods is still missing in literature. The purpose of this work was to provide such a systematic study for two well-known low-signal correction schemes using either the adaptive trimmed mean (ATM) filter or the anisotropic diffusion (AD) filter in the raw counts domain., Methods: Image data were acquired experimentally using an anthropomorphic chest phantom and a benchtop cone-beam CT (CBCT) imaging system. Phantom scans were repeated 50 times at a reduced dose level of 0.5 mGy and a reference level of 1.9 mGy. The measured raw counts at 0.5 mGy underwent LSC using the ATM and AD filters. Two relevant parameters were identified for each filter and approximately one hundred operating points in each parameter space were analyzed. Following LSC and log transformation, FDK reconstruction was performed for each case. Noise and spatial resolution properties were assessed across the parameter spaces that define each LSC filter; the results were summarized through 2D contour maps to better understand the trade-offs between these competing image quality features. 2D noise power spectrum (NPS) and modulation transfer function (MTF) were measured locally at two spatial locations in the field-of-view (FOV): a posterior region contaminated by noise streaks and an anterior region away from noise streaks. An isotropy score metric was introduced to characterize the directional dependence of the NPS and MTF (viz., ϵ NPS and ϵ MTF , respectively), with a range from 0 for highly anisotropic to 1 for perfectly isotropic. The noise magnitude and coarseness were also measured., Results: (a) Both the ATM and AD LSC methods were successful in reducing noise streaks, but their noise and spatial resolution properties were found to be highly anisotropic and shift-variant. (b) NPS isotropy scores in the posterior region were generally improved from ϵ NPS = 0.09 for the images without LSC to the range ϵ NPS = (0.11, 0.67) for ATM and ϵ NPS = (0.06, 0.67) for AD, depending on the filter parameters used. (c) The noise magnitude was reduced across the parameter space of either LSC filter whenever a change along the axis of the controlling parameter led to stronger raw data filtration. Changes in noise magnitude were inversely related to changes in spatial resolution along the direction perpendicular to the streaks. No correlation was found, however, between the contour maps of noise magnitude and the NPS isotropy. (d) Both filters influenced the noise coarseness anisotropically, with coarser noise occurring along directions perpendicular to the noise streaks. The anisotropic noise coarseness was intrinsically and directly related to resolution losses in a given direction: coarseness plots mimic the topography of the 2D MTF, i.e., the coarser the noise, the lower the resolution., Conclusions: Both AD and ATM LSC schemes enable low-dose CBCT imaging. However, it was found that noise magnitude and overall spatial resolution vary considerably across the parameter space for each filter, and more importantly these image quality features are highly anisotropic and shift-variant., (© 2018 American Association of Physicists in Medicine.)

Time-resolved C-arm cone-beam CT (CBCT) angiography (TR-CBCTA) images can be generated from a series of CBCT acquisitions that satisfy data sufficiency condition in analytical image reconstruction theory. In this work, a new technique was developed to generate TR-CBCTA images from a single short-scan CBCT data acquisition with contrast media injection. The reconstruction technique enabling this application is a previously developed image reconstruction technique, synchronized multi-artifact reduction with tomographic reconstruction (SMART-RECON). In this new application, the acquired short-scan CBCT projection data were sorted into a union of several sub-sectors of view angles and each sub-sector of view angles corresponds to an individual image volume to be reconstructed. The SMART-RECON method was then used to jointly reconstruct all of these individual image volumes under two constraints: (1) each individual image volume is maximally consistent with the measured cone-beam projection data within the corresponding view angle sector and (2) the nuclear norm of the image matrix is minimized. The difference between these reconstructed individual image volumes is used to generated the desired subtracted angiograms. To validate the technique, numerical simulation data generated from a fractal tree angiogram phantom were used to quantitatively study the accuracy of the proposed method and retrospective in vivo human subject studies were used to demonstrate the feasibility of generating TR-CBCTA in clinical practice.

In recent years, potential applications of energy-resolved photon counting detectors (PCDs) in the x-ray medical imaging field have been actively investigated. Unlike conventional x-ray energy integration detectors, PCDs count the number of incident x-ray photons within certain energy windows. For PCDs, the interactions between x-ray photons and photoconductor generate electronic voltage pulse signals. The pulse height of each signal is proportional to the energy of the incident photons. By comparing the pulse height with the preset energy threshold values, x-ray photons with specific energies are recorded and sorted into different energy bins. To quantitatively understand the meaning of the energy threshold values, and thus to assign an absolute energy value to each energy bin, energy calibration is needed to establish the quantitative relationship between the threshold values and the corresponding effective photon energies. In practice, the energy calibration is not always easy, due to the lack of well-calibrated energy references for the working energy range of the PCDs. In this paper, a new method was developed to use the precise knowledge of the characteristic K-edge energy of materials to perform energy calibration. The proposed method was demonstrated using experimental data acquired from three K-edge materials (viz., iodine, gadolinium, and gold) on two different PCDs (Hydra and Flite, XCounter, Sweden). Finally, the proposed energy calibration method was further validated using a radioactive isotope (Am-241) with a known decay energy spectrum.

