Data consistency based rigid motion artifact reduction in fan-beam CT

Gradient-based geometry learning for fan-beam CT reconstruction

Objective.Incorporating computed tomography (CT) reconstruction operators into differentiable pipelines has proven beneficial in many applications. Such approaches usually focus on the projection data and keep the acquisition geometry fixed. However, precise knowledge of the acquisition geometry is essential for high quality reconstruction results. In this paper, the differentiable formulation of fan-beam CT reconstruction is extended to the acquisition geometry.Approach.The CT fan-beam reconstruction is analytically derived with respect to the acquisition geometry. This allows to propagate gradient information from a loss function on the reconstructed image into the geometry parameters. As a proof-of-concept experiment, this idea is applied to rigid motion compensation. The cost function is parameterized by a trained neural network which regresses an image quality metric from the motion-affected reconstruction alone.Main results.The algorithm improves the structural similarity index measure (SSIM) from 0.848 for the initial motion-affected reconstruction to 0.946 after compensation. It also generalizes to real fan-beam sinograms which are rebinned from a helical trajectory where the SSIM increases from 0.639 to 0.742.Significance.Using the proposed method, we are the first to optimize an autofocus-inspired algorithm based on analytical gradients. Next to motion compensation, we see further use cases of our differentiable method for scanner calibration or hybrid techniques employing deep models.

Online geometry calibration for retrofit computed tomography from a mouse rotation system and a small-animal imager

BACKGROUND

Computed tomography (CT) generates a three-dimensional rendering that can be used to interrogate a given region or desired structure from any orientation. However, in preclinical research, its deployment remains limited due to relatively high upfront costs. Existing integrated imaging systems that provide merged planar X-ray also dwarfs CT popularity in small laboratories due to their added versatility.

PURPOSE

In this paper, we sought to generate CT-like data using an existing small-animal X-ray imager with a specialized specimen rotation system, or MiSpinner. This setup conforms to the cone-beam CT (CBCT) geometry, which demands high spatial calibration accuracy. Therefore, a simple but robust geometry calibration algorithm is necessary to ensure that the entire imaging system works properly and accurately.

METHODS

Because the rotation system is not permanently affixed, we propose a structure tensor-based two-step online (ST-TSO) geometry calibration algorithm. Specifically, two datasets are needed, namely, calibration and actual measurements. A calibration measurement detects the background of the system forward X-ray projections. A study on the background image reveals the characteristics of the X-ray photon distribution, and thus, provides a reliable estimate of the imaging geometry origin. Actual measurements consisted of an X-ray of the intended object, including possible geometry errors. A comprehensive image processing technique helps to detect spatial misalignment information. Accordingly, the first processing step employs a modified projection matrix-based calibration algorithm to estimate the relevant geometric parameters. Predicted parameters are then fine-tuned in a second processing step by an iterative strategy based on the symmetry property of the sum of projections. Virtual projections calculated from the parameters after two-step processing compensate for the scanning errors and are used for CT reconstruction. Experiments on phantom and mouse imaging data were performed to validate the calibration algorithm.

RESULTS

Once system correction was conducted, CBCT of a CT bar phantom and a cohort of euthanized mice were analyzed. No obvious structure error or spatial artifacts were observed, validating the accuracy of the proposed geometry calibration method. Digital phantom simulation indicated that compared with the preset spatial values, errors in the final estimated parameters could be reduced to 0.05° difference in dominant angle and 0.5-pixel difference in dominant axis bias. The in-plane resolution view of the CT-bar phantom revealed that the resolution approaches 150 μ $\umu$ m.

CONCLUSIONS

A constrained two-step online geometry calibration algorithm has been developed to calibrate an integrated X-ray imaging system, defined by a first-step analytical estimation and a second-step iterative fine-tuning. Test results have validated its accuracy in system correction, thus demonstrating the potential of the described system to be modified and adapted for preclinical research.

Effect of subject motion and gantry rotation speed on image quality and dose delivery in CT-guided radiotherapy

PURPOSE

To investigate the effects of subject motion and gantry rotation speed on computed tomography (CT) image quality over a range of image acquisition speeds for fan-beam (FB) and cone-beam (CB) CT scanners, and quantify the geometric and dosimetric errors introduced by FB and CB sampling in the context of adaptive radiotherapy.

METHODS

Images of motion phantoms were acquired using four CT scanners with gantry rotation speeds of 0.5 s/rotation (denoted FB-0.5), 1.9 s/rotation (FB-1.9), 16.6 s/rotation (CB-16.6), and 60.0 s/rotation (CB-60.0). A phantom presenting various tissue densities undergoing motion with 4-s period and ranging in amplitude from ±0.5 to ±10.0 mm was used to characterize motion artifacts (streaks), motion blur (edge-spread function, ESF), and geometric inaccuracy (excursion of insert centroids and distortion of known shape). An anthropomorphic abdomen phantom undergoing ±2.5-mm motion with 4-s period was used to simulate an adaptive radiotherapy workflow, and relative geometric and dosimetric errors were compared between scanners.

