Incomplete Projection Research Articles

Partial CT for in situ bridge NDE with 950 keV/3.95 MeV X-band linac source

Computed tomography system for in situ NDE of degradation bridges is under development, with portable 950 keV/3.95 MeV X-band linac as x-ray source. Collimator is adopted to reduce scattered X-ray noise and 3D model can be built from sectional images so that it becomes possible to evaluate mechanical characters of bridges referring to structural analysis with reduced stiffness. Furthermore, considering limitation of projection angle range during in situ scanning, recon- struction technique with incomplete projection data is studied with experimental data.

Ordered subset image reconstruction studied by means of total variation minimization and fast first-order method in low dose computed tomograhpy

Low-dose computed tomography(CT) has an advantage to reduce X-rays that are harmful to the body. This paper considers the issue of reconstructing high-quality low-dose CT images from incomplete projection data. Generally, this can be done by statistical image reconstruction methods. However, the huge number of iterations of the statistical reconstruction algorithms leads to long computing time, making them difficult to be of practical value. To solve this problem, we propose a method to alleviate the issue by using total variation minimization and fast first-order method for the ordered subsets. We use Split Bregman alternating direction method to solve the optimization problem. Then, the projection onto convex sets method is used to speed up the convergence rate of the iterative method. Numerical experiments show that the relative reconstruction error of the proposed method can decrease faster than the first-order method of ordered subsets with the same iterative number.

应用投影收缩的压缩感知锥束CT短扫描重建

To solve the problem of image reconstruction of incomplete projection data from a short-scan cone-beam CT, a novel cone-beam CT short-scan reconstruction algorithm was proposed based on projection-contraction method. Aiming at the non-monotonic convergence of the Gradient-Projection Barzilari-Borwein (GPBB) algorithm, the predictor-corrector feature of projection-contraction method was analyzed and incorporated into compressed sensing image reconstruction algorithm. The objective function descent direction and the projection onto convex sets descent direction were combined to correct the results of GPBB algorithm to improve the non-monotonic convergence of GPBB algorithm. Then, the experiments were conducted on simulated projection data and phantom scanning data. The simulated results for 25 sampling angles show that the signal-to-noise ratios of images reconstructed by PCBB algorithm are 9.4870, 9.8027, 3.6159 db higher than those of images reconstructed by Adaptive Steepest Descent-Projection onto Convex Sets algorithm, projection contraction algorithm and GPBB algorithm, respectively. The simulation results indicate that when a small amount of projections are acquired, the new algorithm has effectively suppressed strip artifacts and the reconstructed images show clear edges. The algorithm can greatly improved the qualify of images reconstructed from few projection data.

Review of reconstruction algorithms with incomplete projection data of computed tomography

This paper mainly reviews the progress of methods, and research development in the field of computed tomography(CT) with incomplete projection data, at home and abroad, on limited angle projection data reconstruction with the detector fully covered, and truncated data reconstruction with the detector partially covered. Firstly, the discrete model iterative reconstruction algorithm and the compressed sensing(CS) sampling reconstruction algorithm are discussed for the sparsely uniform and limited-view angle sampling in the case that the detector fully covers the detected object. Secondly, the reconstruction algorithm of back-projection filtration(BPF) for helical cone beam and improved ones for cone beam FDK are discussed in the case that the detector could not fully cover the detected object. This paper could provide the researchers in CT reconstruction field the criticism of methods and summaries. Furthermore, it also points out current focus of the study and the research direction in the future.

An investigation of the challenges in reconstructing PET images of a freely moving animal

