We report on an optimization-based image reconstruction algorithm for contrast enhanced digital breast tomosynthesis (DBT) using dual-energy scanning. The algorithm is designed to enable quantitative imaging of Iodine-based contrast agent by mitigating the depth blur artifact. The depth blurring is controlled by exploiting gradient sparsity of the contrast agent distribution. We find that minimization of directional total variation (TV) is particularly effective at exploiting gradient sparsity for the DBT scan configuration. In this initial work, the contrast agent imaging is performed by reconstructing images from DBT data acquired at source potentials of 30- and 49-kV, followed by weighted subtraction to suppress background glandular structure and isolate the contrast agent distribution. The algorithm is applied to DBT data, acquired with a Siemens Mammomat scanner, of a structured breast phantom with Iodine contrast agent inserts. Results for both in-plane and transverse-plane imaging for directional TV minimization are presented alongside images reconstructed by filtered back-projection for reference. It is seen that directional TV is able to substantially reduce depth blur for the Iodine-based contrast agent objects.
Dual-energy CT (DECT) with limited-angular-range (LAR) data has the potential to reduce radiation dose, scanning time, and motion effect, and avoid collision between the moving gantry and the patient. There are two primary sources of image artifacts, LAR and beam-hardening (BH) effects. Previous works have demonstrated that LAR artifacts can be effectively reduced or eliminated by the directional-total-variation (DTV) constraints on the orthogonal axes of the image array and BH artifacts can be corrected for by using the data-domain decomposition approach with overlapping scanning arcs. In this work, we investigate a one-step method for the simultaneous correction of LAR and BH artifacts for DECT with LAR data, thus enabling flexible scanning configurations, such as completely non-overlapping scanning arcs. Specifically, two scanning configurations, two-orthogonal-arc (TOA) and two-parallel-arc (TPA) configurations, are used to generate data from a digital chest phantom with low and high-kVp spectra. Basis images are reconstructed directly from low- and high-kVp data by solving a non-convex optimization problem with DTV constraints. They can then be combined into monochromatic images for visual inspection and quantitative analysis. The results suggest that accurate monochromatic images can be obtained from TOA and TPA configurations of 90◦ arcs, and that the TOA configuration appears to be more robust to data inconsistencies such as noise.
KEYWORDS: Image restoration, Reconstruction algorithms, Algorithm development, Data modeling, Data acquisition, 3D image reconstruction, 3D image processing, Signal to noise ratio
Electron paramagnetic resonance imaging (EPRI) is a rising technique for preclinical imaging of small animals. The technique uses paramagnetic spin contrast materials to determine the spectral-spatial (SS) distribution of materials within the subject. A widely used EPRI modality employs continuous wave (CW) scanning scheme with Zeeman modulation (ZM). The imaging model in this technique can be related to the Radon transform (RT) of the SS image, and image reconstruction is equivalent to reconstruction from RT data. However, data collection is limited by the finite strength of the magnetic field gradient applied to the subject, and there is a desire to speed up scanning by collecting data only over a limited-angular range (LAR). In this study, we tailor a recently developed DTV algorithm in CT to investigate accurate image reconstruction from RT over LARs in EPRI. The results show that the DTV algorithm can be adapted for image reconstruction of quality comparable to that of images reconstructed from full-angular range (FAR) data, suggesting that algorithms can be developed to enable LAR scanning in CW-ZM EPRI with reduced imaging time.