RESULTS

At ±2.5-mm motion, phantom measurements demonstrated mean ± SD ESF widths of 0.6 ± 0.0, 1.3 ± 0.4, 2.0 ± 1.1, and 2.9 ± 2.0 mm and geometric inaccuracy (excursion) of 2.7 ± 0.4, 4.1 ± 1.2, 2.6 ± 0.7, and 2.0 ± 0.5 mm for the FB-0.5, FB-1.9, CB-16.6, and CB-60.0 scanners, respectively. The results demonstrated nonmonotonic trends with scanner speed for FB and CB geometries. Geometric and dosimetric errors in adaptive radiotherapy plans were largest for the slowest (CB-60.0) scanner and similar for the three faster systems (CB-16.6, FB-1.9, and FB-0.5).

CONCLUSIONS

Clinically standard CB-60.0 demonstrates strong image quality degradation in the presence of subject motion, which is mitigated through faster CBCT or FBCT. Although motion blur is minimized for FB-0.5 and FB-1.9, such systems suffer from increased geometric distortion compared to CB-16.6. Each system reflects tradeoffs in image artifacts and geometric inaccuracies that affect treatment delivery/dosimetric error and should be considered in the design of next-generation CT-guided radiotherapy systems.

Estimating the Center of Rotation of Tomographic Imaging Systems with a Limited Number of Projections

For a tomographic imaging system, image reconstruction quality is dependent on the accurate determination of coordinates for the true center of rotation (COR). A significant COR offset error may introduce ringing, streaking, or other artifacts, while smaller error in determining COR may blur the reconstructed image. Well known COR correction techniques including image registration, center of mass calculation, or reconstruction evaluation work well under certain conditions. However, many of these methods do not consider various real-world cases such as a tilted sensor or non-parallel projections. Furthermore, a limited number of projections introduces stripe artifacts into the image reconstruction that interfere with many of these classic COR correction techniques. In this paper, we propose a revised variance-based algorithm to find the correct COR position automatically prior to tomographic reconstruction. The algorithm was tested on both simulated phantoms and acquired datasets, and our results show improved reconstruction accuracy.

Motion estimation and correction in SPECT, PET and CT

Patient motion impacts single photon emission computed tomography (SPECT), positron emission tomography (PET) and X-ray computed tomography (CT) by giving rise to projection data inconsistencies that can manifest as reconstruction artifacts, thereby degrading image quality and compromising accurate image interpretation and quantification. Methods to estimate and correct for patient motion in SPECT, PET and CT have attracted considerable research effort over several decades. The aims of this effort have been two-fold: to estimate relevant motion fields characterizing the various forms of voluntary and involuntary motion; and to apply these motion fields within a modified reconstruction framework to obtain motion-corrected images. The aims of this review are to outline the motion problem in medical imaging and to critically review published methods for estimating and correcting for the relevant motion fields in clinical and preclinical SPECT, PET and CT. Despite many similarities in how motion is handled between these modalities, utility and applications vary based on differences in temporal and spatial resolution. Technical feasibility has been demonstrated in each modality for both rigid and non-rigid motion, but clinical feasibility remains an important target. There is considerable scope for further developments in motion estimation and correction, and particularly in data-driven methods that will aid clinical utility. State-of-the-art machine learning methods may have a unique role to play in this context.

Appearance Learning for Image-Based Motion Estimation in Tomography

In tomographic imaging, anatomical structures are reconstructed by applying a pseudo-inverse forward model to acquired signals. Geometric information within this process is usually depending on the system setting only, i.e., the scanner position or readout direction. Patient motion therefore corrupts the geometry alignment in the reconstruction process resulting in motion artifacts. We propose an appearance learning approach recognizing the structures of rigid motion independently from the scanned object. To this end, we train a siamese triplet network to predict the reprojection error (RPE) for the complete acquisition as well as an approximate distribution of the RPE along the single views from the reconstructed volume in a multi-task learning approach. The RPE measures the motion-induced geometric deviations independent of the object based on virtual marker positions, which are available during training. We train our network using 27 patients and deploy a 21-4-2 split for training, validation and testing. In average, we achieve a residual mean RPE of 0.013mm with an inter-patient standard deviation of 0.022mm. This is twice the accuracy compared to previously published results. In a motion estimation benchmark the proposed approach achieves superior results in comparison with two state-of-the-art measures in nine out of twelve experiments. The clinical applicability of the proposed method is demonstrated on a motion-affected clinical dataset.

Rigid and non-rigid motion artifact reduction in X-ray CT using attention module

Motion artifacts are a major factor that can degrade the diagnostic performance of computed tomography (CT) images. In particular, the motion artifacts become considerably more severe when an imaging system requires a long scan time such as in dental CT or cone-beam CT (CBCT) applications, where patients generate rigid and non-rigid motions. To address this problem, we proposed a new real-time technique for motion artifacts reduction that utilizes a deep residual network with an attention module. Our attention module was designed to increase the model capacity by amplifying or attenuating the residual features according to their importance. We trained and evaluated the network by creating four benchmark datasets with rigid motions or with both rigid and non-rigid motions under a step-and-shoot fan-beam CT (FBCT) or a CBCT. Each dataset provided a set of motion-corrupted CT images and their ground-truth CT image pairs. The strong modeling power of the proposed network model allowed us to successfully handle motion artifacts from the two CT systems under various motion scenarios in real-time. As a result, the proposed model demonstrated clear performance benefits. In addition, we compared our model with Wasserstein generative adversarial network (WGAN)-based models and a deep residual network (DRN)-based model, which are one of the most powerful techniques for CT denoising and natural RGB image deblurring, respectively. Based on the extensive analysis and comparisons using four benchmark datasets, we confirmed that our model outperformed the aforementioned competitors. Our benchmark datasets and implementation code are available at https://github.com/youngjun-ko/ct_mar_attention.

