On Krylov methods for large-scale CBCT reconstruction.

Krylov subspace methods are a powerful family of iterative solvers for linear systems of equations, which are commonly used for inverse problems due to their intrinsic regularization properties. Moreover, these methods are naturally suited to solve large-scale problems, as they only require matrix-vector products with the system matrix (and its adjoint) to compute approximate solutions, and they display a very fast convergence. Even if this class of methods has been widely researched and studied in the numerical linear algebra community, its use in applied medical physics and applied engineering is still very limited. e.g. in realistic large-scale computed tomography (CT) problems, and more specifically in cone beam CT (CBCT). This work attempts to breach this gap by providing a general framework for the most relevant Krylov subspace methods applied to 3D CT problems, including the most well-known Krylov solvers for non-square systems (CGLS, LSQR, LSMR), possibly in combination with Tikhonov regularization, and methods that incorporate total variation regularization. This is provided within an open source framework: the tomographic iterative GPU-based reconstruction toolbox, with the idea of promoting accessibility and reproducibility of the results for the algorithms presented. Finally, numerical results in synthetic and real-world 3D CT applications (medical CBCT andµ-CT datasets) are provided to showcase and compare the different Krylov subspace methods presented in the paper, as well as their suitability for different kinds of problems.

Source-detector trajectory optimization for CBCT metal artifact reduction based on PICCS reconstruction.

Precise instrument placement plays a critical role in all interventional procedures, especially percutaneous procedures such as needle biopsies, to achieve successful tumor targeting and increased diagnostic accuracy. C-arm cone beam computed tomography (CBCT) has the potential to precisely visualize the anatomy in direct vicinity of the needle and evaluate the adequacy of needle placement during the intervention, allowing for instantaneous adjustment in case of misplacement. However, even with the most advanced C-arm CBCT devices, it can be difficult to identify the exact needle position on CBCT images due to the strong metal artifacts around the needle. In this study, we proposed a framework for customized trajectory design in CBCT imaging based on Prior Image Constrained Compressed Sensing (PICCS) reconstruction with the goal of reducing metal artifacts in needle-based procedures. We proposed to optimize out-of-plane rotations in three-dimensional (3D) space and minimize projection views while reducing metal artifacts at specific volume of interests (VOIs). An anthropomorphic thorax phantom with a needle inserted inside and two tumor models as the imaging targets were used to validate the proposed approach. The performance of the proposed approach was also evaluated for CBCT imaging under kinematic constraints by simulating some collision areas on the geometry of the C-arm. We compared the result of optimized 3D trajectories using the PICCS algorithm and 20 projections with the result of a circular trajectory with sparse view using PICCS and Feldkamp, Davis, and Kress (FDK), both using 20 projections, and the circular FDK method with 313 projections. For imaging targets 1 and 2, the highest values of structural similarity index measure (SSIM) and universal quality index (UQI) between the reconstructed image from the optimized trajectories and the initial CBCT image at the VOI was calculated 0.7521, 0.7308 and 0.7308, 0.7248 respectively. These results significantly outperformed the FDK method (with 20 and 313 projections) and the PICCS method (20 projections) both using the circular trajectory. Our results showed that the proposed optimized trajectories not only significantly reduce metal artifacts but also suggest a dose reduction for needle-based CBCT interventions, considering the small number of projections used. Furthermore, our results showed that the optimized trajectories are compatible with spatially constrained situations and enable CBCT imaging under kinematic constraints when the standard circular trajectory is not feasible.

Extension of the open-source TIGRE toolbox for proton imaging.

Proton irradiation is a well-established method to treat deep-seated tumors in radio oncology. Usually, an X-ray computed tomography (CT) scan is used for treatment planning. Since proton therapy is based on the precise knowledge of the stopping power describing the energy loss of protons in the patient tissues, the Hounsfield units of the planning CT have to be converted. This conversion introduces range errors in the treatment plan, which could be reduced, if the stopping power values were extracted directly from an image obtained using protons instead of X-rays. Since protons are affected by multiple Coulomb scattering, reconstruction of the 3D stopping power map results in limited image quality if the curved proton path is not considered. This work presents a substantial code extension of the open-source toolbox TIGRE for proton CT (pCT) image reconstruction based on proton radiographs including a curved proton path estimate. The code extension and the reconstruction algorithms are GPU-based, allowing to achieve reconstruction results within minutes. The performance of the pCT code extension was tested with Monte Carlo simulated data using three phantoms (Catphan® high resolution and sensitometry modules and a CIRS patient phantom). In the simulations, ideal and non-ideal conditions for a pCT setup were assumed. The obtained mean absolute percentage error was found to be below 1% and up to 8 lp/cm could be resolved using an idealized setup. These findings demonstrate that the presented code extension to the TIGRE toolbox offers the possibility for other research groups to use a fast and accurate open-source pCT reconstruction.