Dual-energy CT (DECT) of limited-angular ranges (LARs) collects data from angular ranges smaller than π for low- and high-kVp scans, and thus may potentially be exploited for reducing scanning time and radiation dose and for avoiding collision between the imaged object and the moving gantry of the scanner. Image artifacts resulting from beam hardening (BH) and limited-angular range (LAR) can be suppressed by using the data-domain decomposition and the directional-total-variation (DTV) algorithm for image reconstruction. In this work, we investigate two-orthogonal-arc (TOA) scanning configuration with overlapping arcs for collecting LAR DECT data, in an effort to reduce LAR artifacts and improve quantitative accuracy of estimated physical quantities. The TOA configuration consists of two arcs, of equal LAR, whose centers are positioned 90° apart, and is designed to reduce the ill-conditionedness of the imaging system matrix. The data are decomposed into basis sinograms, from which basis images are reconstructed using the DTV algorithm. Visual inspection of the monochromatic images and quantitative estimation of the effective atomic numbers suggest that the TOA configuration, as compared to the single-arc (SA) configuration of the same total angular range, can help reduce remaining LAR artifacts and bias in the estimated atomic number relative to the reference values from the full-angular-range data of 360° .
In certain CT applications such as dental CT imaging, a scanning configuration with an offset-detector is often used for extending the field of view (FOV) of the system. While data are truncated on one-side of the detector, it remains possible to accurately reconstruct an image from the truncated data collected over a full-angular range (FAR) of 360° by use of existing analytical-based algorithms such as the FDK algorithm. However, there also exist interests in scanning configurations that collect data only over limited-angular ranges (LARs) for practical considerations, and existing algorithms generally yield reconstructions with significant artifacts from LAR data collected with an offset-detector. It has been demonstrated recently that, for non-truncated data, the directional-total-variation (DTV) algorithm can reconstruct images with significantly reduced artifacts from LAR data. In this work, we developed and tailored the DTV algorithm for image reconstruction from truncated LAR data collected with a scanning configuration employing an offset-detector. We carried out a study on image reconstruction for a number of LAR scanning configurations with an offset-detector of practical interest. The study results demonstrate that the DTV algorithm can be tailored to yield, from truncated LAR data, images with significantly reduced artifacts that are observed otherwise in images obtained with existing analytical-based algorithms.
Phase-contrast CT (PCCT) is an emerging tool that has found numerous applications, including applications to preclinical imaging. There remains a need for reducing the imaging time in current PCCT. One approach to reducing imaging time is to reduce the scanning angular range in PCCT. However, accurate image reconstruction from data collected over a limited angular range (LAR) is challenging because it poses a problem of accurate inversion of the PCCT imaging model that can be highly ill-conditioned in LAR scans. In this work, we conduct an investigation of accurate image reconstruction through inverting the imaging model for LAR scanning configurations in propagation-based (PB) PCCT. We have developed a directional-total-variation (DTV) algorithm for image reconstruction from knowledge of the discrete X-ray transform (DXT) over a LAR for CT imaging. Observing the mathematical similarity between the DXT in CT and the imaging model in PB-PCCT, we develop and tailor the DTV algorithm for image reconstruction from LAR data in PB-PCCT. Results of our study show that the tailored DTV algorithm can yield image reconstruction with reduced LAR artifacts that can be observed otherwise in images reconstructed by use of the existing algorithm in PB-PCCT imaging. For a given LAR, it can be divided into sub arcs of LARs. We also investigate a scanning configuration with two orthogonal arcs of LARs separated by 90° , and observe that the two-orthogonal-arc scanning configuration may allow image reconstruction more accurately than does a single-arc scanning configuration even though the total angular ranges in both scanning configurations are identical. While boundary images can be reconstructed from data, we develop the DTV algorithm for reconstruction of the image, i.e., the refractive index distribution, instead of its boundary image from data in PB-PCCT. Once the image is obtained, the Laplacian operator can be applied to it for yielding its boundary image.
