Correction of center of rotation and projection angle in synchrotron X-ray computed tomography.
ABSTRACT: 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.
Project description:Since X-ray tomography is now widely adopted in many different areas, it becomes more crucial to find a robust routine of handling tomographic data to get better quality of reconstructions. Though there are several existing techniques, it seems helpful to have a more automated method to remove the possible errors that hinder clearer image reconstruction. Here, we proposed an alternative method and new algorithm using the sinogram and the fixed point. An advanced physical concept of Center of Attenuation (CA) was also introduced to figure out how this fixed point is applied to the reconstruction of image having errors we categorized in this article. Our technique showed a promising performance in restoring images having translation and vertical tilt errors.
Project description:To demonstrate the feasibility of reconstructing a cone-beam CT (CBCT) image by deformably altering a prior fan-beam CT (FBCT) image such that it matches the anatomy portrayed in the CBCT projection data set.A prior FBCT image of the patient is assumed to be available as a source image. A CBCT projection data set is obtained and used as a target image set. A parametrized deformation model is applied to the source FBCT image, digitally reconstructed radiographs (DRRs) that emulate the CBCT projection image geometry are calculated and compared to the target CBCT projection data, and the deformation model parameters are adjusted iteratively until the DRRs optimally match the CBCT projection data set. The resulting deformed FBCT image is hypothesized to be an accurate representation of the patient's anatomy imaged by the CBCT system. The process is demonstrated via numerical simulation. A known deformation is applied to a prior FBCT image and used to create a synthetic set of CBCT target projections. The iterative projection matching process is then applied to reconstruct the deformation represented in the synthetic target projections; the reconstructed deformation is then compared to the known deformation. The sensitivity of the process to the number of projections and the DRR/CBCT projection mismatch is explored by systematically adding noise to and perturbing the contrast of the target projections relative to the iterated source DRRs and by reducing the number of projections.When there is no noise or contrast mismatch in the CBCT projection images, a set of 64 projections allows the known deformed CT image to be reconstructed to within a nRMS error of 1% and the known deformation to within a nRMS error of 7%. A CT image nRMS error of less than 4% is maintained at noise levels up to 3% of the mean projection intensity, at which the deformation error is 13%. At 1% noise level, the number of projections can be reduced to 8 while maintaining CT image and deformation errors of less than 4% and 13%, respectively. The method is sensitive to contrast mismatch between the simulated projections and the target projections when the soft-tissue contrast in the projections is low.By using prior knowledge available in a FBCT image, the authors show that a CBCT image can be iteratively reconstructed from a comparatively small number of projection images, thus saving acquisition time and reducing imaging dose. This will enable more frequent daily imaging during radiation therapy. Because the process preserves the CT numbers of the FBCT image, the resulting 3D image intensities will be more accurate than a CBCT image reconstructed via conventional backprojection methods. Reconstruction errors are insensitive to noise at levels beyond what would typically be found in CBCT projection data, but are sensitive to contrast mismatch errors between the CBCT projection data and the DRRs.
Project description:To accelerate iterative algebraic reconstruction algorithms using a cylindrical image grid.Tetrahedron beam computed tomography (TBCT) is designed to overcome the scatter and detector problems of cone beam computed tomography (CBCT). Iterative algebraic reconstruction algorithms have been shown to mitigate approximate reconstruction artifacts that appear at large cone angles, but clinical implementation is limited by their high computational cost. In this study, a cylindrical voxelization method on a cylindrical grid is developed in order to take advantage of the symmetries of the cylindrical geometry. The cylindrical geometry is a natural fit for the circular scanning trajectory employed in volumetric CT methods such as CBCT and TBCT. This method was implemented in combination with the simultaneous algebraic reconstruction technique (SART). Both two- and three-dimensional numerical phantoms as well as a patient CT image were utilized to generate the projection sets used for reconstruction. The reconstructed images were compared to the original phantoms using a set of three figures of merit (FOM).The cylindrical voxelization on a cylindrical reconstruction grid was successfully implemented in combination with the SART reconstruction algorithm. The FOM results showed that the cylindrical reconstructions were able to maintain the accuracy of the Cartesian reconstructions. In three dimensions, the cylindrical method provided better accuracy than the Cartesian methods. At the same time, the cylindrical method was able to provide a speedup factor of approximately 40 while also reducing the system matrix storage size by 2 orders of magnitude.TBCT image reconstruction using a cylindrical image grid was able to provide a significant improvement in the reconstruction time and a more compact system matrix for storage on the hard drive and in memory while maintaining the image quality provided by the Cartesian voxelization on a Cartesian grid.