In this paper, a newly developed statistical model-based image reconstruction [referred to as Simultaneous Multiple Artifacts Reduction in Tomographic RECONstruction (SMART-RECON)] is applied to low dose computer tomography (CT) myocardial perfusion imaging (CT-MPI). This method uses the nuclear norm of the spatial-temporal image matrix of the CT-MPI images as a regularizer, rather than a conventional spatial regularizer that incorporates image smoothness, edge preservation, or spatial sparsity into the reconstruction. In addition to providing the needed noise reduction for low-dose CT-MPI, SMART-RECON provides images with spatial resolution and noise power spectrum (NPS) properties, which are independent of contrast and dose levels. Both numerical simulations and in vivo animal studies were performed to validate the proposed method. In these studies, it was found that: 1) quantitative accuracy of perfusion maps in CT-MPI was well maintained for radiation dose level as low as 10 mAs per image frame, compared with the reference standard of 200 mAs for conventional filtered backprojection; 2) flow-occluded myocardium in the porcine heart was well delineated by SMART-RECON at 10 mAs per frame when compared with model-based image reconstruction using spatial total variation (TV) as the regularizer (referred to as TV-SIR) or spatial-temporal TV (ST-TV-SIR); the CT-MPI results were confirmed with positron-emission tomography imaging; 3) image sharpness in SMART-RECON images was nearly independent of image contrast level and radiation dose level, in stark contrast to TV-SIR and ST-TV-SIR, which displayed a strong dependence on both image contrast and radiation dose levels; and 4) the structure of the dose-normalized NPS for the SMART-RECON method did not depend on dose, while the TV-SIR and ST-TV-SIR NPS structure was dose-dependent.

Purpose: When the scan field of view (SFOV) of a CT system is not large enough to enclose the entire cross-section of the patient, or the patient needs to be positioned partially outside the SFOV for certain clinical applications, truncation artifacts often appear in the reconstructed CT images. Many truncation artifact correction methods perform extrapolations of the truncated projection data based on certain a priori assumptions. The purpose of this work was to develop a novel CT truncation artifact reduction method that directly operates on DICOM images., Materials and Methods: The blooming of pixel values associated with truncation was modeled using exponential decay functions, and based on this model, a discriminative dictionary was constructed to represent truncation artifacts and nonartifact image information in a mutually exclusive way. The discriminative dictionary consists of a truncation artifact subdictionary and a nonartifact subdictionary. The truncation artifact subdictionary contains 1000 atoms with different decay parameters, while the nonartifact subdictionary contains 1000 independent realizations of Gaussian white noise that are exclusive with the artifact features. By sparsely representing an artifact-contaminated CT image with this discriminative dictionary, the image was separated into a truncation artifact-dominated image and a complementary image with reduced truncation artifacts. The artifact-dominated image was then subtracted from the original image with an appropriate weighting coefficient to generate the final image with reduced artifacts. This proposed method was validated via physical phantom studies and retrospective human subject studies. Quantitative image evaluation metrics including the relative root-mean-square error (rRMSE) and the universal image quality index (UQI) were used to quantify the performance of the algorithm., Results: For both phantom and human subject studies, truncation artifacts at the peripheral region of the SFOV were effectively reduced, revealing soft tissue and bony structure once buried in the truncation artifacts. For the phantom study, the proposed method reduced the relative RMSE from 15% (original images) to 11%, and improved the UQI from 0.34 to 0.80., Conclusion: A discriminative dictionary representation method was developed to mitigate CT truncation artifacts directly in the DICOM image domain. Both phantom and human subject studies demonstrated that the proposed method can effectively reduce truncation artifacts without access to projection data., (© 2016 American Association of Physicists in Medicine.)

