Investigation of iterative image reconstruction in low-dose breast CT

An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT.Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process.Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image.Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

Dedicated Cone-Beam Breast CT: Reproducibility of Volumetric Glandular Fraction with Advanced Image Reconstruction Methods

Dedicated cone-beam breast computed tomography (CBBCT) is an emerging modality and provides fully three-dimensional (3D) images of the uncompressed breast at an isotropic voxel resolution. In an effort to translate this modality to breast cancer screening, advanced image reconstruction methods are being pursued. Since radiographic breast density is an established risk factor for breast cancer and CBBCT provides volumetric data, this study investigates the reproducibility of the volumetric glandular fraction (VGF), defined as the proportion of fibroglandular tissue volume relative to the total breast volume excluding the skin. Four image reconstruction methods were investigated: the analytical Feldkamp-Davis-Kress (FDK), a compressed sensing-based fast, regularized, iterative statistical technique (FRIST), a fully supervised deep learning approach using a multi-scale residual dense network (MS-RDN), and a self-supervised approach based on Noise-to-Noise (N2N) learning. Projection datasets from 106 women who participated in a prior clinical trial were reconstructed using each of these algorithms at a fixed isotropic voxel size of (0.273 mm3). Each reconstructed breast volume was segmented into skin, adipose, and fibroglandular tissues, and the VGF was computed. The VGF did not differ among the four reconstruction methods (p = 0.167), and none of the three advanced image reconstruction algorithms differed from the standard FDK reconstruction (p > 0.862). Advanced reconstruction algorithms developed for low-dose CBBCT reproduce the VGF to provide quantitative breast density, which can be used for risk estimation.

Optimization of a customized simultaneous algebraic reconstruction technique algorithm for phase-contrast breast computed tomography

Objective. To introduce the optimization of a customized GPU-based simultaneous algebraic reconstruction technique (cSART) in the field of phase-contrast breast computed tomography (bCT). The presented algorithm features a 3D bilateral regularization filter that can be tuned to yield optimal performance for clinical image visualization and tissues segmentation. Approach. Acquisitions of a dedicated test object and a breast specimen were performed at Elettra, the Italian synchrotron radiation (SR) facility (Trieste, Italy) using a large area CdTe single-photon counting detector. Tomographic images were obtained at 5 mGy of mean glandular dose, with a 32 keV monochromatic x-ray beam in the free-space propagation mode. Three independent algorithms parameters were optimized by using contrast-to-noise ratio (CNR), spatial resolution, and noise texture metrics. The results obtained with the cSART algorithm were compared with conventional SART and filtered back projection (FBP) reconstructions. Image segmentation was performed both with gray scale-based and supervised machine-learning approaches. Main results. Compared to conventional FBP reconstructions, results indicate that the proposed algorithm can yield images with a higher CNR (by 35% or more), retaining a high spatial resolution while preserving their textural properties. Alternatively, at the cost of an increased image ‘patchiness’, the cSART can be tuned to achieve a high-quality tissue segmentation, suggesting the possibility of performing an accurate glandularity estimation potentially of use in the realization of realistic 3D breast models starting from low radiation dose images. Significance. The study indicates that dedicated iterative reconstruction techniques could provide significant advantages in phase-contrast bCT imaging. The proposed algorithm offers great flexibility in terms of image reconstruction optimization, either toward diagnostic evaluation or image segmentation.

Cone-beam breast CT using an offset detector: effect of detector offset and image reconstruction algorithm

Objective.A dedicated cone-beam breast computed tomography (BCT) using a high-resolution, low-noise detector operating in offset-detector geometry has been developed. This study investigates the effects of varying detector offsets and image reconstruction algorithms to determine the appropriate combination of detector offset and reconstruction algorithm.Approach.Projection datasets (300 projections in 360°) of 30 breasts containing calcified lesions that were acquired using a prototype cone-beam BCT system comprising a 40 × 30 cm flat-panel detector with 1024 × 768 detector pixels were reconstructed using Feldkamp-Davis-Kress (FDK) algorithm and served as the reference. The projection datasets were retrospectively truncated to emulate cone-beam datasets with sinograms of 768×768 and 640×768 detector pixels, corresponding to 5 cm and 7.5 cm lateral offsets, respectively. These datasets were reconstructed using the FDK algorithm with appropriate weights and an ASD-POCS-based Fast, total variation-Regularized, Iterative, Statistical reconstruction Technique (FRIST), resulting in a total of 4 offset-detector reconstructions (2 detector offsets × 2 reconstruction methods). Signal difference-to-noise ratio (SDNR), variance, and full-width at half-maximum (FWHM) of calcifications in two orthogonal directions were determined from all reconstructions. All quantitative measurements were performed on images in units of linear attenuation coefficient (1/cm).Results.The FWHM of calcifications did not differ (P > 0.262) among reconstruction algorithms and detector formats, implying comparable spatial resolution. For a chosen detector offset, the FRIST algorithm outperformed FDK in terms of variance and SDNR (P < 0.0001). For a given reconstruction method, the 5 cm offset provided better results.Significance.This study indicates the feasibility of using the compressed sensing-based, FRIST algorithm to reconstruct sinograms from offset-detectors. Among the reconstruction methods and detector offsets studied, FRIST reconstructions corresponding to a 30 cm × 30 cm with 5 cm lateral offset, achieved the best performance. A clinical prototype using such an offset geometry has been developed and installed for clinical trials.