In cone-beam computed tomography (CBCT) imaging, a scanning configuration with an offset-detector is often used for extending the field of view (FOV) of the system. Due to the truncation of data at certain views, data are required to be collected over a full angular range (FAR) of 360◦ for accurate reconstruction by use of existing analytical-based algorithms. However, there exist interests in practical applications for limited-angular-range (LAR) imaging because it may allow for the reduction of radiation dose and scanning time and for the avoidance of the collisions between the moving gantry and scanned objects. Under such imaging conditions, existing algorithms generally yield reconstructions with significant artifacts. In this work, we develop and investigate a directional-total-variation (DTV) algorithm for image reconstruction from partially truncated data collected over LARs. By using the DTV algorithm, we have performed numerical simulation studies with partially truncated data collected from a pelvic phantom over different LARs with an offset-detector CBCT system. The results of the numerical studies demonstrate that the proposed algorithm can yield, from partially truncated LAR data, images with significantly reduced artifacts that are observed otherwise in images obtained with existing analytical-based algorithms.
In computed tomography (CT) imaging, recent developments in reconstruction algorithm and scan configuration design have provided useful tools for image reconstruction from data collected over a limited-angular range (LAR). In this work, we aim to investigate the impact of angular sampling interval on the accuracy of reconstruction from LAR data. In specific, we employ a two-orthogonal-arc scan configuration, and collect data from a numerical chest phantom over an LAR with various angular intervals. We then investigate image reconstruction by using the directional-total-variation (DTV) algorithm and evaluate reconstructions qualitatively and quantitatively. Results show that increased angular sampling interval can degrade image quality. Results of the simulation study also indicate an appropriate interval for sufficient reconstruction accuracy under specific imaging conditions, which provides insights for upper-bound performance of reconstructions in practical use.
Dual-energy CT (DECT) with limited-angular-range (LAR) data is of interest, as it could potentially reduce radiation dose and scanning time and avoid collision of the moving gantry with the imaged subject. In DECT with LAR data, images suffer from LAR and beam-hardening (BH) artifacts. In this work, we investigate the simultaneous correction of LAR and BH artifacts for DECT with LAR data. Under a scanning configuration with overlapping arcs of low- and high-kVp spectra, data are generated from a digital suitcase phantom. A data-domain decomposition method is used to correct for the BH artifacts first, while basis images are reconstructed from the decomposed basis sinograms of LAR by use of the previously developed directional-total-variation (DTV) algorithm to correct for the LAR artifacts. Visual inspection of the monochromatic images and quantitative analysis of estimated atomic numbers suggest that the simultaneous correction of BH and LAR artifacts in DECT can effectively reduce, and almost eliminate, BH and LAR artifacts in monochromatic images from data of LAR as low as 30◦ , and also yield accurately estimated atomic numbers that are almost numerically identical to the reference values from the full-angular-range data of 360° .
In this work, we investigate and develop a method for cross-section image reconstruction from data collected over limited-angular ranges in the context of human-limb imaging. We first design a convex optimization program with constraints on directional image total-variations (TVs), and then tailor a convex primal-dual algorithm, which is referred to as the directional TV (DTV) algorithm, for solving this program. By using the proposed DTV algorithm, we investigate image reconstructions in studies with data collected from numerical thigh phantoms over a limited-angular range of 60◦. The results of the numerical studies demonstrate that the method proposed can yield, from limited-angular-range data, cross-section images with significantly reduced artifacts that are observed otherwise in images obtained with existing algorithms.
KEYWORDS: Digital breast tomosynthesis, Reconstruction algorithms, Digital imaging, Image restoration, Mammography, Algorithm development, Yield improvement
In digital breast tomosynthesis (DBT), in-plane images are of clinical utility, whereas images within transverse planes contain significant artifacts simply because the existing algorithms are not designed for reconstructing accurately images within transverse planes from extremely limited-angular-range data. In this work, we investigate and develop a convex primal-dual (CPD) algorithm that incorporates directional total-variation (DTV) constraints for yielding breast images within transverse planes with substantially reduced artifacts when images are reconstructed from DBT data. We have performed numerical studies to demonstrate that the algorithm proposed has the potential to yield breast images with substantially reduced artifacts within transverse planes observed in images obtained otherwise with existing algorithms.