Purpose: Phantom-based objective image quality assessment methods are widely used in the medical physics community. For a filtered backprojection (FBP) reconstruction-based linear or quasilinear imaging system, the use of this methodology is well justified. Many key image quality metrics acquired with phantom studies can be directly applied to in vivo human subject studies. Recently, a variety of image quality metrics have been investigated for model-based iterative image reconstruction (MBIR) methods and several novel characteristics have been discovered in phantom studies. However, the following question remains unanswered: can certain results obtained from phantom studies be generalized to in vivo animal studies and human subject studies? The purpose of this paper is to address this question., Methods: One of the most striking results obtained from phantom studies is a novel power-law relationship between noise variance of MBIR (σ(2)) and tube current-rotation time product (mAs): σ(2) ∝ (mAs)(-0.4) [K. Li et al., "Statistical model based iterative reconstruction (MBIR) in clinical CT systems: Experimental assessment of noise performance," Med. Phys. 41, 041906 (15pp.) (2014)]. To examine whether the same power-law works for in vivo cases, experimental data from two types of in vivo studies were analyzed in this paper. All scans were performed with a 64-slice diagnostic CT scanner (Discovery CT750 HD, GE Healthcare) and reconstructed with both FBP and a MBIR method (Veo, GE Healthcare). An Institutional Animal Care and Use Committee-approved in vivo animal study was performed with an adult swine at six mAs levels (10-290). Additionally, human subject data (a total of 110 subjects) acquired from an IRB-approved clinical trial were analyzed. In this clinical trial, a reduced-mAs scan was performed immediately following the standard mAs scan; the specific mAs used for the two scans varied across human subjects and were determined based on patient size and clinical indications. The measurements of σ(2) were performed at different mAs by drawing regions-of-interest (ROIs) in the liver and the subcutaneous fat. By applying a linear least-squares regression, the β values in the power-law relationship σ(2) ∝ (mAs)(-β) were measured for the in vivo data and compared with the value found in phantom experiments., Results: For the in vivo swine study, an exponent of β = 0.43 was found for MBIR, and the coefficient of determination (R(2)) for the corresponding least-squares power-law regression was 0.971. As a reference, the β and R(2) values for FBP were found to be 0.98 and 0.997, respectively, from the same study, which are consistent with the well-known σ(2) ∝ (mAs)(-1.0) relationship for linear CT systems. For the human subject study, the measured β values for the MBIR images were 0.41 ± 0.12 in the liver and 0.37 ± 0.12 in subcutaneous fat. In comparison, the β values for the FBP images were 1.04 ± 0.10 in the liver and 0.97 ± 0.12 in subcutaneous fat. The β values of MBIR and FBP obtained from the in vivo studies were found to be statistically equivalent to the corresponding β values from the phantom study within an equivalency interval of [ - 0.1, 0.1] (p < 0.05); across MBIR and FBP, the difference in β was statistically significant (p < 0.05)., Conclusions: Despite the nonlinear nature of the MBIR method, the power-law relationship, σ(2) ∝ (mAs)(-0.4), found from phantom studies can be applied to in vivo animal and human subject studies.

The use of grating based Talbot-Lau interferometry permits the acquisition of differential phase contrast (DPC) imaging with a conventional medical x-ray source and detector. However, due to the limited area of the gratings, limited area of the detector, or both, data truncation image artifacts are often observed in tomographic DPC acquisitions and reconstructions, such as tomosynthesis (limited-angle tomography). When data are truncated in the conventional x-ray absorption tomosynthesis imaging, a variety of methods have been developed to mitigate the truncation artifacts. However, the same strategies used to mitigate absorption truncation artifacts do not yield satisfactory reconstruction results in DPC tomosynthesis reconstruction. In this work,several new methods have been proposed to mitigate data truncation artifacts in a DPC tomosynthesis system. The proposed methods have been validated using experimental data of a mammography accreditation phantom, a bovine udder, as well as several human cadaver breast specimens using a bench-top DPC imaging system at our facility.