High-resolution μ CT imaging for characterizing microcalcification detection performance in breast CT

Purpose: To demonstrate the utility of high-resolution micro-computed tomography ( μ CT ) for determining ground-truth size and shape properties of calcium grains for evaluation of detection performance in breast CT (bCT). Approach: Calcium carbonate grains ( ∼ 200    μ m ) were suspended in 1% agar solution to emulate microcalcifications ( μ Calcs ) within a fibroglandular tissue background. Ground-truth imaging was performed on a commercial μ CT scanner and was used for assessing calcium-grain size and shape, and for generating μ Calc signal profiles. Calcium grains were placed within a realistic breast-shaped phantom and imaged on a prototype bCT system at 3- and 6-mGy mean glandular dose (MGD) levels, and the non-prewhitening detectability was assessed. Additionally, the μ CT -derived signal profiles were used in conjunction with the bCT system characterization (MTF and NPS) to obtain predictions of bCT detectability. Results: Estimated detectability of the calcium grains on the bCT system ranged from 2.5 to 10.6 for 3 mGy and from 3.8 to 15.3 for 6 mGy with large fractions of the grains meeting the Rose criterion for visibility. Segmentation of μ CT images based on morphological operations produced accurate results in terms of segmentation boundaries and segmented region size. A regression model linking bCT detectability to μ Calc parameters indicated significant effects of μ Calc size and vertical position within the breast phantom. Detectability using μ CT -derived detection templates and bCT statistical properties (MTF and NPS) were in good correspondence with those measured directly from bCT ( R 2 > 0.88 ). Conclusions: Parameters derived from μ CT ground-truth data were shown to produce useful characterizations of detectability when compared to estimates derived directly from bCT. Signal profiles derived from μ CT imaging can be used in conjunction with measured or hypothesized statistical properties to evaluate the performance of a system, or system component, that may not currently be available.

Dedicated breast CT: state of the art-Part I. Historical evolution and technical aspects

Dedicated breast CT is an emerging 3D isotropic imaging technology for breast, which overcomes the limitations of 2D compression mammography and limited angle tomosynthesis while providing some of the advantages of magnetic resonance imaging. This first installment in a 2-part review describes the evolution of dedicated breast CT beginning with a historical perspective and progressing to the present day. Moreover, it provides an overview of state-of-the-art technology. Particular emphasis is placed on technical limitations in scan protocol, radiation dose, breast coverage, patient comfort, and image artifact. Proposed methods of how to address these technical challenges are also discussed. KEY POINTS: • Advantages of breast CT include no tissue overlap, improved patient comfort, rapid acquisition, and concurrent assessment of microcalcifications and contrast enhancement. • Current clinical and prototype dedicated breast CT systems differ in acquisition modes, imaging techniques, and detector types. • There are still details to be decided regarding breast CT techniques, such as scan protocol, radiation dose, breast coverage, patient comfort, and image artifact.

A balanced total-variation-Chambolle-Pock algorithm for EPR imaging

Total variation (TV) minimization algorithm is an effective algorithm capable of accurately reconstructing images from sparse projection data in a variety of imaging modalities including computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). The data divergence constrained, TV minimization (DDcTV) model and its Chambolle-Pock (CP) solving algorithm have been proposed for CT. However, when the DDcTV-CP algorithm is applied to 3D EPRI, it suffers from slow convergence rate or divergence. We hypothesize that this is due to the magnitude imbalance between the data fidelity term and the TV regularization term. In this work, we propose a balanced TV (bTV) model incorporating a balance parameter and demonstrate its capability to avoid convergence issues for the 3D EPRI application. Simulation and real experiments show that the DDcTV-CP algorithm cannot guarantee convergence but the bTV-CP algorithm may guarantee convergence and achieve fast convergence by use of an appropriate balance parameter. Experiments also show that underweighting the balance parameter leads to slow convergence, whereas overweighting the balance parameter leads to divergence. The iteration-behavior change-law with the variation of the balance parameter is explained by use of the data tolerance ellipse and gradient descent principle. The findings and insights gained in this work may be applied to other imaging modalities and other constrained optimization problems.