Simultaneous estimation of spectra and basis images in multispectral CT reconstruction employs a data model with unknown spectra. One approach is based on the linearization of the data model, which leads to two linear terms, with regards to the basis image and to the spectrum. The latter one, i.e., the linearized matrix of spectral contribution, is new, to the best of our knowledge, and warrants investigations. In this work, we have characterized the conditioning of the linearized matrix of spectral contribution using singular value decomposition (SVD). We have also proposed a SVD-based preconditioner for the matrix and incorporated it in a constrained optimization problem for recovering the spectrum. The results have showed improved conditioning of the matrix and accurate recovery of the spectrum by use of the SVD-based preconditioner.
Purpose: Inverting the discrete x-ray transform (DXT) with the nonlinear partial volume (NLPV) effect, which we refer to as the NLPV DXT, remains of theoretical and practical interest. We propose an optimization-based algorithm for accurately and directly inverting the NLPV DXT.
Methods: Formulating the inversion of the NLPV DXT as a nonconvex optimization program, we propose an iterative algorithm, referred to as the nonconvex primal-dual (NCPD) algorithm, to solve the problem. We obtain the NCPD algorithm by modifying a first-order primal-dual algorithm to address the nonconvex optimization. Subsequently, we perform quantitative studies to verify and characterize the NCPD algorithm.
Results: In addition to proposing the NCPD algorithm, we perform numerical studies to verify that the NCPD algorithm can reach the devised numerically necessary convergence conditions and, under the study conditions considered, invert the NLPV DXT by yielding numerically accurate image reconstruction.
Conclusion: We have developed and verified with numerical studies the NCPD algorithm for accurate inversion of the NLPV DXT. The study and results may yield insights into the effective compensation for the NLPV artifacts in CT imaging and into the algorithm development for nonconvex optimization programs in CT and other tomographic imaging technologies.
In a standard data model for CT, a single ray often is assumed between a detector bin and the X-ray focal spot even though they are of finite sizes. However, due to their finite sizes, each pair of detector bin and X-ray focal spot necessarily involves multiple rays, thus resulting in the non-linear partial volume (NLPV) effect. When an algorithm developed for a standard data model is applied to data with NLPV effect, it may engender NLPV artifacts in images reconstructed. In the presence of the NLPV effect, data necessarily relates non-linearly to the image of interest, and image reconstruction free of NLPV is thus tantamount to inverting appropriately the non-linear data model. In this work, we develop an optimization-based algorithm for solving the non-linear data model in which the NLPV effect is included, and use the algorithm to investigate the characteristics and reduction of the NLPV artifacts in images reconstructed. The algorithm, motivated by our previous experience in dealing with a non-linear data model in multispectral CT reconstruction, compensates for the NLPV effect by numerically inverting the non-linear data model through solving a non-convex optimization program. The algorithm, referred to as the non-convex Chambolle-Pock (ncCP) algorithm, is used in simulation studies for numerically characterizing the inversion of the non-linear data model and the compensation for the NLPV effect.
In this work, we investigate the non-linear partial volume (NLPV) effect caused by sub-detector sampling in CT. A non-linear log-sum of exponential data model is employed to describe the NLPV effect. Leveraging our previous work on multispectral CT reconstruction dealing with a similar non-linear data model, we propose an optimization-based reconstruction method for correcting the NLPV artifacts by numerically inverting the non-linear model through solving a non-convex optimization program. A non-convex Chambolle-Pock (ncCP) algorithm is developed and tailored to the non-linear data model. Simulation studies are carried out with both discrete and continuous FORBILD head phantom with one high-contrast ear section on the right side, based on a circular 2D fan-beam geometry. The results suggest that, under the data condition in this work, the proposed method can effectively reduce or eliminate the NLPV artifacts caused by the sub-detector ray integration.