Purpose: Wall thickness (WT) is an airway feature of great interest for the assessment of morphological changes in the lung parenchyma. Multidetector computed tomography (MDCT) has recently been used to evaluate airway WT, but the potential risk of radiation-induced carcinogenesis-particularly in younger patients-might limit a wider use of this imaging method in clinical practice. The recent commercial implementation of the statistical model-based iterative reconstruction (MBIR) algorithm, instead of the conventional filtered back projection (FBP) algorithm, has enabled considerable radiation dose reduction in many other clinical applications of MDCT. The purpose of this work was to study the impact of radiation dose and MBIR in the MDCT assessment of airway WT., Methods: An airway phantom was scanned using a clinical MDCT system (Discovery CT750 HD, GE Healthcare) at 4 kV levels and 5 mAs levels. Both FBP and a commercial implementation of MBIR (Veo(TM), GE Healthcare) were used to reconstruct CT images of the airways. For each kV-mAs combination and each reconstruction algorithm, the contrast-to-noise ratio (CNR) of the airways was measured, and the WT of each airway was measured and compared with the nominal value; the relative bias and the angular standard deviation in the measured WT were calculated. For each airway and reconstruction algorithm, the overall performance of WT quantification across all of the 20 kV-mAs combinations was quantified by the sum of squares (SSQs) of the difference between the measured and nominal WT values. Finally, the particular kV-mAs combination and reconstruction algorithm that minimized radiation dose while still achieving a reference WT quantification accuracy level was chosen as the optimal acquisition and reconstruction settings., Results: The wall thicknesses of seven airways of different sizes were analyzed in the study. Compared with FBP, MBIR improved the CNR of the airways, particularly at low radiation dose levels. For FBP, the relative bias and the angular standard deviation of the measured WT increased steeply with decreasing radiation dose. Except for the smallest airway, MBIR enabled significant reduction in both the relative bias and angular standard deviation of the WT, particularly at low radiation dose levels; the SSQ was reduced by 50%-96% by using MBIR. The optimal reconstruction algorithm was found to be MBIR for the seven airways being assessed, and the combined use of MBIR and optimal kV-mAs selection resulted in a radiation dose reduction of 37%-83% compared with a reference scan protocol with a dose level of 1 mGy., Conclusions: The quantification accuracy of airway WT is strongly influenced by radiation dose and reconstruction algorithm. The MBIR algorithm potentially allows the desired WT quantification accuracy to be achieved with reduced radiation dose, which may enable a wider clinical use of MDCT for the assessment of airway WT, particularly for younger patients who may be more sensitive to exposures with ionizing radiation.

Purpose: For a given imaging task and patient size, the optimal selection of x-ray tube potential (kV) and tube current-rotation time product (mAs) is pivotal in achieving the maximal radiation dose reduction while maintaining the needed diagnostic performance. Although contrast-to-noise (CNR)-based strategies can be used to optimize kV/mAs for computed tomography (CT) imaging systems employing the linear filtered backprojection (FBP) reconstruction method, a more general framework needs to be developed for systems using the nonlinear statistical model-based iterative reconstruction (MBIR) method. The purpose of this paper is to present such a unified framework for the optimization of kV/mAs selection for both FBP- and MBIR-based CT systems., Methods: The optimal selection of kV and mAs was formulated as a constrained optimization problem to minimize the objective function, Dose(kV,mAs), under the constraint that the achievable detectability index d'(kV,mAs) is not lower than the prescribed value of d'R for a given imaging task. Since it is difficult to analytically model the dependence of d' on kV and mAs for the highly nonlinear MBIR method, this constrained optimization problem is solved with comprehensive measurements of Dose(kV,mAs) and d'(kV,mAs) at a variety of kV-mAs combinations, after which the overlay of the dose contours and d' contours is used to graphically determine the optimal kV-mAs combination to achieve the lowest dose while maintaining the needed detectability for the given imaging task. As an example, d' for a 17 mm hypoattenuating liver lesion detection task was experimentally measured with an anthropomorphic abdominal phantom at four tube potentials (80, 100, 120, and 140 kV) and fifteen mA levels (25 and 50-700) with a sampling interval of 50 mA at a fixed rotation time of 0.5 s, which corresponded to a dose (CTDIvol) range of [0.6, 70] mGy. Using the proposed method, the optimal kV and mA that minimized dose for the prescribed detectability level of d'R=16 were determined. As another example, the optimal kV and mA for an 8 mm hyperattenuating liver lesion detection task were also measured using the developed framework. Both an in vivo animal and human subject study were used as demonstrations of how the developed framework can be applied to the clinical work flow., Results: For the first task, the optimal kV and mAs were measured to be 100 and 500, respectively, for FBP, which corresponded to a dose level of 24 mGy. In comparison, the optimal kV and mAs for MBIR were 80 and 150, respectively, which corresponded to a dose level of 4 mGy. The topographies of the iso-d' map and the iso-CNR map were the same for FBP; thus, the use of d'- and CNR-based optimization methods generated the same results for FBP. However, the topographies of the iso-d' and iso-CNR map were significantly different in MBIR; the CNR-based method overestimated the performance of MBIR, predicting an overly aggressive dose reduction factor. For the second task, the developed framework generated the following optimization results: for FBP, kV = 140, mA = 350, dose = 37.5 mGy; for MBIR, kV = 120, mA = 250, dose = 18.8 mGy. Again, the CNR-based method overestimated the performance of MBIR. Results of the preliminary in vivo studies were consistent with those of the phantom experiments., Conclusions: A unified and task-driven kV/mAs optimization framework has been developed in this work. The framework is applicable to both linear and nonlinear CT systems such as those using the MBIR method. As expected, the developed framework can be reduced to the conventional CNR-based kV/mAs optimization frameworks if the system is linear. For MBIR-based nonlinear CT systems, however, the developed task-based kV/mAs optimization framework is needed to achieve the maximal dose reduction while maintaining the desired diagnostic performance.