Directional-TV algorithm for image reconstruction from limited-angular-range data

Investigation of image reconstruction from data collected over a limited-angular range in X-ray CT remains a topic of active research because it may yield insight into the development of imaging workflow of practical significance. This reconstruction problem is well-known to be challenging, however, because it is highly ill-conditioned. In the work, we investigate optimization-based image reconstruction from data acquired over a limited-angular range that is considerably smaller than the angular range in short-scan CT. We first formulate the reconstruction problem as a convex optimization program with directional total-variation (TV) constraints applied to the image, and then develop an iterative algorithm, referred to as the directional-TV (DTV) algorithm for image reconstruction through solving the optimization program. We use the DTV algorithm to reconstruct images from data collected over a variety of limited-angular ranges for breast and bar phantoms of clinical- and industrial-application relevance. The study demonstrates that the DTV algorithm accurately recovers the phantoms from data generated over a significantly reduced angular range, and that it considerably diminishes artifacts observed otherwise in reconstructions of existing algorithms. We have also obtained empirical conditions on minimal-angular ranges sufficient for numerically accurate image reconstruction with the DTV algorithm.

Optical conductivity of triple point fermions

As a low-energy effective theory on non-symmorphic lattices, we consider a generic triple point fermion Hamiltonian, which is parameterized by an angular parameterλ. We find strongλdependence in both Drude and interband optical absorption of these systems. The deviation of theT2coefficient of the Drude weight from Dirac/Weyl fermions can be used as a quick way to optically distinguish the triple point degeneracies from the Dirac/Weyl degeneracies. At the particularλ=π/6 point, we find that the 'helicity' reversal optical transition matrix element is identically zero. Nevertheless, deviating from this point, the helicity reversal emerges as an absorption channel.

A residual dense network assisted sparse view reconstruction for breast computed tomography

To develop and investigate a deep learning approach that uses sparse-view acquisition in dedicated breast computed tomography for radiation dose reduction, we propose a framework that combines 3D sparse-view cone-beam acquisition with a multi-slice residual dense network (MS-RDN) reconstruction. Projection datasets (300 views, full-scan) from 34 women were reconstructed using the FDK algorithm and served as reference. Sparse-view (100 views, full-scan) projection data were reconstructed using the FDK algorithm. The proposed MS-RDN uses the sparse-view and reference FDK reconstructions as input and label, respectively. Our MS-RDN evaluated with respect to fully sampled FDK reference yields superior performance, quantitatively and visually, compared to conventional compressed sensing methods and state-of-the-art deep learning based methods. The proposed deep learning driven framework can potentially enable low dose breast CT imaging.

Sparse-view, short-scan, dedicated cone-beam breast computed tomography: image quality assessment

The purpose of this study is to quantify the impact of sparse-view acquisition in short-scan trajectories, compared to 360-degrees full-scan acquisition, on image quality measures in dedicated cone-beam breast computed tomography (BCT). Projection data from 30 full-scan (360-degrees; 300 views) BCT exams with calcified lesions were selected from an existing clinical research database. Feldkamp-Davis-Kress (FDK) reconstruction of the full-scan data served as the reference. Projection data corresponding to two short-scan trajectories, 204 and 270-degrees, which correspond to the minimum and maximum angular range achievable in a cone-beam BCT system were selected. Projection data were retrospectively sampled to provide 225, 180, and 168 views for 270-degrees short-scan, and 170 views for 204-degrees short-scan. Short-scans with 180 and 168 views in 270-degrees used non-uniform angular sampling. A fast, iterative, total variation-regularized, statistical reconstruction technique (FIRST) was used for short-scan image reconstruction. Image quality was quantified by variance, signal-difference to noise ratio (SDNR) between adipose and fibroglandular tissues, full-width at half-maximum (FWHM) of calcifications in two orthogonal directions, as well as, bias and root-mean-squared-error (RMSE) computed with respect to the reference full-scan FDK reconstruction. The median values of bias (8.6 × 10-4-10.3 × 10-4cm-1) and RMSE (6.8 × 10-6-9.8 × 10-6cm-1) in the short-scan reconstructions, computed with the full-scan FDK as the reference were close to, but not zero (P < 0.0001, one-sample median test). The FWHM of the calcifications in the short-scan reconstructions did not differ significantly from the reference FDK reconstruction (P > 0.118), except along the superior-inferior direction for the short-scan reconstruction with 168 views in 270-degrees (P = 0.046). The variance and SDNR from short-scan reconstructions were significantly improved compared to the full-scan FDK reconstruction (P < 0.0001). This study demonstrates the feasibility of the short-scan, sparse-view, compressed sensing-based iterative reconstruction. This study indicates that shorter scan times and reduced radiation dose without sacrificing image quality are potentially feasible.

Artificial intelligence in radiotherapy: a technological review

Radiation therapy (RT) is widely used to treat cancer. Technological advances in RT have occurred in the past 30 years. These advances, such as three-dimensional image guidance, intensity modulation, and robotics, created challenges and opportunities for the next breakthrough, in which artificial intelligence (AI) will possibly play important roles. AI will replace certain repetitive and labor-intensive tasks and improve the accuracy and consistency of others, particularly those with increased complexity because of technological advances. The improvement in efficiency and consistency is important to manage the increasing cancer patient burden to the society. Furthermore, AI may provide new functionalities that facilitate satisfactory RT. The functionalities include superior images for real-time intervention and adaptive and personalized RT. AI may effectively synthesize and analyze big data for such purposes. This review describes the RT workflow and identifies areas, including imaging, treatment planning, quality assurance, and outcome prediction, that benefit from AI. This review primarily focuses on deep-learning techniques, although conventional machine-learning techniques are also mentioned.

