Motion-compensated iterative cone-beam CT image reconstruction with adapted blobs as basis functions

DiFiR-CT: Distance field representation to resolve motion artifacts in computed tomography

BACKGROUND

Motion during data acquisition leads to artifacts in computed tomography (CT) reconstructions. In cases such as cardiac imaging, not only is motion unavoidable, but evaluating the motion of the object is of clinical interest. Reducing motion artifacts has typically been achieved by developing systems with faster gantry rotation or via algorithms which measure and/or estimate the displacement. However, these approaches have had limited success due to both physical constraints as well as the challenge of estimating non-rigid, temporally varying, and patient-specific motion fields.

PURPOSE

To develop a novel reconstruction method which generates time-resolved, artifact-free images without estimation or explicit modeling of the motion.

METHODS

We describe an analysis-by-synthesis approach which progressively regresses a solution consistent with the acquired sinogram. In our method, we focus on the movement of object boundaries. Not only are the boundaries the source of image artifacts, but object boundaries can simultaneously be used to represent both the object as well as its motion over time without the need for an explicit motion model. We represent the object boundaries via a signed distance function (SDF) which can be efficiently modeled using neural networks. As a result, optimization can be performed under spatial and temporal smoothness constraints without the need for explicit motion estimation.

RESULTS

We illustrate the utility of DiFiR-CT in three imaging scenarios with increasing motion complexity: translation of a small circle, heart-like change in an ellipse's diameter, and a complex topological deformation. Compared to filtered backprojection, DiFiR-CT provides high quality image reconstruction for all three motions without hyperparameter tuning or change to the architecture. We also evaluate DiFiR-CT's robustness to noise in the acquired sinogram and found its reconstruction to be accurate across a wide range of noise levels. Lastly, we demonstrate how the approach could be used for multi-intensity scenes and illustrate the importance of the initial segmentation providing a realistic initialization. Code and supplemental movies are available at https://kunalmgupta.github.io/projects/DiFiR-CT.html.

CONCLUSIONS

Projection data can be used to accurately estimate a temporally-evolving scene without the need for explicit motion estimation using a neural implicit representation and analysis-by-synthesis approach.

Motion compensated micro-CT reconstruction for in-situ analysis of dynamic processes

This work presents a framework to exploit the synergy between Digital Volume Correlation (DVC) and iterative CT reconstruction to enhance the quality of high-resolution dynamic X-ray CT (4D-µCT) and obtain quantitative results from the acquired dataset in the form of 3D strain maps which can be directly correlated to the material properties. Furthermore, we show that the developed framework is capable of strongly reducing motion artifacts even in a dataset containing a single 360° rotation.

Statistical content-adapted sampling (SCAS) for 3D Computed Tomography

In this paper, a framework to create a statistical content-adapted sampling (SCAS) for 3D X-ray Computed Tomography (CT) is introduced. SCAS aims at providing an accurate but light reconstruction volume. Based on decision theory, the 3D reconstruction space is sampled from the raw projection data in three steps to directly fit the sample. To do so, the structural information is first extracted from the projections by edge detection. This information is then merged in the reconstruction space, providing a pointcloud which accurately delineates the 3D interfaces of the specimen. From this pointcloud, a 3D mesh, closely fitting the shape of the studied object, is finally built via constrained Delaunay tetrahedralization. To assess the potential of the proposed SCAS for CT imaging, an iterative reconstruction was performed by classical Ordered Subset Simultaneous Algebraic Reconstruction Technique (OS-SART) - with fitting projection operator. The SCAS was evaluated on both numerical and experimental data. Results show that the use of statistical testing enabled the design of a robust, automated and fast method to build accurate pointclouds from a limited number of projections. The 3D meshes generated from these pointclouds are composed of few cells when compared to the regular voxel representation, leading to a downsize in computational cost and achieving up to 90% of memory footprint reduction. Simulations showed that performed reconstruction on such meshes provide accurate description of the object due to the finer sampling at interfaces.