Purpose: To reduce radiation dose in CT imaging, the statistical model based iterative reconstruction (MBIR) method has been introduced for clinical use. Based on the principle of MBIR and its nonlinear nature, the noise performance of MBIR is expected to be different from that of the well-understood filtered backprojection (FBP) reconstruction method. The purpose of this work is to experimentally assess the unique noise characteristics of MBIR using a state-of-the-art clinical CT system., Methods: Three physical phantoms, including a water cylinder and two pediatric head phantoms, were scanned in axial scanning mode using a 64-slice CT scanner (Discovery CT750 HD, GE Healthcare, Waukesha, WI) at seven different mAs levels (5, 12.5, 25, 50, 100, 200, 300). At each mAs level, each phantom was repeatedly scanned 50 times to generate an image ensemble for noise analysis. Both the FBP method with a standard kernel and the MBIR method (Veo(®), GE Healthcare, Waukesha, WI) were used for CT image reconstruction. Three-dimensional (3D) noise power spectrum (NPS), two-dimensional (2D) NPS, and zero-dimensional NPS (noise variance) were assessed both globally and locally. Noise magnitude, noise spatial correlation, noise spatial uniformity and their dose dependence were examined for the two reconstruction methods., Results: (1) At each dose level and at each frequency, the magnitude of the NPS of MBIR was smaller than that of FBP. (2) While the shape of the NPS of FBP was dose-independent, the shape of the NPS of MBIR was strongly dose-dependent; lower dose lead to a "redder" NPS with a lower mean frequency value. (3) The noise standard deviation (σ) of MBIR and dose were found to be related through a power law of σ ∝ (dose)(-β) with the component β ≈ 0.25, which violated the classical σ ∝ (dose)(-0.5) power law in FBP. (4) With MBIR, noise reduction was most prominent for thin image slices. (5) MBIR lead to better noise spatial uniformity when compared with FBP. (6) A composite image generated from two MBIR images acquired at two different dose levels (D1 and D2) demonstrated lower noise than that of an image acquired at a dose level of D1+D2., Conclusions: The noise characteristics of the MBIR method are significantly different from those of the FBP method. The well known tradeoff relationship between CT image noise and radiation dose has been modified by MBIR to establish a more gradual dependence of noise on dose. Additionally, some other CT noise properties that had been well understood based on the linear system theory have also been altered by MBIR. Clinical CT scan protocols that had been optimized based on the classical CT noise properties need to be carefully re-evaluated for systems equipped with MBIR in order to maximize the method's potential clinical benefits in dose reduction and/or in CT image quality improvement., (© 2014 American Association of Physicists in Medicine.)

Purpose: This paper concerns the feasibility of x-ray differential phase contrast (DPC) tomosynthesis imaging using a grating-based DPC benchtop experimental system, which is equipped with a commercial digital flat-panel detector and a medical-grade rotating-anode x-ray tube. An extensive system characterization was performed to quantify its imaging performance., Methods: The major components of the benchtop system include a diagnostic x-ray tube with a 1.0 mm nominal focal spot size, a flat-panel detector with 96 μm pixel pitch, a sample stage that rotates within a limited angular span of ± 30°, and a Talbot-Lau interferometer with three x-ray gratings. A total of 21 projection views acquired with 3° increments were used to reconstruct three sets of tomosynthetic image volumes, including the conventional absorption contrast tomosynthesis image volume (AC-tomo) reconstructed using the filtered-backprojection (FBP) algorithm with the ramp kernel, the phase contrast tomosynthesis image volume (PC-tomo) reconstructed using FBP with a Hilbert kernel, and the differential phase contrast tomosynthesis image volume (DPC-tomo) reconstructed using the shift-and-add algorithm. Three inhouse physical phantoms containing tissue-surrogate materials were used to characterize the signal linearity, the signal difference-to-noise ratio (SDNR), the three-dimensional noise power spectrum (3D NPS), and the through-plane artifact spread function (ASF)., Results: While DPC-tomo highlights edges and interfaces in the image object, PC-tomo removes the differential nature of the DPC projection data and its pixel values are linearly related to the decrement of the real part of the x-ray refractive index. The SDNR values of polyoxymethylene in water and polystyrene in oil are 1.5 and 1.0, respectively, in AC-tomo, and the values were improved to 3.0 and 2.0, respectively, in PC-tomo. PC-tomo and AC-tomo demonstrate equivalent ASF, but their noise characteristics quantified by the 3D NPS were found to be different due to the difference in the tomosynthesis image reconstruction algorithms., Conclusions: It is feasible to simultaneously generate x-ray differential phase contrast, phase contrast, and absorption contrast tomosynthesis images using a grating-based data acquisition setup. The method shows promise in improving the visibility of several low-density materials and therefore merits further investigation.