Imaging the brain of a freely moving small animal using positron emission tomography (PET) while simultaneously observing its behaviour is an important goal for neuroscience. While we have successfully demonstrated the use of line-of-response (LOR) rebinning to correct the head motion of confined animals, a large proportion of events may need to be discarded because they either 'miss' the detector array after transformation or fall out of the acceptance range of a sinogram. The proportion of events that would have been measured had motion not occurred, so-called 'lost events', is expected to be even larger for freely moving animals. Moreover, the data acquisition in the case of a freely moving animal is further complicated by a complex attenuation field. The aims of this study were (a) to characterise the severity of the 'lostevents' problem for the freely moving animal scenario, and(b) to investigate the relative impact of attenuation correction errors on quantitative accuracy of reconstructed images. A phantom study was performed to simulate the uncorrelated motion of a target and non-target sourcevolume. A small animal PET scanner was used to acquirelist-mode data for different sets of phantom positions. The list-mode data were processed using the standard LOR rebinning approach, and multiple frame variants of this designed to reduce discarded events. We found that LOR rebinning caused up to 86 % 'lost events', and artifacts that we attribute to incomplete projections, when applied to a freely moving target. This fraction was reduced by up to 18 % using the variant approaches, resulting in slightly reduced image artifacts. The effect of the non-target compartment on attenuation correction of the target volume was surprisingly small. However, for certain poses where the target and non-target volumes are aligned transaxially in the field-of-view, the attenuation problem becomes more complex and sophisticated correction methods will be required. We conclude that there are limitations with the LOR rebinning approach and simplified attenuation correction for freely moving animals requiring the development and validation of more sophisticated approaches.

Image reconstruction for sparse-view CT and interior CT-introduction to compressed sensing and differentiated backprojection.

New designs of future computed tomography (CT) scanners called sparse-view CT and interior CT have been considered in the CT community. Since these CTs measure only incomplete projection data, a key to put these CT scanners to practical use is a development of advanced image reconstruction methods. After 2000, there was a large progress in this research area briefly summarized as follows. In the sparse-view CT, various image reconstruction methods using the compressed sensing (CS) framework have been developed towards reconstructing clinically feasible images from a reduced number of projection data. In the interior CT, several novel theoretical results on solution uniqueness and solution stability have been obtained thanks to the discovery of a new class of reconstruction methods called differentiated backprojection (DBP). In this paper, we mainly review this progress including mathematical principles of the CS image reconstruction and the DBP image reconstruction for readers unfamiliar with this area. We also show some experimental results from our past research to demonstrate that this progress is not only theoretically elegant but also works in practical imaging situations.

On the incomplete oblique projections method for solving box constrained least squares problems

The aim of this paper is to extend the applicability of the incomplete oblique projections method (IOP) previously introduced by the authors for solving inconsistent linear systems to the box constrained case. The new algorithm employs incomplete projections onto the set of solutions of the augmented system Ax − r = b, together with the box constraints, based on a scheme similar to the one of IOP, adding the conditions for accepting an approximate solution in the box. The theoretical properties of the new algorithm are analyzed, and numerical experiences are presented comparing its performance with some well-known methods.

SU-C-144-07: Maximally Spaced Projection Sequencing in Electron Paramagnetic Resonance Imaging

Purpose: Electron paramagnetic resonance imaging (EPRI) is a projection based imaging modality that noninvasively provides 3D images of absolute oxygen concentration (pO2) in vivo with excellent spatial and pO2 resolution. When studying physiologic parameters, such as tissue pO2, in living animals, the situation is inherently dynamic. This may be due to physical movement during imaging leading to artifacts or physiologically relevant temporal changes in pO2 (i.e. acute hypoxia). In order to properly study such a dynamic system, improvements in temporal resolution and experimental versatility are necessary. Methods: For projection based imaging, uniformly distributed projections Result in efficient use of data for image reconstruction. This has led to the current equal-solid-angle (ESA) spacing of projections for EPRI. However, acquisition sequencing must still be optimized in order to achieve uniformity throughout imaging. An object-independent method for uniform acquisition of projections, using the ESA distribution for the final set of projections, is presented. Each successive projection is selected in such a way as to minimize the electrostatic potential energy between itself and prior projections, when projection direction points are considered to be point charges on the unit sphere. Results: This maximally spaced projection sequencing (MSPS) method significantly improves image quality for intermediate images reconstructed from incomplete projection sets. This enables useful real-time reconstruction. Additionally, the MSPS method provides improved experimental versatility, reduced artifacts, and the ability to adjust temporal resolution post factum to best fit the data and its application. Conclusion: The MSPS method in EPRI provides necessary improvements in order to more appropriately image and study physiologic changes in a dynamic system. This work was supported by grants from the NIH (P41 EB002034 and R01 CA98575).

