Image reconstruction for transmission tomography when projection data are incomplete

A simulated annealing approach for resolution guided homogeneous cryo-electron microscopy image selection

BACKGROUND

Cryo-electron microscopy (Cryo-EM) and tomography (Cryo-ET) have emerged as important imaging techniques for studying structures of macromolecular complexes. In 3D reconstruction of large macromolecular complexes, many 2D projection images of macromolecular complex particles are usually acquired with low signal-to-noise ratio. Therefore, it is meaningful to select multiple images containing the same structure with identical orientation. The selected images are averaged to produce a higher-quality representation of the underlying structure with improved resolution. Existing approaches of selecting such images have limited accuracy and speed.

METHODS

We propose a simulated annealing-based algorithm (SA) to pick the homogeneous image set with best average. Its performance is compared with two baseline methods based on both 2D and 3D datasets. When tested on simulated and experimental 3D Cryo-ET images of Ribosome complex, SA sometimes stopped at a local optimal solution. Restarting is applied to settle this difficulty and significantly improved the performance of SA on 3D datasets.

RESULTS

Experimented on simulated and experimental 2D Cryo-EM images of Ribosome complex datasets respectively with SNR = 10 and SNR = 0.5, our method achieved better accuracy in terms of F-measure, resolution score, and time cost than two baseline methods. Additionally, SA shows its superiority when the proportion of homogeneous images decreases.

CONCLUSIONS

SA is introduced for homogeneous image selection to realize higher accuracy with faster processing speed. Experiments on both simulated and real 2D Cryo-EM and 3D Cryo-ET images demonstrated that SA achieved expressively better performance. This approach serves as an important step for improving the resolution of structural recovery of macromolecular complexes captured by Cryo-EM and Cryo-ET.

Task-based statistical image reconstruction for high-quality cone-beam CT

Task-based analysis of medical imaging performance underlies many ongoing efforts in the development of new imaging systems. In statistical image reconstruction, regularization is often formulated in terms to encourage smoothness and/or sharpness (e.g. a linear, quadratic, or Huber penalty) but without explicit formulation of the task. We propose an alternative regularization approach in which a spatially varying penalty is determined that maximizes task-based imaging performance at every location in a 3D image. We apply the method to model-based image reconstruction (MBIR-viz., penalized weighted least-squares, PWLS) in cone-beam CT (CBCT) of the head, focusing on the task of detecting a small, low-contrast intracranial hemorrhage (ICH), and we test the performance of the algorithm in the context of a recently developed CBCT prototype for point-of-care imaging of brain injury. Theoretical predictions of local spatial resolution and noise are computed via an optimization by which regularization (specifically, the quadratic penalty strength) is allowed to vary throughout the image to maximize local task-based detectability index ([Formula: see text]). Simulation studies and test-bench experiments were performed using an anthropomorphic head phantom. Three PWLS implementations were tested: conventional (constant) penalty; a certainty-based penalty derived to enforce constant point-spread function, PSF; and the task-based penalty derived to maximize local detectability at each location. Conventional (constant) regularization exhibited a fairly strong degree of spatial variation in [Formula: see text], and the certainty-based method achieved uniform PSF, but each exhibited a reduction in detectability compared to the task-based method, which improved detectability up to ~15%. The improvement was strongest in areas of high attenuation (skull base), where the conventional and certainty-based methods tended to over-smooth the data. The task-driven reconstruction method presents a promising regularization method in MBIR by explicitly incorporating task-based imaging performance as the objective. The results demonstrate improved ICH conspicuity and support the development of high-quality CBCT systems.

Iterative metal artifact reduction for x-ray computed tomography using unmatched projector/backprojector pairs

PURPOSE

Metal artifact reduction (MAR) is a major problem and a challenging issue in x-ray computed tomography (CT) examinations. Iterative reconstruction from sinograms unaffected by metals shows promising potential in detail recovery. This reconstruction has been the subject of much research in recent years. However, conventional iterative reconstruction methods easily introduce new artifacts around metal implants because of incomplete data reconstruction and inconsistencies in practical data acquisition. Hence, this work aims at developing a method to suppress newly introduced artifacts and improve the image quality around metal implants for the iterative MAR scheme.