Frequency-Selective Computed Tomography: Applications During Periodic Thoracic Motion

We seek to use computed tomography (CT) to characterize regional lung parenchymal deformation during high-frequency and multi-frequency oscillatory ventilation. Periodic motion of thoracic structures results in artifacts of CT images obtained by standard reconstruction algorithms, especially for frequencies exceeding that of the X-ray source rotation. In this paper, we propose an acquisition and reconstruction technique for high-resolution imaging of the thorax during periodic motion. Our technique relies on phase-binning projections according to the frequency of subject motion relative to the scanner rotation, prior to volumetric reconstruction. The mathematical theory and limitations of the proposed technique are presented, and then validated in a simulated phantom as well as a living porcine subject during oscillatory ventilation. The 4-D image sequences obtained using this frequency-selective reconstruction technique yielded high-spatio-temporal resolution of the thorax during periodic motion. We conclude that the frequency-based selection of CT projections is ideal for characterizing dynamic deformations of thoracic structures that are ordinarily obscured by motion artifact using conventional reconstruction techniques.

Cardiac Image Reconstruction via Nonlinear Motion Correction Based on Partial Angle Reconstructed Images

Even though the X-ray Computed Tomography (CT) scan is considered suitable for fast imaging, motion-artifact-free cardiac imaging is still an important issue, because the gantry rotation speed is not fast enough compared with the heart motion. To obtain a heart image with less motion artifacts, a motion estimation (ME) and motion compensation (MC) approach is usually adopted. In this paper, we propose an ME/MC algorithm that can estimate a nonlinear heart motion model from a sinogram with a rotation angle of less than 360°. In this algorithm, we first assume the heart motion to be nonrigid but linear, and thereby estimate an initial 4-D motion vector field (MVF) during a half rotation by using conjugate partial angle reconstructed images, as in our previous ME/MC algorithm. We then refine the MVF to determine a more accurate nonlinear MVF by maximizing the information potential of a motion-compensated image. Finally, MC is performed by incorporating the determined MVF into the image reconstruction process, and a time-resolved heart image is obtained. By using a numerical phantom, a physical cardiac phantom, and an animal data set, we demonstrate that the proposed algorithm can noticeably improve the image quality by reducing motion artifacts throughout the image.

Data-Driven Affine Deformation Estimation and Correction in Cone Beam Computed Tomography

In computed tomography (CT), motion and deformation during the acquisition lead to streak artefacts and blurring in the reconstructed images. To remedy these artefacts, we introduce an efficient algorithm to estimate and correct for global affine deformations directly on the cone beam projections. The proposed technique is data driven and thus removes the need for markers and/or a tracking system. A relationship between affine transformations and the cone beam transform is proved and used to correct the projections. The deformation parameters that describe deformation perpendicular to the projection direction are estimated for each projection by minimizing a plane-based inconsistency criterion. The criterion compares each projection of the main scan with all projections of a fast reference scan, which is acquired prior or posterior to the main scan. Experiments with simulated and experimental data show that the proposed affine deformation estimation method is able to substantially reduce motion artefacts in cone beam CT images.

Cardiac motion correction based on partial angle reconstructed images in x-ray CT

PURPOSE

Cardiac x-ray CT imaging is still challenging due to heart motion, which cannot be ignored even with the current rotation speed of the equipment. In response, many algorithms have been developed to compensate remaining motion artifacts by estimating the motion using projection data or reconstructed images. In these algorithms, accurate motion estimation is critical to the compensated image quality. In addition, since the scan range is directly related to the radiation dose, it is preferable to minimize the scan range in motion estimation. In this paper, the authors propose a novel motion estimation and compensation algorithm using a sinogram with a rotation angle of less than 360°. The algorithm estimates the motion of the whole heart area using two opposite 3D partial angle reconstructed (PAR) images and compensates the motion in the reconstruction process.