Managing Postoperative Artifacts on Computed Tomography and Magnetic Resonance Imaging

Orthopedic hardware should not be considered a contraindication to computed tomography (CT) or magnetic resonance (MR) imaging. The hardware alloy, the geometry of the hardware, and the orientation of the hardware all affect the magnitude of image artifacts. For commonly encountered alloys, the severity of image artifacts is similar for CT and MR. Cobalt chrome or stainless steel hardware produces the most artifacts; titanium hardware produces the least. In general, image artifacts are most severe adjacent to the hardware. CT image artifacts are related to incomplete X-ray projection data resulting in streaks. These can be mitigated by increasing scan technique and using a smoother reconstruction filter. Hardware with a rectangular cross-sectional shape such as a fixation plate will cause more artifacts than a radially symmetrical device such as an intramedullary nail. Image artifacts at MR are caused by the hardware magnetic susceptibility and the induction of eddy currents within the metal. A turbo spin-echo sequence yields the best results. The use of larger image matrices, thinner slices, and a wide receiver bandwidth are recommended parameter adjustments when imaging patients with hardware. This article discusses how hardware-related artifacts can be minimized by altering scan technique and image reconstruction.

P2-366 The global distribution of dengue: past, present and future impacts of climate change

IntroductionApproximately 2.5 billion people are at risk from dengue. Climate change could drive the epidemic potential of this disease through temperature impacts on both the virus and the mosquito vector....

SU‐E‐J‐179: Clinical Application of 40o Very Limited Angle CBCT (VLA CBCT) for Target Localization of Lung Cancer Patient Who Is Treated with SBRT and ABC in Conventional Radiation Therapy

Purpose: 40o VLA CBCT is used to verify the target position of lung cancer patient treated with x‐ray Stereotactic Body Radiation Therapy (SBRT) and Automatic Breath Coordinator (ABC) using Elekta SynergyTM linear accelerator, and XVITM CBCT. Methods: Limited Angle CBCT (LA CBCT) with 40o scanning angles is determined by (1) the maximum time the patient can hold breath (15–20 seconds) under ABC technique, and (2) the minimum scan angles to reconstruct the target with minimum artifacts due to incomplete projections, and (3) the start and stop angles of the LA CBCT, which is determined by the location of the tumor as well as geometry of the lung. Based upon the phantom study, 40o CBCT (with S20 collimator and H&N reconstruction option) starting from 160 to 200 is the optimum to reconstruct the target in coronal images. In the range of these angles, the target is minimally over‐shadowed by the vertebral bodies and mediastinum, thus the target can be determined in the CBCT images. Free‐breathing (FB) CBCT is taken to determine the maximum range of the target movements, and 4 sets of VLA CBCT are taken to investigate the reproducibility of the VLA CBCT procedure.Results: The target movements with FB CBFT are ∼1cm in lateral and AP direction, and 2.5cm in Sup/Inf direction. The average motions during 4 breadth‐hold procedures are less than 5mm, which is on the order of uncertainties in intra/inter user variation. Also, VLA CBCTˈs are taken every 3 fields of the treatment. Their movements are the same ranges. Conclusions: The VLA CBCT is very effective to evaluate the target movements in the middle of the lung and to acquire images (20 seconds for VLA CBCT vs 2minutes for conventional 360o CBCT). Also, patient dose is reduced from 3–4cGy with standard CBCTto<0.1cGy.

Model‐based optoacoustic inversions with incomplete projection data

Optoacoustic imaging is an emerging noninvasive imaging modality that can resolve optical contrast through several millimeters to centimeters of tissue with diffraction-limited resolution of ultrasound. Yet, quantified reconstruction of tissue absorption maps requires optoacoustic signals to be collected from as many locations around the object as possible. In many tomographic imaging scenarios, however, only limited-view or partial projection data are available, which has been shown to generate image artifacts and overall loss of quantification accuracy. In this article, the recently introduced interpolated-matrix-model optoacoustic inversion method is tested in different limited-view scenarios and compared to the standard backprojection algorithm. Both direct (TGSVD) and iterative (PLSQR) regularization methods are proposed to improve the accuracy of image reconstructions with their performance tested on simulated and experimental data. While for full-view tomographic data the model-based inversion has been generally shown to attain higher reconstruction accuracy compared to backprojection algorithms, the incomplete tomographic datasets lead to ill-conditioned forward matrices and, consequently, to error-prone inversions, with strong artifacts following a distinct ripple-type pattern. The proposed regularization techniques are shown to stabilize the inversion and eliminate the artifacts. Overall, it has been determined that the regularized interpolated-matrix-model-based optoacoustic inversions show higher accuracy than reconstructions with the standard backprojection algorithm. Finally, the combination of model-based inversion with PLSQR or TGSVD regularization methods can lead to an accurate reconstruction of limited-projection angle optoacoustic data and practical systems for optoacoustic imaging in many realistic cases where the full-view dataset is unavailable.