Deep Learning-based Inaccuracy Compensation in Reconstruction of High Resolution XCT Data

While X-ray computed tomography (XCT) is pushed further into the micro- and nanoscale, the limitations of various tool components and object motion become more apparent. For high-resolution XCT, it is necessary but practically difficult to align these tool components with sub-micron precision. The aim is to develop a novel reconstruction methodology that considers unavoidable misalignment and object motion during the data acquisition in order to obtain high-quality three-dimensional images and that is applicable for data recovery from incomplete datasets. A reconstruction software empowered by sophisticated correction modules that autonomously estimates and compensates artefacts using gradient descent and deep learning algorithms has been developed and applied. For motion estimation, a novel computer vision methodology coupled with a deep convolutional neural network approach provides estimates for the object motion by tracking features throughout the adjacent projections. The model is trained using the forward projections of simulated phantoms that consist of several simple geometrical features such as sphere, triangle and rectangular. The feature maps extracted by a neural network are used to detect and to classify features done by a support vector machine. For missing data recovery, a novel deep convolutional neural network is used to infer high-quality reconstruction data from incomplete sets of projections. The forward and back projections of simulated geometric shapes from a range of angular ranges are used to train the model. The model is able to learn the angular dependency based on a limited angle coverage and to propose a new set of projections to suppress artefacts. High-quality three-dimensional images demonstrate that it is possible to effectively suppress artefacts caused by thermomechanical instability of tool components and objects resulting in motion, by center of rotation misalignment and by inaccuracy in the detector position without additional computational efforts. Data recovery from incomplete sets of projections result in directly corrected projections instead of suppressing artefacts in the final reconstructed images. The proposed methodology has been proven and is demonstrated for a ball bearing sample. The reconstruction results are compared to prior corrections and benchmarked with a commercially available reconstruction software. Compared to conventional approaches in XCT imaging and data analysis, the proposed methodology for the generation of high-quality three-dimensional X-ray images is fully autonomous. The methodology presented here has been proven for high-resolution micro-XCT and nano-XCT, however, is applicable for all length scales.

Rigid motion artifact reduction in CT using extended difference function

BACKGROUND

In computed tomography (CT), a patient motion would result in degraded spatial resolution and image artifacts.

OBJECTIVE

To eliminate motion artifacts, this study presents a method to estimate the motion parameters from sinograms based on extended difference function.

METHODS

Based on our previous work, we first divide the projection data into two parts according to view angles and take Radon transform. Then, we calculate the extended difference functions and search for the minimum points. The relative displacements can be determined by the minimum points, and the motion can be estimated by the relationships between the relative displacements and motion parameters. Finally, we introduce the estimated parameters into the reconstruction process to compensate for the motion effects.

RESULTS

The simulation results show that the running times can reduce by about 30% than our previous work. In phantom experiments, the relative mean rotation excursion (RMRE) and relative mean translation excursion (RMTE) of the new method are lower than the conventional Helgason-Ludwig consistency condition (HLCC) based method and comparable to our previous work. Compare with the HLCC method, the root mean square error (RMSE) of the new method also reduces, while the Pearson correlation coefficient (CC) and mean structural similarity index (MSSIM) increase.

CONCLUSIONS

The proposed new method yields the improved performance on accuracy of motion estimation with higher computational efficiency, and thus it can produce high-quality images.

Effect of gantry rotation speed and scan mode on peristalsis motion artifact frequency and severity at abdominal CT

PURPOSE

The purpose of the study was to understand the effect of CT gantry speed and axial vs. helical scan mode on the frequency and severity of bowel peristalsis artifacts.

METHOD

We retrospectively identified 150 oncologic abdominopelvic CT scans obtained on a 256 slice CT scanner: 50 scans obtained with Axial mode and 0.5-s gantry rotation time (Slow-Axial); 50 with Axial mode and 0.28-s gantry rotation time (Fast-Axial); and 50 scans with Helical mode and 0.28-s gantry rotation time (Fast-Helical). The patients included 74 women and 76 men with a mean age of 61 years (range 22-85 years). Two readers viewed all CT scans to record the presence and severity of bowel peristalsis artifact, location of artifact (stomach, duodenum/jejunum, ileum, and colon) and artifact location relative to bowel interface (gas-bowel, fluid-bowel, and gas-fluid). The severity of artifacts was recorded subjectively on a 3-point scale, and objectively based on maximum length of the artifact.

RESULTS

Peristalsis artifact was more commonly seen with Slow-Axial scan acquisition (37 of 50 patient scans, or 74%) than Fast-Axial (15 in 50 patient scans, or 30%, p < 0.001) and Fast-Helical (22 of 50 patient scans, or 44%, p < 0.005). The bowel segment distribution and severity of peristalsis artifacts were not significantly different between scan techniques.

CONCLUSION

Peristalsis artifacts are common at abdominopelvic CT scans. Fast gantry rotation speed significantly reduces the frequency of bowel peristalsis artifacts and should be a consideration when imaging of bowel and structures near bowel is critical.