Cone-beam artifact may be observed in the images reconstructed from circular trajectory data by use of the FDK algorithm or its variants for an imaged subject with longitudinally strong contrast variation in advanced diagnostic CT with a large number of detector rows. Existing algorithms have limited success in correcting for the effect of the cone-beam artifacts especially on the reconstruction of low-contrast soft-tissue. In the work, we investigate and develop optimization-based reconstruction algorithms to compensate for the cone-beam artifacts in the reconstruction of low-contrast anatomies. Specifically, we investigate the impact of optimization-based reconstruction design based upon different data-fidelity terms on the artifact correction by using the Chambolle- Pock (CP) algorithm tailored to each of the specific data-fidelity terms considered. We performed numerical studies with real data collected with the 320-slice Canon Medical System CT scanner, demonstrated the effectiveness of the optimization-based reconstruction design, and identified the optimization-based reconstruction that corrects most effectively for the cone-beam artifacts.
C-arm cone-beam CT (CBCT) is adopted rapidly for imaging-guidance in interventional and surgical procedures. However, measured CBCT data are truncated often due to the limited detector size especially in the presence of additional interventional devices outside the imaging field of view (FOV). In our previous work, it has been demonstrated that a constrained optimization-based reconstruction with an additional data-derivative fidelity term can effectively suppress the truncation artifacts. In this work, in attempt to evaluate the optimization-based reconstruction, two task-relevant metrics, are proposed for characterization of the recovery of the low-contrast objects and the reduction of streak artifacts. Results demonstrate that the optimization program and the associated CP algorithms can significantly reduce streak artifacts, leading to improved visualization of lowcontrast structures in the reconstruction relative to clinical FDK reconstruction.
Kilo-voltage cone-beam computed tomography (CBCT) plays an important role in image guided radiation therapy (IGRT) by providing 3D spatial information of tumor potentially useful for optimizing treatment planning. In current IGRT CBCT system, reconstructed images obtained with analytic algorithms, such as FDK algorithm and its variants, may contain artifacts. In an attempt to compensate for the artifacts, we investigate optimization-based reconstruction algorithms such as the ASD-POCS algorithm for potentially reducing arti- facts in IGRT CBCT images. In this study, using data acquired with a physical phantom and a patient subject, we demonstrate that the ASD-POCS reconstruction can significantly reduce artifacts observed in clinical re- constructions. Moreover, patient images reconstructed by use of the ASD-POCS algorithm indicate a contrast level of soft-tissue improved over that of the clinical reconstruction. We have also performed reconstructions from sparse-view data, and observe that, for current clinical imaging conditions, ASD-POCS reconstructions from data collected at one half of the current clinical projection views appear to show image quality, in terms of spatial and soft-tissue-contrast resolution, higher than that of the corresponding clinical reconstructions.
There exists interest in designing a PET system with reduced detectors due to cost concerns, while not significantly compromising the PET utility. Recently developed optimization-based algorithms, which have demonstrated the potential clinical utility in image reconstruction from sparse CT data, may be used for enabling such design of innovative PET systems. In this work, we investigate a PET configuration with reduced number of detectors, and carry out preliminary studies from patient data collected by use of such sparse-PET configuration. We consider an optimization problem combining Kullback-Leibler (KL) data fidelity with an image TV constraint, and solve it by using a primal-dual optimization algorithm developed by Chambolle and Pock. Results show that advanced algorithms may enable the design of innovative PET configurations with reduced number of detectors, while yielding potential practical PET utilities.
X-ray fluorescence computed tomography (XFCT) is a synchrotron-based imaging modality employed for mapping the distribution of elements within slices or volumes of intact specimens. A pencil beam of external radiation is used to stimulate emission of characteristic X-rays from within a sample, which is scanned and rotated through the pencil beam in a first-generation tomographic geometry. It has long been believed that for each slice, the acquired measurement lines must
span the entire object at every projection view over 180 degrees to avoid reconstructing images with so-called truncation artifacts. However, recent developments in tomographic reconstruction theory have overturned those long-held beliefs about minimum-data requirements and shown that it is possible to obtain exact reconstruction of ROIs from truncated projections. In this work, we show how to exploit these developments to allow for region of interest imaging in XFCT.