Modified adaptive algebraic tomographic reconstruction of gas distribution from incomplete projection by a two-wavelength absorption scheme

A modified adaptive algebraic reconstruction technique (MAART) with an auto-adjustment relaxation parameter and smoothness regularization is developed to reveal the tomographic reconstruction of H2O distribution in combustion from incomplete projections. Determinations of relaxation parameter and regularization factor are discussed with regard to the consideration of improvement in reconstruction and reduction of computational burden. A two-wavelength scheme from tunable diode laser absorption measurement, 7444.36 and 7185.59 cm ?1, is used to simplify the nonlinear solution problem for obtaining the tomographic distributions of concentration and temperature simultaneously. Results of calculations demonstrate that MAART can perform the reconstruction results more efficiently with little complex modification and much lower iterations as compared with the traditional algebraic reconstruction technique (ART) or simultaneous iterative reconstruction technique (SIRT) methods. The stability of the algorithm is studied by reconstruction from projections with random noise at different levels to demonstrate the dependence of reconstruction results on precise line-of-sight measurements.

Image reconstruction exploiting object sparsity in boundary-enhanced X-ray phase-contrast tomography

Propagation-based X-ray phase-contrast tomography (PCT) seeks to reconstruct information regarding the complex-valued refractive index distribution of an object. In many applications, a boundary-enhanced image is sought that reveals the locations of discontinuities in the real-valued component of the refractive index distribution. We investigate two iterative algorithms for few-view image reconstruction in boundary-enhanced PCT that exploit the fact that a boundary-enhanced PCT image, or its gradient, is often sparse. In order to exploit object sparseness, the reconstruction algorithms seek to minimize the l(1)-norm or TV-norm of the image, subject to data consistency constraints. We demonstrate that the algorithms can reconstruct accurate boundary-enhanced images from highly incomplete few-view projection data.

A Patient Set-up Protocol Based on Partially Blocked Cone-beam CT

Three-dimensional x-ray cone-beam CT (CBCT) is being increasingly used in radiation therapy. Since the whole treatment course typically lasts several weeks, the repetitive x-ray imaging results in large radiation dose delivered on the patient. In the current radiation therapy treatment, CBCT is mainly used for patient set-up, and a rigid transformation of the CBCT data from the planning CT data is also assumed. For an accurate rigid registration, it is not necessary to acquire a full 3D image. In this paper, we propose a patient set-up protocol based on partially blocked CBCT. A sheet of lead strips is inserted between the x-ray source and the scanned patient. From the incomplete projection data, only several axial slices are reconstructed and used in the image registration for patient set-up. Since the radiation is partially blocked, the dose delivered onto the patient is significantly reduced, with an additional benefit of reduced scatter signals. The proposed approach is validated using experiments on two anthropomorphic phantoms. As x-ray beam blocking ratio increases, more dose reduction is achieved, while the patient set-up error also increases. To investigate this tradeoff, two lead sheets with different strip widths are implemented, which correspond to radiation dose reduction of approximately 6 and approximately 11, respectively. We compare the registration results using the partially blocked CBCT with those using the regular CBCT. Both lead sheets achieve high patient set-up accuracies. It is seen that, using the lead sheet with radiation dose reduction by a factor of approximately 11, the patient set-up error is still less than 1mm in translation and less than 0.2 degrees in rotation. The comparison of the reconstructed images also shows that the image quality of the illuminated slices in the partially blocked CBCT is much improved over that in the regular CBCT.