Optimization based beam-hardening correction in CT under data integral invariant constraint

In computed tomography (CT), the polychromatic characteristics of x-ray photons, which are emitted from a source, interact with materials and are absorbed by a detector, may lead to beam-hardening effect in signal detection and image formation, especially in situations where materials of high attenuation (e.g. the bone or metal implants) are in the x-ray beam. Usually, a beam-hardening correction (BHC) method is used to suppress the artifacts induced by bone or other objects of high attenuation, in which a calibration-oriented iterative operation is carried out to determine a set of parameters for all situations. Based on the Helgasson-Ludwig consistency condition (HLCC), an optimization based method has been proposed by turning the calibration-oriented iterative operation of BHC into solving an optimization problem sustained by projection data. However, the optimization based HLCC-BHC method demands the engagement of a large number of neighboring projection views acquired at relatively high and uniform angular sampling rate, hindering its application in situations where the angular sampling in projection view is sparse or non-uniform. By defining an objective function based on the data integral invariant constraint (DIIC), we again turn BHC into solving an optimization problem sustained by projection data. As it only needs a pair of projection views at any view angle, the proposed BHC method can be applicable in the challenging scenarios mentioned above. Using the projection data simulated by computer, we evaluate and verify the proposed optimization based DIIC-BHC method's performance. Moreover, with the projection data of a head scan by a multi-detector row MDCT, we show the proposed DIIC-BHC method's utility in clinical applications.

Correction of center of rotation and projection angle in synchrotron X-ray computed tomography

An error in tomographic reconstruction parameters can result considerable artifacts in the reconstructed image, particularly in micro-computed tomography and nano-computed tomography. This study involved designing an automatic method for efficiently correcting errors resulting from incorrectly determined rotational axes and projection angles. In this method, errors are corrected by minimizing the “total variation” of a reconstructed image, and minimization is accomplished by using the gradient descent method. Compared with two previous methods, the proposed method achieved the best reconstruction results.

Markerless motion estimation for motion-compensated clinical brain imaging

Motion-compensated brain imaging can dramatically reduce the artifacts and quantitative degradation associated with voluntary and involuntary subject head motion during positron emission tomography (PET), single photon emission computed tomography (SPECT) and computed tomography (CT). However, motion-compensated imaging protocols are not in widespread clinical use for these modalities. A key reason for this seems to be the lack of a practical motion tracking technology that allows for smooth and reliable integration of motion-compensated imaging protocols in the clinical setting. We seek to address this problem by investigating the feasibility of a highly versatile optical motion tracking method for PET, SPECT and CT geometries. The method requires no attached markers, relying exclusively on the detection and matching of distinctive facial features. We studied the accuracy of this method in 16 volunteers in a mock imaging scenario by comparing the estimated motion with an accurate marker-based method used in applications such as image guided surgery. A range of techniques to optimize performance of the method were also studied. Our results show that the markerless motion tracking method is highly accurate (<2 mm discrepancy against a benchmarking system) on an ethnically diverse range of subjects and, moreover, exhibits lower jitter and estimation of motion over a greater range than some marker-based methods. Our optimization tests indicate that the basic pose estimation algorithm is very robust but generally benefits from rudimentary background masking. Further marginal gains in accuracy can be achieved by accounting for non-rigid motion of features. Efficiency gains can be achieved by capping the number of features used for pose estimation provided that these features adequately sample the range of head motion encountered in the study. These proof-of-principle data suggest that markerless motion tracking is amenable to motion-compensated brain imaging and holds good promise for a practical implementation in clinical PET, SPECT and CT systems.

Geometry and energy constrained projection extension

BACKGROUND

In clinical computed tomography (CT) applications, when a patient is obese or improperly positioned, the final tomographic scan is often partially truncated. Images directly reconstructed by the conventional reconstruction algorithms suffer from severe cupping and direct current bias artifacts. Moreover, the current methods for projection extension have limitations that preclude incorporation from clinical workflows, such as prohibitive computational time for iterative reconstruction, extra radiation dose, hardware modification, etc.METHOD:In this study, we first established a geometrical constraint and estimated the patient habitus using a modified scout configuration. Then, we established an energy constraint using the integral invariance of fan-beam projections. Two constraints were extracted from the existing CT scan process with minimal modification to the clinical workflows. Finally, we developed a novel dual-constraint based optimization model that can be rapidly solved for projection extrapolation and accurate local reconstruction.

RESULTS

Both numerical phantom and realistic patient image simulations were performed, and the results confirmed the effectiveness of our proposed approach.

CONCLUSION

We establish a dual-constraint-based optimization model and correspondingly develop an accurate extrapolation method for partially truncated projections. The proposed method can be readily integrated into the clinical workflow and efficiently solved by using a one-dimensional optimization algorithm. Moreover, it is robust for noisy cases with various truncations and can be further accelerated by GPU based parallel computing.