By adding a Talbot-Lau interferometer to a conventional x-ray absorption computed tomography (CT) imaging system, both differential phase contrast (DPC) signal and absorption contrast signal can be simultaneously measured from the same set of CT measurements. The imaging performance of such multi-contrast x-ray CT imaging systems can be characterized with standard metrics such as noise variance, noise power spectrum, contrast-to-noise ratio, modulation transfer function (MTF), and task-based detectability index. Among these metrics, the measurement of the MTF can be challenging in DPC-CT systems due to several confounding factors such as phase wrapping and the difficulty of using fine wires as probes. To address these technical challenges, this paper discusses a viable and reliable method to experimentally measure the MTF of DPC-CT. It has been found that the spatial resolution of DPC-CT is degraded, when compared to that of the corresponding absorption CT, due to the presence of a source grating G0 in the Talbot-Lau interferometer. An effective MTF was introduced and experimentally estimated to describe the impact of the Talbot-Lau interferometer on the system MTF.

Purpose: The ionizing radiation imparted to patients during computed tomography exams is raising concerns. This paper studies the performance of a scheme called dose reduction using prior image constrained compressed sensing (DR-PICCS). The purpose of this study is to characterize the effects of a statistical model of x-ray detection in the DR-PICCS framework and its impact on spatial resolution., Methods: Both numerical simulations with known ground truth and in vivo animal dataset were used in this study. In numerical simulations, a phantom was simulated with Poisson noise and with varying levels of eccentricity. Both the conventional filtered backprojection (FBP) and the PICCS algorithms were used to reconstruct images. In PICCS reconstructions, the prior image was generated using two different denoising methods: a simple Gaussian blur and a more advanced diffusion filter. Due to the lack of shift-invariance in nonlinear image reconstruction such as the one studied in this paper, the concept of local spatial resolution was used to study the sharpness of a reconstructed image. Specifically, a directional metric of image sharpness, the so-called pseudopoint spread function (pseudo-PSF), was employed to investigate local spatial resolution., Results: In the numerical studies, the pseudo-PSF was reduced from twice the voxel width in the prior image down to less than 1.1 times the voxel width in DR-PICCS reconstructions when the statistical model was not included. At the same noise level, when statistical weighting was used, the pseudo-PSF width in DR-PICCS reconstructed images varied between 1.5 and 0.75 times the voxel width depending on the direction along which it was measured. However, this anisotropy was largely eliminated when the prior image was generated using diffusion filtering; the pseudo-PSF width was reduced to below one voxel width in that case. In the in vivo study, a fourfold improvement in CNR was achieved while qualitatively maintaining sharpness; images also had a qualitatively more uniform noise spatial distribution when including a statistical model., Conclusions: DR-PICCS enables to reconstruct CT images with lower noise than FBP and the loss of spatial resolution can be mitigated to a large extent. The introduction of statistical modeling in DR-PICCS may improve some noise characteristics, but it also leads to anisotropic spatial resolution properties. A denoising method, such as the directional diffusion filtering, has been demonstrated to reduce anisotropy in spatial resolution effectively when it was combined with DR-PICCS with statistical modeling.