METHODS

A CT system scans the thoracic area including the heart over an angular range of 180° + α + β, where α and β denote the detector fan angle and an additional partial angle, respectively. The obtained cone-beam projection data are converted into cone-parallel geometry via row-wise fan-to-parallel rebinning. Two conjugate 3D PAR images, whose center projection angles are separated by 180°, are then reconstructed with an angular range of β, which is considerably smaller than a short scan range of 180° + α. Although these images include limited view angle artifacts that disturb accurate motion estimation, they have considerably better temporal resolution than a short scan image. Hence, after preprocessing these artifacts, the authors estimate a motion model during a half rotation for a whole field of view via nonrigid registration between the images. Finally, motion-compensated image reconstruction is performed at a target phase by incorporating the estimated motion model. The target phase is selected as that corresponding to a view angle that is orthogonal to the center view angles of two conjugate PAR images. To evaluate the proposed algorithm, digital XCAT and physical dynamic cardiac phantom datasets are used. The XCAT phantom datasets were generated with heart rates of 70 and 100 bpm, respectively, by assuming a system rotation time of 300 ms. A physical dynamic cardiac phantom was scanned using a slowly rotating XCT system so that the effective heart rate will be 70 bpm for a system rotation speed of 300 ms.

RESULTS

In the XCAT phantom experiment, motion-compensated 3D images obtained from the proposed algorithm show coronary arteries with fewer motion artifacts for all phases. Moreover, object boundaries contaminated by motion are well restored. Even though object positions and boundary shapes are still somewhat different from the ground truth in some cases, the authors see that visibilities of coronary arteries are improved noticeably and motion artifacts are reduced considerably. The physical phantom study also shows that the visual quality of motion-compensated images is greatly improved.

CONCLUSIONS

The authors propose a novel PAR image-based cardiac motion estimation and compensation algorithm. The algorithm requires an angular scan range of less than 360°. The excellent performance of the proposed algorithm is illustrated by using digital XCAT and physical dynamic cardiac phantom datasets.

Blob parameter selection for image representation

A technique for optimizing parameters for image representation using blob basis functions is presented and demonstrated. The exact choice of the basis functions significantly influences the quality of the image representation. It has been previously established that using spherically symmetric volume elements (blobs) as basis functions, instead of the more traditional voxels, yields superior representations of real objects, provided that the parameters that occur in the definition of the family of blobs are appropriately tuned. The technique presented in this paper makes use of an extra degree of freedom, which has been previously ignored, in the blob parameter space. The efficacy of the resulting parameters is illustrated.

Motion-compensated cone beam computed tomography using a conjugate gradient least-squares algorithm and electrical impedance tomography imaging motion data

Cone beam computed tomography (CBCT) is an imaging modality that has been used in image-guided radiation therapy (IGRT). For applications such as lung radiation therapy, CBCT images are greatly affected by the motion artefacts. This is mainly due to low temporal resolution of CBCT. Recently, a dual modality of electrical impedance tomography (EIT) and CBCT has been proposed, in which the high temporal resolution EIT imaging system provides motion data to a motion-compensated algebraic reconstruction technique (ART)-based CBCT reconstruction software. High computational time associated with ART and indeed other variations of ART make it less practical for real applications. This paper develops a motion-compensated conjugate gradient least-squares (CGLS) algorithm for CBCT. A motion-compensated CGLS offers several advantages over ART-based methods, including possibilities for explicit regularization, rapid convergence and parallel computations. This paper for the first time demonstrates motion-compensated CBCT reconstruction using CGLS and reconstruction results are shown in limited data CBCT considering only a quarter of the full dataset. The proposed algorithm is tested using simulated motion data in generic motion-compensated CBCT as well as measured EIT data in dual EIT-CBCT imaging.

Fiducial marker-based correction for involuntary motion in weight-bearing C-arm CT scanning of knees. Part I. Numerical model-based optimization

PURPOSE

Human subjects in standing positions are apt to show much more involuntary motion than in supine positions. The authors aimed to simulate a complicated realistic lower body movement using the four-dimensional (4D) digital extended cardiac-torso (XCAT) phantom. The authors also investigated fiducial marker-based motion compensation methods in two-dimensional (2D) and three-dimensional (3D) space. The level of involuntary movement-induced artifacts and image quality improvement were investigated after applying each method.