Correction of patient motion in cone-beam CT using 3D-2D registration

Cone-beam CT (CBCT) is increasingly common in guidance of interventional procedures, but can be subject to artifacts arising from patient motion during fairly long (~5-60 s) scan times. We present a fiducial-free method to mitigate motion artifacts using 3D-2D image registration that simultaneously corrects residual errors in the intrinsic and extrinsic parameters of geometric calibration. The 3D-2D registration process registers each projection to a prior 3D image by maximizing gradient orientation using the covariance matrix adaptation-evolution strategy optimizer. The resulting rigid transforms are applied to the system projection matrices, and a 3D image is reconstructed via model-based iterative reconstruction. Phantom experiments were conducted using a Zeego robotic C-arm to image a head phantom undergoing 5-15 cm translations and 5-15° rotations. To further test the algorithm, clinical images were acquired with a CBCT head scanner in which long scan times were susceptible to significant patient motion. CBCT images were reconstructed using a penalized likelihood objective function. For phantom studies the structural similarity (SSIM) between motion-free and motion-corrected images was  >0.995, with significant improvement (p  <  0.001) compared to the SSIM values of uncorrected images. Additionally, motion-corrected images exhibited a point-spread function with full-width at half maximum comparable to that of the motion-free reference image. Qualitative comparison of the motion-corrupted and motion-corrected clinical images demonstrated a significant improvement in image quality after motion correction. This indicates that the 3D-2D registration method could provide a useful approach to motion artifact correction under assumptions of local rigidity, as in the head, pelvis, and extremities. The method is highly parallelizable, and the automatic correction of residual geometric calibration errors provides added benefit that could be valuable in routine use.

Motion compensation for cone-beam CT using Fourier consistency conditions

In cone-beam CT, involuntary patient motion and inaccurate or irreproducible scanner motion substantially degrades image quality. To avoid artifacts this motion needs to be estimated and compensated during image reconstruction. In previous work we showed that Fourier consistency conditions (FCC) can be used in fan-beam CT to estimate motion in the sinogram domain. This work extends the FCC to [Formula: see text] cone-beam CT. We derive an efficient cost function to compensate for [Formula: see text] motion using [Formula: see text] detector translations. The extended FCC method have been tested with five translational motion patterns, using a challenging numerical phantom. We evaluated the root-mean-square-error and the structural-similarity-index between motion corrected and motion-free reconstructions. Additionally, we computed the mean-absolute-difference (MAD) between the estimated and the ground-truth motion. The practical applicability of the method is demonstrated by application to respiratory motion estimation in rotational angiography, but also to motion correction for weight-bearing imaging of knees. Where the latter makes use of a specifically modified FCC version which is robust to axial truncation. The results show a great reduction of motion artifacts. Accurate estimation results were achieved with a maximum MAD value of 708 μm and 1184 μm for motion along the vertical and horizontal detector direction, respectively. The image quality of reconstructions obtained with the proposed method is close to that of motion corrected reconstructions based on the ground-truth motion. Simulations using noise-free and noisy data demonstrate that FCC are robust to noise. Even high-frequency motion was accurately estimated leading to a considerable reduction of streaking artifacts. The method is purely image-based and therefore independent of any auxiliary data.

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.

Rigid motion artifact reduction in CT using frequency domain analysis

BACKGROUND

It is often unrealistic to assume that the subject remains stationary during a computed tomography (CT) imaging scan. A patient rigid motion can be decomposed into a translation and a rotation around an origin. How to minimize the motion impact on image quality is important.

OBJECTIVE

To eliminate artifacts caused by patient rigid motion during a CT scan, this study investigated a new method based on frequency domain analysis to estimate and compensate motion impact.

METHODS

Motion parameters was first determined by the magnitude correlation of projections in frequency domain. Then, the estimated parameters were applied to compensate for the motion effects in the reconstruction process. Finally, this method was extended to helical CT.

RESULTS

In fan-beam CT experiments, the simulation results showed that the proposed method was more accurate and faster on the performance of motion estimation than using Helgason-Ludwig consistency condition method (HLCC). Furthermore, the reconstructed images on both simulated and human head experiments indicated that the proposed method yielded superior results in artifact reduction.

CONCLUSIONS

The proposed method is a new tool for patient motion compensation, with a potential for practical application. It is not only applicable to motion correction in fan-beam CT imaging, but also to helical CT.

Fully 3D geometrical calibration for an X-ray grating-based imaging system

The Precision of geometric parameters is the key requirement for grating-based phase-contrast CT and attenuation-based CT in cone-beam geometry. By extending our fan-beam geometric calibration work via Locally Linear Embedding (LLE) into the cone-beam case, here we calibrate the geometric parameters of our in-house phase-contrast CT system with attenuation projection data. Numerical and experimental studies show that the LLE-based calibration method is feasible to calibrate 8 parameters of the cone-beam geometry that improves reconstruction quality significantly.

Reduction of peristalsis-related gastrointestinal streak artifacts with dual-energy CT: a patient and phantom study

OBJECTIVE

The purpose of the study was to assess the ability of rapid-kV switching (rs) dual-energy computed tomography (DECT) to reduce peristalsis-related streak artifact.

METHODS

rsDECT images of 100 consecutive patients (48 male, 52 female, mean age 57 years) were retrospectively evaluated in this institutional review board-approved study. Image reconstructions included virtual monochromatic 70 and 120 keV images, as well as iodine(-water) and water(-iodine) material decomposition images. We recorded the presence and severity of artifacts qualitatively (4-point scale) and quantitatively [iodine/water concentrations, Hounsfield units, gray scale values (GY)] and compared to corresponding unaffected reference tissue. Similar measures were obtained in DECT images of a peristalsis phantom. Wilcoxon signed-rank and paired t tests were used to compare results between different image reconstructions.

RESULTS

Peristalsis-related streak artifacts were found in 49 (49%) of the DECT examinations. Artifacts were significantly more severe in 70, 120, and water(-iodine) images than in iodine(-water) images (qualitative readout P < 0.001, each). Quantitative measurements were significantly different between the artifact and the reference tissue in 70, 120 keV, and water(-iodine) images (P < 0.001 for both HU and GY for each image reconstruction), but not significantly different in iodine(-water) images (iodine concentrations P = 0.088 and GY P = 0.111). Similar results were seen in the peristalsis DECT phantom study.