Purpose: Prior image constrained compressed sensing (PICCS) is an image reconstruction framework that takes advantage of a prior image to improve the image quality of CT reconstructions. An interesting question that remains to be investigated is whether or not the introduction of a statistical model of the photon detection in the PICCS reconstruction framework can improve the performance of the algorithm when dealing with high noise projection datasets. The goal of the research presented in this paper is to characterize the noise properties of images reconstructed using PICCS with and without statistical modeling. This paper investigates these properties in the clinical context of time-resolved contrast-enhanced CT., Methods: Both numerical phantom studies and an Institutional Review Board approved human subject study were used in this research. The conventional filtered backprojection (FBP), and PICCS with and without the statistical model were applied to each dataset. The prior image used in PICCS was generated by averaging over FBP reconstructions from different time frames of the time-resolved CT exam, thus reducing the noise level. Numerical studies were used to evaluate if the noise characteristics are altered for varying levels of noise, as well as for different object shapes. The dataset acquired in vivo was used to verify that the conclusions reached from numerical studies translate adequately to a clinical case. The results were analyzed using a variety of qualitative and quantitative metrics such as the universal image quality index, spatial maps of the noise standard deviations, the noise uniformity, the noise power spectrum, and the model-observer detectability., Results: The noise characteristics of PICCS were shown to depend on the noise level contained in the data, the level of eccentricity of the object, and whether or not the statistical model was applied. Most differences in the characteristics were observed in the regime of low incident x-ray fluence. No substantial difference was observed between PICCS with and without statistics in the high fluence domain. Objects with a semi-major axis ratio below 0.85 were more accurately reconstructed with lower noise using the statistical implementation. Above that range, for mostly circular objects, the PICCS implementation without the statistical model yielded more accurate images and a lower noise level. At all levels of eccentricity, the noise spatial distribution was more uniform and the model-observer detectability was greater for PICCS with the statistical model. The human subject study was consistent with the results obtained using numerical simulations., Conclusions: For mildly eccentric objects in the low noise regime, PICCS without the noise model yielded equal or better noise level and image quality than the statistical formulation. However, in a vast majority of cases, images reconstructed using statistical PICCS have a noise power spectrum that facilitated the detection of model lesions. The inclusion of a statistical model in the PICCS framework does not always result in improved noise characteristics.

C-arm cone-beam CT could replace preoperative multi-detector CT scans in the cardiac interventional setting. However, cardiac gating results in view angle undersampling and the small size of the detector results in projection data truncation. These problems are incompatible with conventional tomographic reconstruction algorithms. In this paper, the prior image constrained compressed sensing (PICCS) reconstruction method was adapted to solve these issues. The performance of the proposed method was compared to that of FDK, FDK with extrapolated projection data (E-FDK), and total variation-based compressed sensing. A canine projection dataset acquired using a clinical C-arm imaging system supplied realistic cardiac motion and anatomy for this evaluation. Three different levels of truncation were simulated. The relative root mean squared error and the universal image quality index were used to quantify the reconstruction accuracy. Three main conclusions were reached. (1) The adapted version of the PICCS algorithm offered the highest image quality and reconstruction accuracy. (2) No meaningful variation in performance was observed when the amount of truncation was changed. (3) This study showed evidence that accurate interior tomography with an undersampled acquisition is possible for realistic objects if a prior image with minimal artifacts is available.

X-ray scatter is a significant problem in cone-beam computed tomography when thicker objects and larger cone angles are used, as scattered radiation can lead to reduced contrast and CT number inaccuracy. Advances have been made in x-ray computed tomography (CT) by incorporating a high quality prior image into the image reconstruction process. In this paper, we extend this idea to correct scatter-induced shading artifacts in cone-beam CT image-guided radiation therapy. Specifically, this paper presents a new scatter correction algorithm which uses a prior image with low scatter artifacts to reduce shading artifacts in cone-beam CT images acquired under conditions of high scatter. The proposed correction algorithm begins with an empirical hypothesis that the target image can be written as a weighted summation of a series of basis images that are generated by raising the raw cone-beam projection data to different powers, and then, reconstructing using the standard filtered backprojection algorithm. The weight for each basis image is calculated by minimizing the difference between the target image and the prior image. The performance of the scatter correction algorithm is qualitatively and quantitatively evaluated through phantom studies using a Varian 2100 EX System with an on-board imager. Results show that the proposed scatter correction algorithm using a prior image with low scatter artifacts can substantially mitigate scatter-induced shading artifacts in both full-fan and half-fan modes.

Dual energy computed tomography (DECT) is currently a subject of extensive investigation. DECT is currently implemented using either a dual source scanner with high and low kVp data acquired from separate sources or a single source scanner with both high and low kVp data acquired in an alternating manner. Both methods require dedicated hardware to enable data acquisition and image reconstruction for DECT. In this paper, we present a method to enable DECT using a single x-ray source with a slow kVp switching data acquisition. The enabling reconstruction technique allowing for the reduction in slew rate is the prior image constrained compressed sensing (PICCS) algorithm. When a slow kVp switching data acquisition method is used, the projection data with high and low kVp values are undersampled and the conventional filtered backprojection (FBP) image reconstruction does not enable streaking artifact-free images for material decomposition in DECT. In this paper, all of the acquired high and low kVp projection data were used to generate a prior image using the conventional FBP method. The PICCS algorithm was then used to reconstruct both high and low kVp images to enable material decomposition in the image domain. Both numerical simulations and physical phantom experimental studies were conducted to validate the proposed DECT scheme. The results demonstrate that a slew rate corresponding to 123 views at high and low kVp (high and low kVp values used for dual energy decomposition) is sufficient for the PICCS-based DECT method. In contrast, the slew rate should be high enough to obtain over 500 projections at each kVp for artifact-free reconstruction using an FBP-based DECT method.