Cone-beam breast computed tomography using ultra-fast image reconstruction with constrained, total-variation minimization for suppression of artifacts

Compressed sensing based iterative reconstruction algorithms for computed tomography such as adaptive steepest descent-projection on convex sets (ASD-POCS) are attractive due to their applicability in incomplete datasets such as sparse-view data and can reduce radiation dose to the patients while preserving image quality. Although IR algorithms reduce image noise compared to analytical Feldkamp-Davis-Kress (FDK) algorithm, they may generate artifacts, particularly along the periphery of the object. One popular solution is to use finer image-grid followed by down-sampling. This approach is computationally intensive but may be compensated by reducing the field of view. Our proposed solution is to replace the algebraic reconstruction technique within the original ASD-POCS by ordered subsets-simultaneous algebraic reconstruction technique (OS-SART) and with initialization using FDK image. We refer to this method as Fast, Iterative, TV-Regularized, Statistical reconstruction Technique (FIRST). In this study, we investigate FIRST for cone-beam dedicated breast CT with large image matrix. The signal-difference to noise ratio (SDNR), the difference of the mean value and the variance of adipose and fibroglandular tissues for both FDK and FIRST reconstructions were determined. With FDK serving as the reference, the root-mean-square error (RMSE), bias, and the full-width at half-maximum (FWHM) of microcalcifications in two orthogonal directions were also computed. Our results suggest that FIRST is competitive to the finer image-grid method with shorter reconstruction time. Images reconstructed using the FIRST do not exhibit artifacts and outperformed FDK in terms of image noise. This suggests the potential of this approach for radiation dose reduction in cone-beam breast CT.

Cone-beam breast CT features associated with HER2/neu overexpression in patients with primary breast cancer

OBJECTIVES

To identify the relationship between human epidermal growth factor receptor 2 (HER2) status and cone-beam breast CT (CBBCT) characteristics in surgically resected breast cancer.

METHODS

Preoperative CBBCT of patients with BI-RADS 4 or 5 lesions identified on mammography or ultrasound and dense or very dense breast tissue were retrospectively evaluated in 181 surgically resected breast cancer (triple-negative excluded) between May 2012 and November 2014. A set of CBBCT descriptors was semiquantitatively assessed by consensus double reading. Reader reproducibility was analyzed. Multivariable logistic regression analysis using backward elimination (BEA) with the Wald criterion was performed to identify independent predictive factors of harboring HER2/neu. Principle component analysis (PCA) was used to determine characteristics that might differentiate HER2 status. Receiver operating characteristic (ROC) curve analyses were conducted to determine the predictive capability.

RESULTS

HER2 positive was found in 101 (55.8%) of 181 patients. Inter-observer agreement was high for characteristics' assessment. Based on BEA, pathologic grade, maximum dimension, lobulation, ΔCT, and calcification morphology were confirmed as independent predictive factors of HER2/neu overexpression. PCA showed that calcification- and border-related characteristics were the most important for differentiation. ROC curve analyses showed that CBBCT features (AUC = 0.853) were superior to clinicopathologic features (AUC = 0.613, p < 0.001) and comparable with combination (AUC = 0.856, p = 0.866).

CONCLUSIONS

CBBCT features could be used to prognosticate HER2 status independently, which are potentially complementary to histopathologic result and helpful in guiding biopsy.

KEY POINTS

• Dmax, lobulation, ΔCT, and calcification morphology are independent predictors of HER2 status. • CBBCT features are superior to clinicopathologic features in HER2+/- discrimination. • CBBCT features are comparable with combination with clinicopathologic features in HER2+/- discrimination.

Dedicated cone-beam breast CT using laterally-shifted detector geometry: Quantitative analysis of feasibility for clinical translation

BACKGROUND

High-resolution, low-noise detectors with minimal dead-space at chest-wall could improve posterior coverage and microcalcification visibility in the dedicated cone-beam breast CT (CBBCT). However, the smaller field-of-view necessitates laterally-shifted detector geometry to enable optimizing the air-gap for x-ray scatter rejection.

OBJECTIVE

To evaluate laterally-shifted detector geometry for CBBCT with clinical projection datasets that provide for anatomical structures and lesions.