Project description:X-ray 3D tomographic techniques are powerful tools for investigating the morphology and internal structures of specimens. A common strategy for obtaining 3D tomography is to capture a series of 2D projections from different X-ray illumination angles of specimens mounted on a finely calibrated rotational stage. However, the reconstruction quality of 3D tomography relies on the precision and stability of the rotational stage, i.e. the accurate alignment of the 2D projections in the correct three-dimensional positions. This is a crucial problem for nano-tomographic techniques due to the non-negligible mechanical imperfection of the rotational stages at the nanometer level which significantly degrades the spatial resolution of reconstructed 3-D tomography. Even when using an X-ray micro-CT with a highly stabilized rotational stage, thermal effects caused by the CT system are not negligible and may cause sample drift. Here, we propose a markerless image auto-alignment algorithm based on an iterative method. This algorithm reduces the traditional projection matching method into two simplified matching problems and it is much faster and more reliable than traditional methods. This algorithm can greatly decrease hardware requirements for both nano-tomography and data processing and can be easily applied to other tomographic techniques, such as X-ray micro-CT and electron tomography.
Project description:The Antikythera Mechanism is an extraordinarily complex ancient Greek astronomical calculating device whose mode of operation is now relatively well understood particularly since imaging studies in 2005 revealed gears and inscriptions which were previously illegible. Unfortunately, the highest resolution X-ray computed tomography image of the largest fragment had some errors which meant that the reconstructed images were not as clear as had been expected. Here, the original X-ray data have been reanalysed and reconstructed. The new X-ray computed tomography images have improved contrast and resolution, leading to better clarity and legibility. The improvement in image quality is characterised and some examples of writing on the Mechanism which can now be read with increased confidence are given.
Project description:Prior image constrained compressed sensing (PICCS) is an image reconstruction framework which incorporates an often available prior image into the compressed sensing objective function. The images are reconstructed using an optimization procedure. In this paper, several alternative unconstrained minimization methods are used to implement PICCS. The purpose is to study and compare the performance of each implementation, as well as to evaluate the performance of the PICCS objective function with respect to image quality.Six different minimization methods are investigated with respect to convergence speed and reconstruction accuracy. These minimization methods include the steepest descent (SD) method and the conjugate gradient (CG) method. These algorithms require a line search to be performed. Thus, for each minimization algorithm, two line searching algorithms are evaluated: a backtracking (BT) line search and a fast Newton-Raphson (NR) line search. The relative root mean square error is used to evaluate the reconstruction accuracy. The algorithm that offers the best convergence speed is used to study the performance of PICCS with respect to the prior image parameter α and the data consistency parameter λ. PICCS is studied in terms of reconstruction accuracy, low-contrast spatial resolution, and noise characteristics. A numerical phantom was simulated and an animal model was scanned using a multirow detector computed tomography (CT) scanner to yield the projection datasets used in this study.For λ within a broad range, the CG method with Fletcher-Reeves formula and NR line search offers the fastest convergence for an equal level of reconstruction accuracy. Using this minimization method, the reconstruction accuracy of PICCS was studied with respect to variations in α and λ. When the number of view angles is varied between 107, 80, 64, 40, 20, and 16, the relative root mean square error reaches a minimum value for α ≈ 0.5. For values of α near the optimal value, the spatial resolution of the reconstructed image remains relatively constant and the noise texture is very similar to that of the prior image, which was reconstructed using the filtered backprojection (FBP) algorithm.Regarding the performance of the minimization methods, the nonlinear CG method with NR line search yields the best convergence speed. Regarding the performance of the PICCS image reconstruction, three main conclusions can be reached. (1) The performance of PICCS is optimal when the weighting parameter of the prior image parameter is selected to be near α = 0.5. (2) The spatial resolution measured for static objects in images reconstructed using PICCS from undersampled datasets is not degraded with respect to the fully-sampled reconstruction for α near its optimal value. (3) The noise texture of PICCS reconstructions is similar to that of the prior image, which was reconstructed using the conventional FBP method.