METHODS

An optical tracking system with eight cameras and seven retroreflective markers enabled us to track involuntary motion of the lower body of nine healthy subjects holding a squat position at 60° of flexion. The XCAT-based knee model was developed using the 4D XCAT phantom and the optical tracking data acquired at 120 Hz. The authors divided the lower body in the XCAT into six parts and applied unique affine transforms to each so that the motion (6 degrees of freedom) could be synchronized with the optical markers' location at each time frame. The control points of the XCAT were tessellated into triangles and 248 projection images were created based on intersections of each ray and monochromatic absorption. The tracking data sets with the largest motion (Subject 2) and the smallest motion (Subject 5) among the nine data sets were used to animate the XCAT knee model. The authors defined eight skin control points well distributed around the knees as pseudo-fiducial markers which functioned as a reference in motion correction. Motion compensation was done in the following ways: (1) simple projection shifting in 2D, (2) deformable projection warping in 2D, and (3) rigid body warping in 3D. Graphics hardware accelerated filtered backprojection was implemented and combined with the three correction methods in order to speed up the simulation process. Correction fidelity was evaluated as a function of number of markers used (4-12) and marker distribution in three scenarios.

RESULTS

Average optical-based translational motion for the nine subjects was 2.14 mm (± 0.69 mm) and 2.29 mm (± 0.63 mm) for the right and left knee, respectively. In the representative central slices of Subject 2, the authors observed 20.30%, 18.30%, and 22.02% improvements in the structural similarity (SSIM) index with 2D shifting, 2D warping, and 3D warping, respectively. The performance of 2D warping improved as the number of markers increased up to 12 while 2D shifting and 3D warping were insensitive to the number of markers used. The minimum required number of markers for 2D shifting, 2D warping, and 3D warping was 4-6, 12, and 8, respectively. An even distribution of markers over the entire field of view provided robust performance for all three correction methods.

CONCLUSIONS

The authors were able to simulate subject-specific realistic knee movement in weight-bearing positions. This study indicates that involuntary motion can seriously degrade the image quality. The proposed three methods were evaluated with the numerical knee model; 3D warping was shown to outperform the 2D methods. The methods are shown to significantly reduce motion artifacts if an appropriate marker setup is chosen.

Improving best-phase image quality in cardiac CT by motion correction with MAM optimization

PURPOSE

Research in image reconstruction for cardiac CT aims at using motion correction algorithms to improve the image quality of the coronary arteries. The key to those algorithms is motion estimation, which is currently based on 3-D/3-D registration to align the structures of interest in images acquired in multiple heart phases. The need for an extended scan data range covering several heart phases is critical in terms of radiation dose to the patient and limits the clinical potential of the method. Furthermore, literature reports only slight quality improvements of the motion corrected images when compared to the most quiet phase (best-phase) that was actually used for motion estimation. In this paper a motion estimation algorithm is proposed which does not require an extended scan range but works with a short scan data interval, and which markedly improves the best-phase image quality.

METHODS

Motion estimation is based on the definition of motion artifact metrics (MAM) to quantify motion artifacts in a 3-D reconstructed image volume. The authors use two different MAMs, entropy, and positivity. By adjusting the motion field parameters, the MAM of the resulting motion-compensated reconstruction is optimized using a gradient descent procedure. In this way motion artifacts are minimized. For a fast and practical implementation, only analytical methods are used for motion estimation and compensation. Both the MAM-optimization and a 3-D/3-D registration-based motion estimation algorithm were investigated by means of a computer-simulated vessel with a cardiac motion profile. Image quality was evaluated using normalized cross-correlation (NCC) with the ground truth template and root-mean-square deviation (RMSD). Four coronary CT angiography patient cases were reconstructed to evaluate the clinical performance of the proposed method.

RESULTS

For the MAM-approach, the best-phase image quality could be improved for all investigated heart phases, with a maximum improvement of the NCC value by 100% and of the RMSD value by 81%. The corresponding maximum improvements for the registration-based approach were 20% and 40%. In phases with very rapid motion the registration-based algorithm obtained better image quality, while the image quality of the MAM algorithm was superior in phases with less motion. The image quality improvement of the MAM optimization was visually confirmed for the different clinical cases.