In classical tomosynthesis, the x-ray source generally is moved along a curve segment, such as a circular trajectory, within a plane that is perpendicular to the detector plane. Studies suggest that when the angular coverage and number of projection views are limited, it can be difficult to reconstruct accurate images within planes perpendicular to the detector plane in classical tomosynthesis. In this work, we investigate imaging strategies in tomosynthesis using trajectories that are not confined within a plane perpendicular to the detector plane. We expect that such trajectories can increase data information and thus lead reconstructed images with improved quality. Numerical studies were conducted for evaluating the image-reconstruction quality in classical tomosynthesis and tomosynthesis with trajectories that are not confined within a plane perpendicular to the detector plane. The results of the studies indicated that, with the same number of views, (or equivalenntly, the same amount of image radiation), data acquired in tomosynthesis with the trajectories that are not confined within a plane perpendicluar to the detector plane generally contain more information than that acquired with classical tomosynthesis and can thus yield images with improved quality.
X-ray differential phase-contrast tomography (DPCT) is a method for reconstructing the spatial distribution of
the X-ray refractive index within an object from knowledge of differential projection data. Assuming geometrical
optics wave propagation, these data describe the angles by which the probing optical beams are deflected by
the object due to refraction. Phase-sensitive X-ray imaging methods such as diffraction enhanced imaging can
measure the required beam-deflection data, and are being actively developed for medical imaging applications.
In this work, we investigate and demonstrate the applicability of algorithms recently developed for conventional
tomography for obtaining region-of-interest images in DPCT from knowledge of truncated differential projection
data. A preliminary numerical study is conducted to validate and demonstrate the proposed reconstruction
algorithm.
KEYWORDS: Breast, Computed tomography, Reconstruction algorithms, Image restoration, CT reconstruction, Data acquisition, Medical imaging, Scanners, 3D image processing, Algorithm development
Current dedicated, cone-beam breast CT scanners generally use a circular
scanning configuration largely because it is relatively easy to implement
mechanically. It is also well-known, however, that a circular scanning
configuration produces insufficient cone-beam data for reconstrucing
accurate 3D breast images. Approximate algorithms, such as FDK has
been widely applied to reconstruct images from circular cone-beam
data. In the FDK reconstruction, it is possible to observe artifacts such as
intensity decay for locations that are not within the plane containing
the circular source trajectory. Such artifacts may potentially lead
to false positive and/or false negative diagnosis of breast cancer.
Non-circular imaging configurations may provide data sufficient for accurate image reconstruction.
In this work, we implement, investigate innovative, non-circular scanning
configurations such as helical and saddle configurations for data
acquisition on a dedicated, cone-beam breast CT scanner, and develop
novel algorithms to reconstruct accurate 3D images from these data.
A dedicated, cone-beam breast CT scanner capable of performing non-circular
scanning configurations was used in this research. We have investigated
different scanning configurations, including helical and saddle configurations.
A Defrise disk phantom and a dead mouse were scanned by use of these
configurations. For each configuration, cone-beam data were acquired
at 501 views over each turn. We have reconstructed images using our
BPF algorithm from data acquired with the helical scanning
configuration.
Some of the recently developed image reconstruction algorithms for cone-beam computed tomography (CBCT)
involve the computation of the finite Hilbert transform. We have previously studied noise property of the finite
Hilbert transform and observed that it can be used for potentially improving the image noise property within a region
of interest (ROI) in IGRT. Imaging radiation dose is one of the critical issues in IGRT, and in addition to existing dose-reduction
schemes by use of ROI imaging, it is possible to achieve further patient dose reduction through modulating
beam intensity so that a sub-ROI in the ROI be exposed by high flux of x-ray photons and the rest of the ROI be
exposed by low flux of them. In this work, we investigate the technique for obtaining sub-ROI images, which is
supposed to include the target under treatment, with high contrast-to-noise ratio (CNR) and the images within the rest
of the ROI with low CNR. Numerical studies have been conducted as a preliminary in this work.