CONCLUSIONS

Peristalsis-related streak artifacts seen in 70, 120 keV, and water(-iodine) images are substantially reduced in iodine(-water) images at rsDECT.

Full data consistency conditions for cone-beam projections with sources on a plane

Cone-beam consistency conditions (also known as range conditions) are mathematical relationships between different cone-beam projections, and they therefore describe the redundancy or overlap of information between projections. These redundancies have often been exploited for applications in image reconstruction. In this work we describe new consistency conditions for cone-beam projections whose source positions lie on a plane. A further restriction is that the target object must not intersect this plane. The conditions require that moments of the cone-beam projections be polynomial functions of the source positions, with some additional constraints on the coefficients of the polynomials. A precise description of the consistency conditions is that the four parameters of the cone-beam projections (two for the detector, two for the source position) can be expressed with just three variables, using a certain formulation involving homogeneous polynomials. The main contribution of this work is our demonstration that these conditions are not only necessary, but also sufficient. Thus the consistency conditions completely characterize all redundancies, so no other independent conditions are possible and in this sense the conditions are full. The idea of the proof is to use the known consistency conditions for 3D parallel projections, and to then apply a 1996 theorem of Edholm and Danielsson that links parallel to cone-beam projections. The consistency conditions are illustrated with a simulation example.

The feasibility of head motion tracking in helical CT: a step toward motion correction

PURPOSE

To establish a practical and accurate motion tracking method for the development of rigid motion correction methods in helical x-ray computed tomography (CT).

METHODS

A commercially available optical motion tracking system provided 6 degrees of freedom pose measurements at 60 Hz. A 4 × 4 calibration matrix was determined to convert raw pose data acquired in tracker coordinates to a fixed CT coordinate system with origin at the isocenter of the scanner. Two calibration methods, absolute orientation (AO), and a new method based on image registration (IR), were compared by means of landmark analysis and correlation coefficient in phantom images coregistered using the derived motion transformations.

RESULTS

Transformations calculated using the IR-derived calibration matrix were found to be more accurate, with positional errors less than 0.5 mm (mean RMS), and highly correlated image voxel intensities. The AO-derived calibration matrix yielded larger mean RMS positional errors (≈ 1.0 mm), and poorer correlation coefficients.

CONCLUSIONS

The authors have demonstrated the feasibility of accurate motion tracking for retrospective motion correction in helical CT. Their new IR-based calibration method based on image registration and function minimization was simpler to perform and delivered more accurate calibration matrices. This technique is a useful tool for future work on rigid motion correction in helical CT and potentially also other imaging modalities.

Automated motion correction for in vivo optical projection tomography

In in vivo optical projection tomography (OPT), object motion will significantly reduce the quality and resolution of the reconstructed image. Based on the well-known Helgason-Ludwig consistency condition (HLCC), we propose a novel method for motion correction in OPT under parallel beam illumination. The method estimates object motion from projection data directly and does not require any other additional information, which results in a straightforward implementation. We decompose object movement into translation and rotation, and discuss how to correct for both translation and general motion simultaneously. Since finding the center of rotation accurately is critical in OPT, we also point out that the system's geometrical offset can be considered as object translation and therefore also calibrated through the translation estimation method. In order to verify the algorithm effectiveness, both simulated and in vivo OPT experiments are performed. Our results demonstrate that the proposed approach is capable of decreasing movement artifacts significantly thus providing high quality reconstructed images in the presence of object motion.

Simulation tools for two-dimensional experiments in x-ray computed tomography using the FORBILD head phantom

Mathematical phantoms are essential for the development and early stage evaluation of image reconstruction algorithms in x-ray computed tomography (CT). This note offers tools for computer simulations using a two-dimensional (2D) phantom that models the central axial slice through the FORBILD head phantom. Introduced in 1999, in response to a need for a more robust test, the FORBILD head phantom is now seen by many as the gold standard. However, the simple Shepp-Logan phantom is still heavily used by researchers working on 2D image reconstruction. Universal acceptance of the FORBILD head phantom may have been prevented by its significantly higher complexity: software that allows computer simulations with the Shepp-Logan phantom is not readily applicable to the FORBILD head phantom. The tools offered here address this problem. They are designed for use with Matlab®, as well as open-source variants, such as FreeMat and Octave, which are all widely used in both academia and industry. To get started, the interested user can simply copy and paste the codes from this PDF document into Matlab® M-files.