CONCLUSIONS

The proposed method allows a software-based best-phase image quality improvement in coronary CT angiography. A short scan data interval at the target heart phase is sufficient, no additional scan data in other cardiac phases are required. The algorithm is therefore directly applicable to any standard cardiac CT acquisition protocol.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Extracting respiratory signals from thoracic cone beam CT projections

The patient respiratory signal associated with the cone beam CT (CBCT) projections is important for lung cancer radiotherapy. In contrast to monitoring an external surrogate of respiration, such a signal can be extracted directly from the CBCT projections. In this paper, we propose a novel local principal component analysis (LPCA) method to extract the respiratory signal by distinguishing the respiration motion-induced content change from the gantry rotation-induced content change in the CBCT projections. The LPCA method is evaluated by comparing with three state-of-the-art projection-based methods, namely the Amsterdam Shroud method, the intensity analysis method and the Fourier-transform-based phase analysis method. The clinical CBCT projection data of eight patients, acquired under various clinical scenarios, were used to investigate the performance of each method. We found that the proposed LPCA method has demonstrated the best overall performance for cases tested and thus is a promising technique for extracting a respiratory signal. We also identified the applicability of each existing method.

A fully four-dimensional, iterative motion estimation and compensation method for cardiac CT

PURPOSE

To develop a new fully four-dimensional (4D), iterative image reconstruction algorithm for cardiac CT that alternates the following two methods: estimation of a time-dependent motion vector field (MVF) of the heart from image data and reconstruction of images using the estimated MVF and projection data.

METHODS

Volumetric image data at different cardiac phase points were obtained using electrocardiogram-gated CT. Motion estimation (ME) and motion-compensated image reconstruction (MCR) were performed alternately until convergence was achieved. The ME method estimated the cardiac MVF using 4D nonrigid image registration between a cardiac reference phase and all the other phases. The nonrigid deformation of the heart was modeled using cubic B-splines. The cost function consisted of a sum of squared weighted differences and spatial and temporal regularization terms. A nested conjugate gradient optimization algorithm was applied to minimize the cost function and estimate the MVFs. Cardiac images were reconstructed using a motion-tracking algorithm that utilized the MVFs estimated by the ME method. The reconstructed images supplied the input to the ME of the next iteration. The performance of the proposed method was evaluated using four patient data sets acquired with a 64-slice CT scanner. The heart rates of the patients ranged from 52 to 71 beats/min.

RESULTS

Motion artifacts were significantly reduced, and the image quality increased with the number of iterations. Without MCR, the right coronary artery (RCA) was deformed into an arc in axial images of rapid phases. With the proposed method the RCA appeared sharper and was reconstructed similar in shape to the reconstruction at the quiescent phase at mid-diastole. The boundary between the interventricular septum and the right ventricle was also clearer and sharper using the proposed algorithm. The steepness of the transition range at a rapid phase (35% R-R) was increased from 6.8 HU∕pixel to 11.5 HU∕pixel. The ME-MCR algorithm converged in just four iterations.

CONCLUSION

We developed a fully 4D image reconstruction method that alternates ME and MCR algorithms in an iterative fashion. Performance tests using clinical patient data resulted in reduced motion artifacts.

New iterative cone beam CT reconstruction software: parameter optimisation and convergence study

Cone beam computed tomography (CBCT) provides a volumetric image reconstruction from tomographic projection data. Image quality is the main concern for reconstruction in comparison to conventional CT. The reconstruction algorithm used is clearly important and should be carefully designed, developed and investigated before it can be applied clinically. The Multi-Instrument Data Analysis System (MIDAS) tomography software originally designed for geophysical applications has been modified to CBCT image reconstruction. In CBCT reconstruction algorithms, iterative methods offer the potential to generate high quality images and would be an advantage especially for down-sampling projection data. In this paper, studies of the CBCT iterative algorithms implemented in MIDAS are presented. Stability, convergence rate, quality of reconstructed image and edge recovery are suggested as the main criteria for monitoring reconstructive performance. Accordingly, the selection of relaxation parameter and number of iterations are studied in detail. Results are presented, where images are reconstructed from full and down-sampled cone beam CT projection data using iterative algorithms. Various iterative algorithms have been implemented and the best selection of the iteration number and relaxation parameters are investigated for ART. Optimal parameters are chosen where the errors in projected data as well as image errors are minimal.