METHODS

CBBCT projection datasets (n = 17 breasts) acquired with a 40×30 cm detector (1024×768-pixels, 0.388-mm pixels) were truncated along the fan-angle to emulate 20.3×30 cm, 22.2×30 cm and 24.1×30 cm detector formats and correspond to 20, 120, 220 pixels overlap in conjugate views, respectively. Feldkamp-Davis-Kress (FDK) algorithm with 3 different weighting schemes were used for reconstruction. Visual analysis for artifacts and quantitative analysis of root-mean-squared-error (RMSE), absolute difference between truncated and 40×30 cm reconstructions (Diff), and its power spectrum (PSDiff) were performed.

RESULTS

Artifacts were observed for 20.3×30 cm, but not for other formats. The 24.1×30 cm provided the best quantitative results with RMSE and Diff (both in units of μ, cm-1) of 4.39×10-3±1.98×10-3 and 4.95×10-4±1.34×10-4, respectively. The PSDiff (>0.3 cycles/mm) was in the order of 10-14μ2mm3 and was spatial-frequency independent.

CONCLUSIONS

Laterally-shifted detector CBBCT with at least 220 pixels overlap in conjugate views (24.1×30 cm detector format) provides quantitatively accurate and artifact-free image reconstruction.

Regularization strategies in statistical image reconstruction of low-dose x-ray CT: A review

Statistical image reconstruction (SIR) methods have shown potential to substantially improve the image quality of low-dose x-ray computed tomography (CT) as compared to the conventional filtered back-projection (FBP) method. According to the maximum a posteriori (MAP) estimation, the SIR methods are typically formulated by an objective function consisting of two terms: (a) a data-fidelity term that models imaging geometry and physical detection processes in projection data acquisition, and (b) a regularization term that reflects prior knowledge or expectations of the characteristics of the to-be-reconstructed image. SIR desires accurate system modeling of data acquisition, while the regularization term also has a strong influence on the quality of reconstructed images. A variety of regularization strategies have been proposed for SIR in the past decades, based on different assumptions, models, and prior knowledge. In this paper, we review the conceptual and mathematical bases of these regularization strategies and briefly illustrate their efficacies in SIR of low-dose CT.

Block-matching sparsity regularization-based image reconstruction for low-dose computed tomography

PURPOSE

Low-dose computed tomography (CT) imaging has been widely explored because it can reduce the radiation risk to human bodies. This presents challenges in improving the image quality because low radiation dose with reduced tube current and pulse duration introduces severe noise. In this study, we investigate block-matching sparsity regularization (BMSR) and devise an optimization problem for low-dose image reconstruction.

METHOD

The objective function of the program is built by combining the sparse coding of BMSR and analysis error, which is subject to physical data measurement. A practical reconstruction algorithm using hard thresholding and projection-onto-convex-set for fast and stable performance is developed. An efficient scheme for the choices of regularization parameters is analyzed and designed.

RESULTS

In the experiments, the proposed method is compared with a conventional edge preservation method and adaptive dictionary-based iterative reconstruction. Experiments with clinical images and real CT data indicate that the obtained results show promising capabilities in noise suppression and edge preservation compared with the competing methods.

CONCLUSIONS

A block-matching-based reconstruction method for low-dose CT is proposed. Improvements in image quality are verified by quantitative metrics and visual comparisons, thereby indicating the potential of the proposed method for real-life applications.

Human and model observer performance for lesion detection in breast cone beam CT images with the FDK reconstruction

We investigate the detectability of breast cone beam computed tomography images using human and model observers and the variations of exponent, β, of the inverse power-law spectrum for various reconstruction filters and interpolation methods in the Feldkamp-Davis-Kress (FDK) reconstruction. Using computer simulation, a breast volume with a 50% volume glandular fraction and a 2mm diameter lesion are generated and projection data are acquired. In the FDK reconstruction, projection data are apodized using one of three reconstruction filters; Hanning, Shepp-Logan, or Ram-Lak, and back-projection is performed with and without Fourier interpolation. We conduct signal-known-exactly and background-known-statistically detection tasks. Detectability is evaluated by human observers and their performance is compared with anthropomorphic model observers (a non-prewhitening observer with eye filter (NPWE) and a channelized Hotelling observer with either Gabor channels or dense difference-of-Gaussian channels). Our results show that the NPWE observer with a peak frequency of 7cyc/degree attains the best correlation with human observers for the various reconstruction filters and interpolation methods. We also discover that breast images with smaller β do not yield higher detectability in the presence of quantum noise.