Micro-CT scanning has become an accepted standard for anatomical imaging in small animal disease and genome mutation models. Concurrently, perfusion imaging via tracking contrast dynamics after injection of an iodinated contrast agent is a well-established tool for clinical CT scanners. However, perfusion imaging is not yet commercially available on the micro-CT platform due to limitations in both radiation dose and temporal resolution. Recent hardware developments in micro-CT scanners enable continuous imaging of a given volume through the use of a slip-ring gantry. Now that dynamic CT imaging is feasible, data may be acquired to measure tissue perfusion using a micro-CT scanner (CT Imaging, Erlangen, Germany). However, rapid imaging using micro-CT scanners leads to high image noise in individual time frames. Using the standard filtered backprojection (FBP) image reconstruction, images are prohibitively noisy for calculation of voxel-by-voxel perfusion maps. In this study, we apply prior image constrained compressed sensing (PICCS) to reconstruct images with significantly lower noise variance. In perfusion phantom experiments performed on a micro-CT scanner, the PICCS reconstruction enabled a reduction to 1/16 of the noise variance of standard FBP reconstruction, without compromising the spatial or temporal resolution. This enables a significant increase in dose efficiency, and thus, significantly less exposure time is needed to acquire images amenable to perfusion processing. This reduction in required irradiation time enables voxel-by-voxel perfusion maps to be generated on micro-CT scanners. Sample perfusion maps using a deconvolution-based perfusion analysis are included to demonstrate the improvement in image quality using the PICCS algorithm.

Of all available reconstruction methods, statistical iterative reconstruction algorithms appear particularly promising since they enable accurate physical noise modeling. The newly developed compressive sampling/compressed sensing (CS) algorithm has shown the potential to accurately reconstruct images from highly undersampled data. The CS algorithm can be implemented in the statistical reconstruction framework as well. In this study, we compared the performance of two standard statistical reconstruction algorithms (penalized weighted least squares and q-GGMRF) to the CS algorithm. In assessing the image quality using these iterative reconstructions, it is critical to utilize realistic background anatomy as the reconstruction results are object dependent. A cadaver head was scanned on a Varian Trilogy system at different dose levels. Several figures of merit including the relative root mean square error and a quality factor which accounts for the noise performance and the spatial resolution were introduced to objectively evaluate reconstruction performance. A comparison is presented between the three algorithms for a constant undersampling factor comparing different algorithms at several dose levels. To facilitate this comparison, the original CS method was formulated in the framework of the statistical image reconstruction algorithms. Important conclusions of the measurements from our studies are that (1) for realistic neuro-anatomy, over 100 projections are required to avoid streak artifacts in the reconstructed images even with CS reconstruction, (2) regardless of the algorithm employed, it is beneficial to distribute the total dose to more views as long as each view remains quantum noise limited and (3) the total variation-based CS method is not appropriate for very low dose levels because while it can mitigate streaking artifacts, the images exhibit patchy behavior, which is potentially harmful for medical diagnosis.

Recently, x-ray differential phase contrast computed tomography (DPC-CT) has been experimentally implemented using a conventional tube combined with gratings. Images were reconstructed using a parallel-beam reconstruction formula. However, parallel-beam reconstruction formulae are not applicable when the parallel-beam approximation fails. In this paper, we present a new image reconstruction formula for fan-beam DPC-CT. There are several novel features of the new image reconstruction formula: (i) when the scanning angular range of data acquisition is larger than pi + gamma(m) (gamma(m) is the full fan angle), the entire field of view can be exactly reconstructed; (ii) when the scanning angular range is smaller than pi + gamma(m), a local region of interest (ROI) can be exactly reconstructed; (iii) it enables an exact reconstruction for a local ROI when the projection data are truncated at some view angles; (iv) it enlarges the imaging field of view when the detector is asymmetrically placed. In this last case, the data are truncated from every view angle. Numerical simulations have been conducted to validate the new reconstruction formula.