The back-projection filtration (BPF)algorithm is capable of reconstructing
ROI images from truncated data acquired with
a wide class of general trajectories. However, it has been observed
that, similar to other algorithms for convergent beam geometries,
the BPF algorithm involves a spatially varying
weighting factor in the backprojection step.
This weighting factor can not only increase the computation
load, but also amplify the noise in reconstructed images
The weighting factor can be eliminated
by appropriately rebinning the measured cone-beam
data into fan-parallel-beam data. Such an appropriate data rebinning
not only removes the weighting factor, but also retain other favorable
properties of the BPF algorithm. In this work, we conduct a preliminary
study of the rebinned BPF algorithm and its noise property. Specifically,
we consider an application in which the detector and source can move in
several directions for achieving ROI data acquisition. The combined
motion of the detector and source generally forms a complex trajectory.
We investigate in this work image reconstruction within an ROI from data
acquired in this kind of applications.
Chord-based algorithms can eliminate cone-beam artifacts in images reconstructed from a clinical computed
tomography (CT) scanner. The feasibility of using chord-based reconstruction algorithms was evaluated with
three clinical CT projection data sets.
The first projection data set was acquired using a clinical
64-channel CT scanner (Philips Brilliance 64) that
consisted of an axial scan from a quality assurance phantom. Images were reconstructed using (1) a full-scan
FDK algorithm, (2) a short-scan FDK algorithm, and (3) the
chord-based backprojection filtration algorithm
(BPF) using full-scan data. The BPF algorithm was capable of reproducing the morphology of the phantom
quite well, but exhibited significantly less noise than the two FDK reconstructions as well as the reconstruction
obtained from the clinical scanner.
The second and third data sets were obtained from scans of a head phantom and a patient's thorax. For both
of these data sets, the BPF reconstructions were comparable to the short-scan FDK reconstructions in terms of
image quality, although sharper features were indistinct in the BPF reconstructions.
This research demonstrates the feasibility of chord-based algorithms for reconstructing images from clinical
CT projection data sets and provides a framework for implementing and testing algorithmic innovations.
In this work, we introduced an algorithm for image reconstruction in helical cone-beam CT based upon the backprojection-filtration (BPF) algorithm. This algorithm is a backprojection-filtration-type algorithm that reconstructs images from rebinned data. It retains the properties of the original BPF algorithm in that it requires minimum data and can reconstruct ROI images from truncated data. More importantly, due to the elimination of the spatially-variant weighting factor in the backprojection, it may improve the noise properties in reconstructed images. We have performed computer-simulation studies to investigate the ROI-image reconstruction and noise properties of this algorithm, and the quantitative results verify and demonstrate the proposed algorithm.
Usage of the backprojection filtration (BPF) algorithm for reconstructing images from motion-contaminated fan-beam data may result in motion-induced streak artifacts, which appear in the direction of the chords on which images are reconstructed. These streak artifacts, which are most pronounced along chords tangent to the edges of the moving object, may be suppressed by use of the weighted BPF (WBPF) algorithm, which can exploit the inherent redundancies in fan-beam data. More specifically, reconstructions using full-scan and short-scan data can allow for substantial suppression of these streaks, whereas those using reduced-scan data can allow for partial suppression. Since multiple different reconstructions of the same chord can be obtained by varying the amount of redundant data used, we have laid the groundwork for a possible method to characterize the amount of motion encoded within the data used for reconstructing an image on a particular chord. Furthermore, since motion artifacts in WBPF reconstructions using full-scan and short-scan data appear similar to those in corresponding fan-beam filtered backprojection (FFBP) reconstructions for the cases performed in this study, the BPF and WBPF algorithms potentially may be used to arrive at a more fundamental characterization of how motion artifacts appear in FFBP reconstructions.