Automated quantification of three-dimensional subject motion to monitor image quality in high-resolution peripheral quantitative computed tomography

Subject motion during acquisition of high-resolution peripheral quantitative computed tomography (HR-pQCT) results in image artifacts and interferes with quantification of bone architecture used to study bone-related diseases such as osteoporosis. We propose an automatic method to measure physical subject motion that frequently takes place during acquisition. Three measures derived from projection data are proposed to quantify motion artifacts: in-plane translation (ε(T)) and in-plane rotation (ε(R)) utilizing projection moments and longitudinal translation (ε(z)) based on tracking projection profiles. Validation was performed using a phantom containing sections of distal human cadaver radii attached to a mechanical device to precisely control in-plane rotation and longitudinal translation that was intentionally performed during HR-pQCT data acquisition. Motion measured by the new automated technique was compared to the known applied motion, and related to percent errors in morphological parameters quantifying bone properties. It was determined that of the three proposed measures, ε(T) best captured a quantified representation of image quality. ε(T) linearly relates to true physical in-plane translational motion (r(2) = 0.95, p<0.001) and is independent from longitudinal translational motion as well as the object being scanned. Additionally, ε(z) captures large longitudinal movements and combines well with ε(T) to fully characterize physical motion artifacts. The magnitude of ε(T) corresponds to morphological parameter error and is an excellent basis to select high-quality images. Morphological parameter errors from these experiments confirmed our earlier computer simulations which showed that increased subject motion resulted in artificially higher trabecular number, and artificially lower bone mineral density and cortical thickness. The magnitude and, notably, the uncertainty of the morphological errors increased with increased physical motion, and this impedes a direct linear compensation of parameter errors. The automated method presented provides a basis for consistent and objective quality assurance for HR-pQCT scanning, and addresses an important challenge for this novel imaging modality that is rapidly becoming an important basis for assessment and monitoring of bone quality.

Quantitative characterization of subject motion in HR-pQCT images of the distal radius and tibia

Image quality degradation due to subject motion is a common artifact affecting in vivo high-resolution peripheral quantitative computed tomography (HR-pQCT) of bones. These artifacts confound the accuracy and reproducibility of bone density, geometry, and cortical and trabecular structure measurements. Observer-based systems for grading image quality and criteria for deciding when to repeat an acquisition and post hoc data quality control remain highly subjective and non-standardized. This study proposes an objective, quantitative technique for measuring subject motion in HR-pQCT acquisitions from raw projection data, using image similarity measures applied to parallelized projections at 0° and 180°. A total of 88 HR-pQCT exams with repeated acquisitions of the distal radius (N = 54) or distal tibia (N = 34) of 49 women (age = 59 ± 14 year) and 3 men (46 ± 2 year) were retrospectively evaluated. All images were graded from 1 (no visible motion artifacts) to 5 (severe motion artifacts) according to the manufacturer-suggested image quality grading system. In addition, to serve as the reference case without motion artifacts, two cadaveric wrist and two ankle specimens were imaged twice with repositioning. The motion-induced error was calculated as the percent difference in each bone parameter for the paired scans with and without visually apparent motion artifacts. Quantitative motion estimates (QMEs) for each motion-degraded scan were calculated using two different image similarity measures: sum of squared differences (SSD) and normalized cross-correlation (NCC). The mean values of QME(SSD) and QME(NCC) increased with the image quality grade for both radius and tibia. Quality grades were differentiated between grades 2 and 3 using QME(SSD), but not with QME(NCC), in addition to between grades 4 and 5. Both QMEs correlated significantly to the motion-induced errors in the measurements and their empirical relationship was derived. Subject motion had greater impact on the precision of trabecular structure indices than on the densitometric indices. The results of this study may provide a basis for establishing a threshold for motion artifacts in accordance to the study design as well as a standardized quality control protocol across operators and imaging centers.

Fourier properties of the fan-beam sinogram

PURPOSE

P. R. Edholm, R. M. Lewitt, and B. Lindholm, "Novel properties of the Fourier decomposition of the sinogram," in Proceedings of the International Workshop on Physics and Engineering of Computerized Multidimensional Imaging and Processing [Proc. SPIE 671, 8-18 (1986)] described properties of a parallel beam projection sinogram with respect to its radial and angular frequencies. The purpose is to perform a similar derivation to arrive at corresponding properties of a fan-beam projection sinogram for both the equal-angle and equal-spaced detector sampling scenarios.

METHODS

One of the derived properties is an approximately zero-energy region in the two-dimensional Fourier transform of the full fan-beam sinogram. This region is in the form of a double-wedge, similar to the parallel beam case, but different in that it is asymmetric with respect to the frequency axes. The authors characterize this region for a point object and validate the derived properties in both a simulation and a head CT data set. The authors apply these results in an application using algebraic reconstruction.

RESULTS

In the equal-angle case, the domain of the zero region is (q,k) for which / k/(k-q) / > R/L, where q and k are the frequency variables associated with the detector and view angular positions, respectively, R is the radial support of the object, and L is the source-to-isocenter distance. A filter was designed to retain only sinogram frequencies corresponding to a specified radial support. The filtered sinogram was used to reconstruct the same radial support of the head CT data. As an example application of this concept, the double-wedge filter was used to computationally improve region of interest iterative reconstruction.

CONCLUSIONS

Interesting properties of the fan-beam sinogram exist and may be exploited in some applications.

Image-based iterative compensation of motion artifacts in computed tomography

PURPOSE

This article presents an iterative method for compensation of motion artifacts for slowly rotating computed tomography (CT) systems. Patient's motion introduces inconsistencies among projections and yields severe reconstruction artifacts for free-breathing acquisitions. Streaks and doubling of structures can appear and the resolution is limited by strong blurring.

METHODS

The rationale of the proposed motion compensation method is to iteratively correct the reconstructed image by first decomposing the perceived motion in projection space, then reconstructing the motion artifacts in image space, and finally subtracting the artifacts from an initial image. The initial image is reconstructed from the acquired data and might contain motion blur artifacts but, nevertheless, is considered as a reference for estimating the reconstruction artifacts.