A line fiducial method for geometric calibration of cone-beam CT systems with diverse scan trajectories

Modern cone-beam CT systems, especially C-arms, are capable of diverse source-detector orbits. However, geometric calibration of these systems using conventional configurations of spherical fiducials (BBs) may be challenged for novel source-detector orbits and system geometries. In part, this is because the BB configurations are designed with careful forethought regarding the intended orbit so that BB marker projections do not overlap in projection views. Examples include helical arrangements of BBs (Rougee et al 1993 Proc. SPIE 1897 161-9) such that markers do not overlap in projections acquired from a circular orbit and circular arrangements of BBs (Cho et al 2005 Med. Phys. 32 968-83). As a more general alternative, this work proposes a calibration method based on an array of line-shaped, radio-opaque wire segments. With this method, geometric parameter estimation is accomplished by relating the 3D line equations representing the wires to the 2D line equations of their projections. The use of line fiducials simplifies many challenges with fiducial recognition and extraction in an orbit-independent manner. For example, their projections can overlap only mildly, for any gantry pose, as long as the wires are mutually non-coplanar in 3D. The method was tested in application to circular and non-circular trajectories in simulation and in real orbits executed using a mobile C-arm prototype for cone-beam CT. Results indicated high calibration accuracy, as measured by forward and backprojection/triangulation error metrics. Triangulation errors on the order of microns and backprojected ray deviations uniformly less than 0.2 mm were observed in both real and simulated orbits. Mean forward projection errors less than 0.1 mm were observed in a comprehensive sweep of different C-arm gantry angulations. Finally, successful integration of the method into a CT imaging chain was demonstrated in head phantom scans.

Detector Blur and Correlated Noise Modeling for Digital Breast Tomosynthesis Reconstruction

This paper describes a new image reconstruction method for digital breast tomosynthesis (DBT). The new method incorporates detector blur into the forward model. The detector blur in DBT causes correlation in the measurement noise. By making a few approximations that are reasonable for breast imaging, we formulated a regularized quadratic optimization problem with a data-fit term that incorporates models for detector blur and correlated noise (DBCN). We derived a computationally efficient separable quadratic surrogate (SQS) algorithm to solve the optimization problem that has a non-diagonal noise covariance matrix. We evaluated the SQS-DBCN method by reconstructing DBT scans of breast phantoms and human subjects. The contrast-to-noise ratio and sharpness of microcalcifications were analyzed and compared with those by the simultaneous algebraic reconstruction technique. The quality of soft tissue lesions and parenchymal patterns was examined. The results demonstrate the potential to improve the image quality of reconstructed DBT images by incorporating the system physics model. This paper is a first step toward model-based iterative reconstruction for DBT.

Sampling limits for electron tomography with sparsity-exploiting reconstructions

Electron tomography (ET) has become a standard technique for 3D characterization of materials at the nano-scale. Traditional reconstruction algorithms such as weighted back projection suffer from disruptive artifacts with insufficient projections. Popularized by compressed sensing, sparsity-exploiting algorithms have been applied to experimental ET data and show promise for improving reconstruction quality or reducing the total beam dose applied to a specimen. Nevertheless, theoretical bounds for these methods have been less explored in the context of ET applications. Here, we perform numerical simulations to investigate performance of ℓ₁-norm and total-variation (TV) minimization under various imaging conditions. From 36,100 different simulated structures, our results show specimens with more complex structures generally require more projections for exact reconstruction. However, once sufficient data is acquired, dividing the beam dose over more projections provides no improvements-analogous to the traditional dose-fraction theorem. Moreover, a limited tilt range of ±75° or less can result in distorting artifacts in sparsity-exploiting reconstructions. The influence of optimization parameters on reconstructions is also discussed.

Superiorized algorithm for reconstruction of CT images from sparse-view and limited-angle polyenergetic data

Recent work in CT image reconstruction has seen increasing interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed heuristic which provides an automatic procedure to 'superiorize' an iterative image reconstruction algorithm with respect to a chosen objective function, such as TV. Under certain conditions, the superiorized algorithm is guaranteed to find a solution that is as satisfactory as any found by the original algorithm with respect to satisfying the constraints of the problem; this solution is also expected to be superior with respect to the chosen objective. Most work on superiorization has used reconstruction algorithms which assume a linear measurement model, which in the case of CT corresponds to data generated from a monoenergetic x-ray beam. Many CT systems generate x-rays from a polyenergetic spectrum, however, in which the measured data represent an integral of object attenuation over all energies in the spectrum. This inconsistency with the linear model produces the well-known beam hardening artifacts, which impair analysis of CT images. In this work we superiorize an iterative algorithm for reconstruction from polyenergetic data, using both TV and an anisotropic TV (ATV) penalty. We apply the superiorized algorithm in numerical phantom experiments modeling both sparse-view and limited-angle scenarios. In our experiments, the superiorized algorithm successfully finds solutions which are as constraints-compatible as those found by the original algorithm, with significantly reduced TV and ATV values. The superiorized algorithm thus produces images with greatly reduced sparse-view and limited angle artifacts, which are also largely free of the beam hardening artifacts that would be present if a superiorized version of a monoenergetic algorithm were used.