TIGRE-VarianCBCT for on-board cone-beam computed tomography, an open-source toolkit for imaging, dosimetry and clinical research.

We presented TIGRE-VarianCBCT, an open-source toolkit Matlab-GPU for Varian on-board cone-beam CT with particular emphasis to address challenges in raw data preprocessing, artifacts correction, tomographic reconstruction and image post-processing. The aim of this project is to provide not only a tool to bridge the gap between clinical usage of CBCT scan data and research algorithms but also a framework that breaks down the imaging chain into individual processes so that research effort can be focused on a specific part. The entire imaging chain, module-based architecture, data flow and techniques used in the creation of the toolkit are presented. Raw scan data are first decoded to extract X-ray fluoro image series and set up the imaging geometry. Data conditioning operations including scatter correction, normalization, beam-hardening correction, ring removal are performed sequentially. Reconstruction is supported by TIGRE with FDK as well as a variety of iterative algorithms. Pixel-to-HU mapping is calibrated by a CatphanTM 504 phantom. Imaging dose in CTDIw is calculated in an empirical formula. The performance was validated on real patient scans with good agreement with respect to vendor-designed program. Case studies in scan protocol optimization, low dose imaging and iterative algorithm comparison demonstrated its substantial potential in performing scan data based clinical studies. The toolkit is released under the BSD license, imposing minimal restrictions on its use and distribution. The toolkit is accessible as a module at https://github.com/CERN/TIGRE.

Toward on-the-fly trajectory optimization for C-arm CBCT under strong kinematic constraints.

Cone beam computed tomography (CBCT) has become a vital tool in interventional radiology. Usually, a circular source-detector trajectory is used to acquire a three-dimensional (3D) image. Kinematic constraints due to the patient size or additional medical equipment often cause collisions with the imager while performing a full circular rotation. In a previous study, we developed a framework to design collision-free, patient-specific trajectories for the cases in which circular CBCT is not feasible. Our proposed trajectories included enough information to appropriately reconstruct a particular volume of interest (VOI), but the constraints had to be defined before the intervention. As most collisions are unpredictable, performing an on-the-fly trajectory optimization is desirable. In this study, we propose a search strategy that explores a set of trajectories that cover the whole collision-free area and subsequently performs a search locally in the areas with the highest image quality. Selecting the best trajectories is performed using simulations on a prior diagnostic CT volume which serves as a digital phantom for simulations. In our simulations, the Feature SIMilarity Index (FSIM) is used as the objective function to evaluate the imaging quality provided by different trajectories. We investigated the performance of our methods using three different anatomical targets inside the Alderson-Rando phantom. We used FSIM and Universal Quality Image (UQI) to evaluate the final reconstruction results. Our experiments showed that our proposed trajectories could achieve a comparable image quality in the VOI compared to the standard C-arm circular CBCT. We achieved a relative deviation less than 10% for both FSIM and UQI metrics between the reconstructed images from the optimized trajectories and the standard C-arm CBCT for all three targets. The whole trajectory optimization took approximately three to four minutes.

Short Scan Source-detector Trajectories for Target-based CBCT.

We proposed a target-based cone beam computed tomography (CBCT) imaging framework in order to optimize a free three dimensional (3D) source-detector trajectory by incorporating prior 3D image data. We aim to enable CBCT systems to provide topical information about a region of interest (ROI) using a short-scan trajectory with a reduced number of projections. The best projection views are selected by maximizing an objective function fed by the image quality by means of applying different x-ray positions on the digital phantom data. Finally, an optimized trajectory is selected which is applied to a C-arm device able to perform general source-detector positioning. An Alderson-Rando head phantom is used in order to investigate the performance of the proposed framework. Our experiments showed that the optimized trajectory could achieve a comparable image quality in the ROI with respect to the reference C-arm CBCT while using approximately one-quarter of projections. An angular range of 156° was used for the optimized trajectory.

Optimization for customized trajectories in cone beam computed tomography.