RESULTS

Qualitative and quantitative figures are shown for experiments based on numerically simulated projections of a sequence of clinical images resulting from a respiratory-gated helical CT acquisition. The border of the diaphragm becomes progressively sharper and the contrast improves for small structures in the lungs.

CONCLUSIONS

The originality of the technique stems from the fact that the patient motion is not explicitly estimated but the motion artifacts are reconstructed in image space. This approach could provide sharp static anatomical images on interventional C-arm systems or on slowly rotating X-ray equipments in radiotherapy.

Exact image reconstruction with triple-source saddle-curve cone-beam scanning

In this paper, we propose an exact shift-invariant filtered backprojection (FBP) algorithm for triple-source saddle-curve cone-beam CT. In this imaging geometry, the x-ray sources are symmetrically positioned along a circle, and the trajectory of each source is a saddle curve. Then, we extend Yang's formula from the single-source case to the triple-source case. The saddle curves can be divided into four parts to yield four datasets. Each of them contains three data segments associated with different saddle curves, respectively. Images can be reconstructed on the planes orthogonal to the z-axis. Each plane intersects the trajectories at six points (or three points at the two ends) which can be used to define the filtering directions. Then, we discuss the properties of these curves and study the case of 2N+1 sources (N>or=2). A necessary condition and a sufficient condition are given to find efficient curves. Finally, we perform numerical simulations to demonstrate the feasibility of our triple-source saddle-curve approach. The results show that the triple-source geometry is advantageous for high temporal resolution imaging, especially important for cardiac imaging and small animal imaging.

Exact image reconstruction with triple-source saddle-curve cone-beam scanning

In this paper, we propose an exact shift-invariant filtered backprojection (FBP) algorithm for triple-source saddle-curve cone-beam CT. In this imaging geometry, the x-ray sources are symmetrically positioned along a circle, and the trajectory of each source is a saddle curve. Then, we extend Yang's formula from the single-source case to the triple-source case. The saddle curves can be divided into four parts to yield four datasets. Each of them contains three data segments associated with different saddle curves, respectively. Images can be reconstructed on the planes orthogonal to the z-axis. Each plane intersects the trajectories at six points (or three points at the two ends) which can be used to define the filtering directions. Then, we discuss the properties of these curves and study the case of 2N+1 sources (N>or=2). A necessary condition and a sufficient condition are given to find efficient curves. Finally, we perform numerical simulations to demonstrate the feasibility of our triple-source saddle-curve approach. The results show that the triple-source geometry is advantageous for high temporal resolution imaging, especially important for cardiac imaging and small animal imaging.

4D MAP image reconstruction incorporating organ motion

Four-dimensional respiratory correlated computed tomography (4D RCCT) has been widely used for studying organ motion. Most current algorithms use binning techniques which introduce artifacts that can seriously hamper quantitative motion analysis. In this paper, we develop an algorithm for tracking organ motion which uses raw time-stamped data and simultaneously reconstructs images and estimates deformations in anatomy. This results in a reduction of artifacts and an increase in signal-to-noise ratio (SNR). In the case of CT, the increased SNR enables a reduction in dose to the patient during scanning. This framework also facilitates the incorporation of fundamental physical properties of organ motion, such as the conservation of local tissue volume. We show in this paper that this approach is accurate and robust against noise and irregular breathing for tracking organ motion. A detailed phantom study is presented, demonstrating accuracy and robustness of the algorithm. An example of applying this algorithm to real patient image data is also presented, demonstrating the utility of the algorithm in reducing artifacts.

Continuous and discrete data rebinning in time-of-flight PET

This paper investigates data compression methods for time-of-flight (TOF) positron emission tomography (PET), which rebin the 3-D TOF measurements into a set of 2-D TOF data for a stack of transaxial slices. The goal of this work is to develop rebinning algorithms that are more accurate than the TOF single-slice-rebinning (TOF-SSRB) method proposed by Mullani in 1982. Two approaches are explored. The first one is based on a partial differential equation, which expresses a consistency condition for TOF-PET data with a Gaussian TOF profile. From this equation we derive an analytical rebinning algorithm, which is unbiased in the limit of continuous sampling. The second approach is discrete: each 2-D rebinned data sample is calculated as a linear combination of the 3-D TOF samples in the same axial plane parallel to the axis of the scanner. The coefficients of the linear combination are precomputed by optimizing a cost function which enforces both accuracy and good variance reduction, models the TOF profile, the axial PSF of the LORs, and the specific sampling scheme of the scanner. Measurements of a thorax phantom on a prototype TOF-PET scanner with a resolution of 550 ps show that the proposed discrete method improves the bias-variance trade-off and is a promising alternative to TOF-SSRB when data compression is required to achieve clinically acceptable reconstruction time.

An outlook on x-ray CT research and development

Over the past decade, computed tomography (CT) theory, techniques and applications have undergone a rapid development. Since CT is so practical and useful, undoubtedly CT technology will continue advancing biomedical and non-biomedical applications. In this outlook article, we share our opinions on the research and development in this field, emphasizing 12 topics we expect to be critical in the next decade: analytic reconstruction, iterative reconstruction, local/interior reconstruction, flat-panel based CT, dual-source CT, multi-source CT, novel scanning modes, energy-sensitive CT, nano-CT, artifact reduction, modality fusion, and phase-contrast CT. We also sketch several representative biomedical applications.

Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning

The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area.