Project description:The application of optical projection tomography to in-vivo experiments is limited by specimen movement during the acquisition. We present a set of mathematical correction methods applied to the acquired data stacks to correct for movement in both directions of the image plane. These methods have been applied to correct experimental data taken from in-vivo optical projection tomography experiments in Caenorhabditis elegans. Successful reconstructions for both fluorescence and white light (absorption) measurements are shown. Since no difference between movement of the animal and movement of the rotation axis is made, this approach at the same time removes artifacts due to mechanical drifts and errors in the assumed center of rotation.
Project description:Optical projection tomography (OPT) provides a non-invasive 3-D imaging modality that can be applied to longitudinal studies of live disease models, including in zebrafish. Current limitations include the requirement of a minimum number of angular projections for reconstruction of reasonable OPT images using filtered back projection (FBP), which is typically several hundred, leading to acquisition times of several minutes. It is highly desirable to decrease the number of required angular projections to decrease both the total acquisition time and the light dose to the sample. This is particularly important to enable longitudinal studies, which involve measurements of the same fish at different time points. In this work, we demonstrate that the use of an iterative algorithm to reconstruct sparsely sampled OPT data sets can provide useful 3-D images with 50 or fewer projections, thereby significantly decreasing the minimum acquisition time and light dose while maintaining image quality. A transgenic zebrafish embryo with fluorescent labelling of the vasculature was imaged to acquire densely sampled (800 projections) and under-sampled data sets of transmitted and fluorescence projection images. The under-sampled OPT data sets were reconstructed using an iterative total variation-based image reconstruction algorithm and compared against FBP reconstructions of the densely sampled data sets. To illustrate the potential for quantitative analysis following rapid OPT data acquisition, a Hessian-based method was applied to automatically segment the reconstructed images to select the vasculature network. Results showed that 3-D images of the zebrafish embryo and its vasculature of sufficient visual quality for quantitative analysis can be reconstructed using the iterative algorithm from only 32 projections-achieving up to 28 times improvement in imaging speed and leading to total acquisition times of a few seconds.
Project description:The development of computed tomography (CT) image reconstruction methods that significantly reduce patient radiation exposure, while maintaining high image quality is an important area of research in low-dose CT imaging. We propose a new penalized weighted least squares (PWLS) reconstruction method that exploits regularization based on an efficient Union of Learned TRAnsforms (PWLS-ULTRA). The union of square transforms is pre-learned from numerous image patches extracted from a dataset of CT images or volumes. The proposed PWLS-based cost function is optimized by alternating between a CT image reconstruction step, and a sparse coding and clustering step. The CT image reconstruction step is accelerated by a relaxed linearized augmented Lagrangian method with ordered-subsets that reduces the number of forward and back projections. Simulations with 2-D and 3-D axial CT scans of the extended cardiac-torso phantom and 3-D helical chest and abdomen scans show that for both normal-dose and low-dose levels, the proposed method significantly improves the quality of reconstructed images compared to PWLS reconstruction with a nonadaptive edge-preserving regularizer. PWLS with regularization based on a union of learned transforms leads to better image reconstructions than using a single learned square transform. We also incorporate patch-based weights in PWLS-ULTRA that enhance image quality and help improve image resolution uniformity. The proposed approach achieves comparable or better image quality compared to learned overcomplete synthesis dictionaries, but importantly, is much faster (computationally more efficient).