PURPOSE: We developed a target-based cone beam computed tomography (CBCT) imaging framework for optimizing an unconstrained three dimensional (3D) source-detector trajectory by incorporating prior image information. Our main aim is to enable a CBCT system to provide topical information about the target using a limited angle noncircular scan orbit with a minimal number of projections. Such a customized trajectory should include enough information to sufficiently reconstruct a particular volume of interest (VOI) under kinematic constraints, which may result from the patient size or additional surgical or radiation therapy-related equipment. METHODS: A patient-specific model from a prior diagnostic computed tomography (CT) volume is used as a digital phantom for CBCT trajectory simulations. Selection of the best projection views is accomplished through maximizing an objective function fed by the imaging quality provided by different x-ray positions on the digital phantom data. The final optimized trajectory includes a limited angular range and a minimal number of projections which can be applied to a C-arm device capable of general source-detector positioning. The performance of the proposed framework is investigated in experiments involving an in-house-built box phantom including spherical targets as well as an Alderson-Rando head phantom. In order to quantify the image quality of the reconstructed image, we use the average full-width-half-maximum (FWHMavg ) for the spherical target and feature similarity index (FSIM), universal quality index (UQI), and contrast-to-noise ratio (CNR) for an anatomical target. RESULTS: Our experiments based on both the box and head phantom showed that optimized trajectories could achieve a comparable image quality in the VOI with respect to the standard C-arm circular CBCT while using approximately one quarter of projections. We achieved a relative deviation <7% for FWHMavg between the reconstructed images from the optimized trajectories and the standard C-arm CBCT for all spherical targets. Furthermore, for the anatomical target, the relative deviation of FSIM, UQI, and CNR between the reconstructed image related to the proposed trajectory and the standard C-arm circular CBCT was found to be 5.06%, 6.89%, and 8.64%, respectively. We also compared our proposed trajectories to circular trajectories with equivalent angular sampling as the optimized trajectories. Our results show that optimized trajectories can outperform simple partial circular trajectories in the VOI in term of image quality. Typically, an angular range between 116° and 152° was used for the optimized trajectories. CONCLUSION: We demonstrated that applying limited angle noncircular trajectories with optimized orientations in 3D space can provide a suitable image quality for particular image targets and has a potential for limited angle and low-dose CBCT-based interventions under strong spatial constraints.

Numerically robust tetrahedron-based tomographic forward and backward projectors on parallel architectures.

X-ray tomographic reconstruction typically uses voxel basis functions to represent volumetric images. Due to the structure in voxel basis representations, efficient ray-tracing methods exist allowing fast, GPU accelerated implementations. Tetrahedral mesh basis functions are a valuable alternative to voxel based image representations as they provide flexible, inhomogeneous partitions which can be used to provide reconstructions with reduced numbers of elements or with arbitrarily fine object surface representations. We thus present a robust parallelizable ray-tracing method for volumetric tetrahedral domains developed specifically for Computed Tomography image reconstruction. Tomographic image reconstruction requires algorithms that are robust to numerical errors in floating point arithmetic whilst typical data sizes encountered in tomography require the algorithm to be parallelisable in GPUs which leads to additional constraints on algorithm choices. Based on these considerations, this article presents numerical solutions to the design of efficient ray-tracing algorithms for the projection and backprojection operations. Initial reconstruction results using CAD data to define a triangulation of the domain demonstrate the advantages of our method and contrast tetrahedral mesh based reconstructions to voxel based methods.

Parameter selection in limited data cone-beam CT reconstruction using edge-preserving total variation algorithms.

There are a number of powerful total variation (TV) regularization methods that have great promise in limited data cone-beam CT reconstruction with an enhancement of image quality. These promising TV methods require careful selection of the image reconstruction parameters, for which there are no well-established criteria. This paper presents a comprehensive evaluation of parameter selection in a number of major TV-based reconstruction algorithms. An appropriate way of selecting the values for each individual parameter has been suggested. Finally, a new adaptive-weighted projection-controlled steepest descent (AwPCSD) algorithm is presented, which implements the edge-preserving function for CBCT reconstruction with limited data. The proposed algorithm shows significant robustness compared to three other existing algorithms: ASD-POCS, AwASD-POCS and PCSD. The proposed AwPCSD algorithm is able to preserve the edges of the reconstructed images better with fewer sensitive parameters to tune.

A general method for motion compensation in x-ray computed tomography.

Motion during data acquisition is a known source of error in medical tomography, resulting in blur artefacts in the regions that move. It is critical to reduce these artefacts in applications such as image-guided radiation therapy as a clearer image translates into a more accurate treatment and the sparing of healthy tissue close to a tumour site. Most research in 4D x-ray tomography involving the thorax relies on respiratory phase binning of the acquired data and reconstructing each of a set of images using the limited subset of data per phase. In this work, we demonstrate a motion-compensation method to reconstruct images from the complete dataset taken during breathing without recourse to phase-binning or breath-hold techniques. As long as the motion is sufficiently well known, the new method can accurately reconstruct an image at any time during the acquisition time span. It can be applied to any iterative reconstruction algorithm.