Optimization-based image reconstruction with artifact reduction in C-arm CBCT

We investigate an optimization-based reconstruction, with an emphasis on image-artifact reduction, from data collected in C-arm cone-beam computed tomography (CBCT) employed in image-guided interventional procedures. In the study, an image to be reconstructed is formulated as a solution to a convex optimization program in which a weighted data divergence is minimized subject to a constraint on the image total variation (TV); a data-derivative fidelity is introduced in the program specifically for effectively suppressing dominant, low-frequency data artifact caused by, e.g. data truncation; and the Chambolle-Pock (CP) algorithm is tailored to reconstruct an image through solving the program. Like any other reconstructions, the optimization-based reconstruction considered depends upon numerous parameters. We elucidate the parameters, illustrate their determination, and demonstrate their impact on the reconstruction. The optimization-based reconstruction, when applied to data collected from swine and patient subjects, yields images with visibly reduced artifacts in contrast to the reference reconstruction, and it also appears to exhibit a high degree of robustness against distinctively different anatomies of imaged subjects and scanning conditions of clinical significance. Knowledge and insights gained in the study may be exploited for aiding in the design of practical reconstructions of truly clinical-application utility.

Artifact reduction in short-scan CBCT by use of optimization-based reconstruction

Increasing interest in optimization-based reconstruction in research on, and applications of, cone-beam computed tomography (CBCT) exists because it has been shown to have to potential to reduce artifacts observed in reconstructions obtained with the Feldkamp-Davis-Kress (FDK) algorithm (or its variants), which is used extensively for image reconstruction in current CBCT applications. In this work, we carried out a study on optimization-based reconstruction for possible reduction of artifacts in FDK reconstruction specifically from short-scan CBCT data. The investigation includes a set of optimization programs such as the image-total-variation (TV)-constrained data-divergency minimization, data-weighting matrices such as the Parker weighting matrix, and objects of practical interest for demonstrating and assessing the degree of artifact reduction. Results of investigative work reveal that appropriately designed optimization-based reconstruction, including the image-TV-constrained reconstruction, can reduce significant artifacts observed in FDK reconstruction in CBCT with a short-scan configuration.

Investigation of cone-beam CT image quality trade-off for image-guided radiation therapy

It is well-known that projections acquired over an angular range slightly over 180° (so-called short scan) are sufficient for fan-beam reconstruction. However, due to practical imaging conditions (projection data and reconstruction image discretization, physical factors, and data noise), the short-scan reconstructions may have different appearances and properties from the full-scan (scans over 360°) reconstructions. Nevertheless, short-scan configurations have been used in applications such as cone-beam CT (CBCT) for head-neck-cancer image-guided radiation therapy (IGRT) that only requires a small field of view due to the potential reduced imaging time and dose. In this work, we studied the image quality trade-off for full, short, and full/short scan configurations with both conventional filtered-backprojection (FBP) reconstruction and iterative reconstruction algorithms based on total-variation (TV) minimization for head-neck-cancer IGRT. Anthropomorphic and Catphan phantoms were scanned at different exposure levels with a clinical scanner used in IGRT. Both visualization- and numerical-metric-based evaluation studies were performed. The results indicate that the optimal exposure level and number of views are in the middle range for both FBP and TV-based iterative algorithms and the optimization is object-dependent and task-dependent. The optimal view numbers decrease with the total exposure levels for both FBP and TV-based algorithms. The results also indicate there are slight differences between FBP and TV-based iterative algorithms for the image quality trade-off: FBP seems to be more in favor of larger number of views while the TV-based algorithm is more robust to different data conditions (number of views and exposure levels) than the FBP algorithm. The studies can provide a general guideline for image-quality optimization for CBCT used in IGRT and other applications.

Extracting Information From Previous Full-Dose CT Scan for Knowledge-Based Bayesian Reconstruction of Current Low-Dose CT Images

Markov random field (MRF) model has been widely employed in edge-preserving regional noise smoothing penalty to reconstruct piece-wise smooth images in the presence of noise, such as in low-dose computed tomography (LdCT). While it preserves edge sharpness, its regional smoothing may sacrifice tissue image textures, which have been recognized as useful imaging biomarkers, and thus it may compromise clinical tasks such as differentiating malignant vs. benign lesions, e.g., lung nodules or colon polyps. This study aims to shift the edge-preserving regional noise smoothing paradigm to texture-preserving framework for LdCT image reconstruction while retaining the advantage of MRF's neighborhood system on edge preservation. Specifically, we adapted the MRF model to incorporate the image textures of muscle, fat, bone, lung, etc. from previous full-dose CT (FdCT) scan as a priori knowledge for texture-preserving Bayesian reconstruction of current LdCT images. To show the feasibility of the proposed reconstruction framework, experiments using clinical patient scans were conducted. The experimental outcomes showed a dramatic gain by the a priori knowledge for LdCT image reconstruction using the commonly-used Haralick texture measures. Thus, it is conjectured that the texture-preserving LdCT reconstruction has advantages over the edge-preserving regional smoothing paradigm for texture-specific clinical applications.

