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° .
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.
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.
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 and characterize optimization-based image reconstruction from list-mode TOFPET data collected by using a digital TOF-PET scanner with reduced detectors, while seeking possibly to maintain the image quality and volume coverage. In particular, we focused on two patterns of sparse configurations, in both of which the total number of crystals is reduced to 50% of the corresponding clinical TOF-PET scanner. The reconstruction problem from data of the two sparse configurations is formulated as the solution to an image-TV-constrained, data-KLminimization optimization problem, and the image is reconstructed by use of an algorithm tailored from a Chambolle and Pock (CP) algorithm through solving the optimization problem. The characteristics of each sparse configuration was investigated by assessing the corresponding reconstructions visually and quantitatively. Results of the study suggest that certain sparse TOF-PET configurations may yield images with quality and volume coverage comparable to that obtained with current clinical TOF-PET scanner that has densely populated detectors.
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.
Time-of-flight (TOF) positron emission tomography (PET) has gained remarkable development recently due to the advances in scintillator, silicon photomultipliers (SiPM), and fast electronics. However, current clinical reconstruction algorithms in TOF-PET are still based on ordered-subset-expectation-maximization (OSEM) and its variants, which may face challenges in non-conventional imaging applications, such as fast imaging within short scan time. In this work, we propose an image-TV constrained optimization problem, and tailor a primal- dual algorithm for solving the problem and reconstructing images. We collect list-mode data of a Jaszczak phantom with a prototype digital TOF-PET scanner. We focus on investigating image reconstruction from data collected within reduced scan time, and thus of lower count levels. Results of the study indicate that our proposed algorithm can 1) yield image reconstruction with suppressed noise, extended axial volume coverage, and improved spatial resolution over that obtained in conventional reconstructions, and 2) yield reconstructions with potential clinical utility from data collected within shorter scan time.
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.
Photon counting x-ray detectors (PCD) offer a great potential for energy-resolved imaging that would allow for promising applications such as low-dose imaging, quantitative contrast-enhanced imaging, as well as spectral tissue decomposition. However, physical processes in photon counting detectors produce undesirable effects like charge sharing and pulse-pile up that can adversely affect the imaging application. Existing detector response models for photon counting detectors have mainly used either X-ray fluorescence imaging or radionuclides to calibrate their detector and estimate the model parameters. The purpose of our work was to apply one such model to our photon counting detector and to determine the model parameters from transmission measurements. This model uses a polynomial fit to model the charge sharing response and energy resolution of the detector as well as an Aluminum filter to model the modification of the spectrum by the X-ray. Our experimental setup includes a Si-based photon counting detector to generate transmission spectra from multiple materials at varying thicknesses. Materials were selected so as to exhibit k-edges within the 15-35 keV region. We find that transmission measurements can be used to successfully model the detector response. Ultimately, this approach could be used for practical detector energy calibration. A fully validated detector response model will allow for exploration of imaging applications for a given detector.
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.
We report on the development of silicon strip detectors for energy-resolved clinical mammography. Typically, X-ray integrating detectors based on scintillating cesium iodide CsI(Tl) or amorphous selenium (a-Se) are used in most commercial systems. Recently, mammography instrumentation has been introduced based on photon counting Si strip detectors. The required performance for mammography in terms of the output count rate, spatial resolution, and dynamic range must be obtained with sufficient field of view for the application, thus requiring the tiling of pixel arrays and particular scanning techniques. Room temperature Si strip detector, operating as direct conversion x-ray sensors, can provide the required speed when connected to application specific integrated circuits (ASICs) operating at fast peaking times with multiple fixed thresholds per pixel, provided that the sensors are designed for rapid signal formation across the X-ray energy ranges of the application. We present our methods and results from the optimization of Si-strip detectors for contrast enhanced spectral mammography. We describe the method being developed for quantifying iodine contrast using the energy-resolved detector with fixed thresholds. We demonstrate the feasibility of the method by scanning an iodine phantom with clinically relevant contrast levels.
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