Two-dimensional tomography for gas concentration and temperature distributions based on tunable diode laser absorption spectroscopy

A tomography system is presented that uses wavelength-scanned direct absorption of two transitions of a target species (NH3 in the demonstration experiment) to determine the distributions of gas concentration and temperature. The absorption measurements are performed simultaneously from four platforms that each rotate a beam from a single laser through an 11° arc, acquiring a data set from all four laser platforms in 100 ms to enable observation of dynamic flow events. The laser is wavelength scanned through two absorption transitions with different internal energy producing two sets of equations with species mole fraction and temperature as independent variables. The mole fraction and temperature distributions are reconstructed using the algebraic reconstruction technique (ART) for this set of incomplete projections. A numerical simulation is used to evaluate the measurement accuracy for measurements of an NH3 mixture escaping from an open pipe. This phantom distribution is then realized in the laboratory and the measurement strategy is demonstrated using a tunable diode laser absorption spectroscopy (TDLAS) measurement using a single laser near 1.5 µm to scan adjacent transitions in NH3. The reconstruction of NH3 concentration and gas temperature is compared with independently determined values to illustrate the fidelity of the tomographically reconstructed distributions for the NH3 mole fraction assuming a fixed temperature and for unknown mole fraction and temperature. Potential extensions of this research in the future include evaluation of other reconstruction algorithms and investigation of the dynamic distribution of various gases for combustion diagnostics.

Reconstruction From Limited-Angle Projections Based on $\delta-u$ Spectrum Analysis

This paper proposes a sparse representation of an image using discrete delta-u functions. A delta-u function is defined as the product of a Kronecker delta function and a step function. Based on the sparse representation, we have developed a novel and effective method for reconstructing an image from limited-angle projections. The method first estimates the parameters of the sparse representation from the incomplete projection data, and then directly calculates the image to be reconstructed. Experiments have shown that the proposed method can effectively recover the missing data and reconstruct images more accurately than the total-variation (TV) regularized reconstruction method.

Limited-view photoacoustic imaging based on linear-array detection and filtered mean-backprojection-iterative reconstruction

Most existing photoacoustic tomography techniques require collecting complete projection data that are acquired on a defined circle surrounding the object. However, in clinical application, the object can only be approached from a limited angle mostly. Furthermore, with the incomplete projection data acquired in limited view, the general filtered backprojection algorithm will streak image artifacts nearby the reconstructed location of absorbers. In this paper, we present a limited-view-scanning photoacoustic imaging system with a linear transducer array and develop a filtered mean-backprojection-iteration (FMBPI) algorithm to reconstruct the absorbed optical deposit distribution. The FMBPI algorithm combines the terseness of the filtered backprojection algorithm with the accuracy of the iterative reconstruction algorithm. Numerical simulation and experimental results validate that the algorithm can effectively reconstruct high-quality image with limited-view data. It is also demonstrated that with the FMBPI algorithm, the limited-view-scanning multielement photoacoustic imaging system has a great potential to be applied in fast noninvasive clinic diagnosis of breast cancer at the early stage.

Deflection tomographic reconstruction of a complex flow field from incomplete projection data

Tomographic techniques are used for the investigation of complex flow fields by means of deflectometric methods. In this experiment, a modified algebraic reconstruction technique (ART) was applied to moiré deflection tomography. The algorithm was derived from the basic deflection formula and the deflection angles were used directly in iteration, which is completely different from the conventional ARTs with integral calculation that are commonly used in deflection tomography. A smoothing scheme was employed to improve the reconstruction under ill-posed conditions. The reconstruction technique was tested using simulated data for incompleteness conditions similar to those found in the experimental data. The complex density field with an opaque object in a supersonic wind tunnel was reconstructed from limited view angle projections, and the experimental reconstruction was then compared with the result obtained from the computational fluid dynamic analysis. The following paper details the experiment and discusses some measurement errors that occurred in the process.

Implicit regularization of the incomplete oblique projections method

AbstractThe aim of this paper is to improve the performance of the incomplete oblique projections method (IOP), previously introduced by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method employs incomplete oblique projections onto the set of solutions of the augmented system Ax−r=b, and converges to a weighted least squares solution of the system Ax=b. Many tomographic image reconstruction problems are such that the limitation of the range of rays makes the model underdetermined, the discretized linear system is rank‐deficient, the nullspace is non‐trivial, and the minimal norm least squares solution may be far away from the true image. In a previous paper, we have added a quadratic term reflecting neighboring pixel information to the standard least squares model for improving the quality of the reconstructed images. In this paper we replace the quadratic function by a more general regularizing function avoiding the modification of the original system. The key idea is to perform a joint optimization of the norm of the residual and of the regularizing function in each iteration. The theoretical properties of this new algorithm are analyzed, and numerical experiments are presented comparing its performance with other well‐known methods. They show that the new approach improves the quality of the reconstructed images.