A formula was recently described by Clackdoyle et. al. for image reconstruction within a region of interest (ROI) from knowledge of its truncated 2D Radon transform. In this work, we present an alternative, simple derivation of the formula by using the well-known relationship between the parallel-beam and fan-beam geometries. Based upon our derivation, the role of parameter t in the formula in ROI-image reconstruction can be clearly identified. We show that the parameter t determines the size of a reconstructible ROI from parallel-beam data containing truncations. Numerical studies were performed to by use of the formula with different t. We show that the formula yields ROI images with smaller sizes and lower quality than does our backprojection filtration algorithm.
In this work, we investigate exact image reconstruction
within a 3D region of interest from data acquired with
a circle-arc trajectory. In particular, the data
may contain both longitudinal and transverse truncations.
This work may find applications
in lung or heart imaging using a C-arm scanner.
When the arc portion of the trajectory is posterior
or anterior to the patient, exact images within the
lung or heart region can be reconstructed from truncated
data.
Recently, a 3D filtered-backprojection (FBP)-based algorithm for image reconstruction on PI-line segments in a helical cone-beam CT scan has been developed (Zou and Pan, 2004). In the present work, we derive new reconstruction algorithms for circular cone-beam scans based upon this algorithm and a concept of virtual PI-line. We prove that, in the case of conventional full- and short-scan, the newly derived algorithms are mathematically identical to existing algorithms. More importantly, in the case of reduced-scans in which the scanning angle range is less than that in a short-scan, the new algorithms can yield exact region of interest (ROI) reconstruction in mid-plane and approximate ROI reconstruction in off-mid-planes. We have performed a preliminary numerical study that verifies our theoretical assertions.
In fan-beam computed tomography (CT), one may be interested in image reconstruction in a region of interest (ROI) from truncated data acquired over an angular range less than half-scan data. We developed recently a backprojection filtration (BPF) algorithm to reconstruct an ROI image from reduced scan data containing data truncations. In a reduced scan, the truncated data may still contain redundancy. In this work, we describe a new algorithm that can exploit data redundancy in truncated data for potentially suppressing the aliasing and noise artifacts in reconstructed images.
We have performed numerical studies to demonstrate the BPF algorithm.
Recent algorithm development for image reconstruction for cone-beam CT has tackled exact image reconstruction for very general scanning configurations. The heart of the new algorithms is the concept of reconstruction on the chordn of a general source trajectory. Volume ROI reconstruction becomes possible by concatenating the chords on which the image has been obtained. For some scanning trajectories there maybe points in the image space where the image can theoretically be obtained exactly, yet no chord intersects these points. This article provides a consistency condition, based on the ideas of John's equation, that may be used to rebin cone-beam data so that all points satisfying Tuy's condition are reconstructible
by a chord algorithm.
In many applications of circular cone-beam CT, it is not uncommon that the size of the field of view (FOV) is smaller than that of the imaging object, thus leading to transverse truncation in projection data. Exact reconstruction in any region is not possible from such truncated data using conventional algorithms. Recently, an exact algorithm for image reconstruction on PI-line segments in helical cone-beam CT has been proposed. This algorithm, which we refer to as the backprojection-filtration (BPF) algorithm, can naturally address the problem of exact region of interest (ROI) reconstruction from such truncated data. In this work, we modified this algorithm to reconstructing images in circular cone-beam scan. The unique property of this modified algorithm is that it can reconstruct exact ROIs in midplane and approximate ROIs in other planes from transversely truncated data. We have performed computer-simulation studies to validate the theoretical assertions. Preliminary results demonstrate that the proposed algorithm provides a solution to the truncation problems caused by limited FOV size.
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