Towards breast tomography with synchrotron radiation at Elettra: first images

The aim of the SYRMA-CT collaboration is to set-up the first clinical trial of phase-contrast breast CT with synchrotron radiation (SR). In order to combine high image quality and low delivered dose a number of innovative elements are merged: a CdTe single photon counting detector, state-of-the-art CT reconstruction and phase retrieval algorithms. To facilitate an accurate exam optimization, a Monte Carlo model was developed for dose calculation using GEANT4. In this study, high isotropic spatial resolution (120 μm)(3) CT scans of objects with dimensions and attenuation similar to a human breast were acquired, delivering mean glandular doses in the range of those delivered in clinical breast CT (5-25 mGy). Due to the spatial coherence of the SR beam and the long distance between sample and detector, the images contain, not only absorption, but also phase information from the samples. The application of a phase-retrieval procedure increases the contrast-to-noise ratio of the tomographic images, while the contrast remains almost constant. After applying the simultaneous algebraic reconstruction technique to low-dose phase-retrieved data sets (about 5 mGy) with a reduced number of projections, the spatial resolution was found to be equal to filtered back projection utilizing a four fold higher dose, while the contrast-to-noise ratio was reduced by 30%. These first results indicate the feasibility of clinical breast CT with SR.

Low-dose CT statistical iterative reconstruction via modified MRF regularization

It is desirable to reduce the excessive radiation exposure to patients in repeated medical CT applications. One of the most effective ways is to reduce the X-ray tube current (mAs) or tube voltage (kVp). However, it is difficult to achieve accurate reconstruction from the noisy measurements. Compared with the conventional filtered back-projection (FBP) algorithm leading to the excessive noise in the reconstructed images, the approaches using statistical iterative reconstruction (SIR) with low mAs show greater image quality. To eliminate the undesired artifacts and improve reconstruction quality, we proposed, in this work, an improved SIR algorithm for low-dose CT reconstruction, constrained by a modified Markov random field (MRF) regularization. Specifically, the edge-preserving total generalized variation (TGV), which is a generalization of total variation (TV) and can measure image characteristics up to a certain degree of differentiation, was introduced to modify the MRF regularization. In addition, a modified alternating iterative algorithm was utilized to optimize the cost function. Experimental results demonstrated that images reconstructed by the proposed method could not only generate high accuracy and resolution properties, but also ensure a higher peak signal-to-noise ratio (PSNR) in comparison with those using existing methods.

An Effective CUDA Parallelization of Projection in Iterative Tomography Reconstruction

Projection and back-projection are the most computationally intensive parts in Computed Tomography (CT) reconstruction, and are essential to acceleration of CT reconstruction algorithms. Compared to back-projection, parallelization efficiency in projection is highly limited by racing condition and thread unsynchronization. In this paper, a strategy of Fixed Sampling Number Projection (FSNP) is proposed to ensure the operation synchronization in the ray-driven projection with Graphical Processing Unit (GPU). Texture fetching is also used utilized to further accelerate the interpolations in both projection and back-projection. We validate the performance of this FSNP approach using both simulated and real cone-beam CT data. Experimental results show that compare to the conventional approach, the proposed FSNP method together with texture fetching is 10~16 times faster than the conventional approach based on global memory, and thus leads to more efficient iterative algorithm in CT reconstruction.

Algorithm-enabled exploration of image-quality potential of cone-beam CT in image-guided radiation therapy

Kilo-voltage (KV) cone-beam computed tomography (CBCT) unit mounted onto a linear accelerator treatment system, often referred to as on-board imager (OBI), plays an increasingly important role in image-guided radiation therapy. While the FDK algorithm is currently used for reconstructing images from clinical OBI data, optimization-based reconstruction has also been investigated for OBI CBCT. An optimization-based reconstruction involves numerous parameters, which can significantly impact reconstruction properties (or utility). The success of an optimization-based reconstruction for a particular class of practical applications thus relies strongly on appropriate selection of parameter values. In the work, we focus on tailoring the constrained-TV-minimization-based reconstruction, an optimization-based reconstruction previously shown of some potential for CBCT imaging conditions of practical interest, to OBI imaging through appropriate selection of parameter values. In particular, for given real data of phantoms and patient collected with OBI CBCT, we first devise utility metrics specific to OBI-quality-assurance tasks and then apply them to guiding the selection of parameter values in constrained-TV-minimization-based reconstruction. The study results show that the reconstructions are with improvement, relative to clinical FDK reconstruction, in both visualization and quantitative assessments in terms of the devised utility metrics.

Compressive sensing in medical imaging

The promise of compressive sensing, exploitation of compressibility to achieve high quality image reconstructions with less data, has attracted a great deal of attention in the medical imaging community. At the Compressed Sensing Incubator meeting held in April 2014 at OSA Headquarters in Washington, DC, presentations were given summarizing some of the research efforts ongoing in compressive sensing for x-ray computed tomography and magnetic resonance imaging systems. This article provides an expanded version of these presentations. Sparsity-exploiting reconstruction algorithms that have gained popularity in the medical imaging community are studied, and examples of clinical applications that could benefit from compressive sensing ideas are provided. The current and potential future impact of compressive sensing on the medical imaging field is discussed.