METHODS

The proposed method consists of two steps based on the general iterative MAR framework. An uncorrected image is initially reconstructed, and the corresponding metal trace is obtained. The iterative reconstruction method is then used to reconstruct images from the unaffected sinogram. In the reconstruction step of this work, an iterative strategy utilizing unmatched projector/backprojector pairs is used. A ramp filter is introduced into the back-projection procedure to restrain the inconsistency components in low frequencies and generate more reliable images of the regions around metals. Furthermore, a constrained total variation (TV) minimization model is also incorporated to enhance efficiency. The proposed strategy is implemented based on an iterative FBP and an alternating direction minimization (ADM) scheme, respectively. The developed algorithms are referred to as "iFBP-TV" and "TV-FADM," respectively. Two projection-completion-based MAR methods and three iterative MAR methods are performed simultaneously for comparison.

RESULTS

The proposed method performs reasonably on both simulation and real CT-scanned datasets. This approach could reduce streak metal artifacts effectively and avoid the mentioned effects in the vicinity of the metals. The improvements are evaluated by inspecting regions of interest and by comparing the root-mean-square errors, normalized mean absolute distance, and universal quality index metrics of the images. Both iFBP-TV and TV-FADM methods outperform other counterparts in all cases. Unlike the conventional iterative methods, the proposed strategy utilizing unmatched projector/backprojector pairs shows excellent performance in detail preservation and prevention of the introduction of new artifacts.

CONCLUSIONS

Qualitative and quantitative evaluations of experimental results indicate that the developed method outperforms classical MAR algorithms in suppressing streak artifacts and preserving the edge structural information of the object. In particular, structures lying close to metals can be gradually recovered because of the reduction of artifacts caused by inconsistency effects.

A metal artifact reduction method for a dental CT based on adaptive local thresholding and prior image generation

Background

Metal artifacts appearing as streaks and shadows often compromise readability of computed tomography (CT) images. Particularly in a dental CT in which high resolution imaging is crucial for precise preparation of dental implants or orthodontic devices, reduction of metal artifacts is very important. However, metal artifact reduction algorithms developed for a general medical CT may not work well in a dental CT since teeth themselves also have high attenuation coefficients.

Methods

To reduce metal artifacts in dental CT images, we made prior images by weighted summation of two images: one, a streak-reduced image reconstructed from the metal-region-modified projection data, and the other a metal-free image reconstructed from the original projection data followed by metal region deletion. To make the streak-reduced image, we precisely segmented the metal region based on adaptive local thresholding, and then, we modified the metal region on the projection data using linear interpolation. We made forward projection of the prior image to make the prior projection data. We replaced the pixel values at the metal region in the original projection data with the ones taken from the prior projection data, and then, we finally reconstructed images from the replaced projection data. To validate the proposed method, we made computational simulations and also we made experiments on teeth phantoms using a micro-CT. We compared the results with the ones obtained by the fusion prior-based metal artifact reduction (FP-MAR) method.

Results

In the simulation studies using a bilateral prostheses phantom and a dental phantom, the proposed method showed a performance similar to the FP-MAR method in terms of the edge profile and the structural similarity index when an optimal global threshold was chosen for the FP-MAR method. In the imaging studies of teeth phantoms, the proposed method showed a better performance than the FP-MAR method in reducing the streak artifacts without introducing any contrast anomaly.

Conclusions

The simulation and experimental imaging studies suggest that the proposed method can be used for reducing metal artifacts in dental CT images.

Line Integral Alternating Minimization Algorithm for Dual-Energy X-Ray CT Image Reconstruction

We propose a new algorithm, called line integral alternating minimization (LIAM), for dual-energy X-ray CT image reconstruction. Instead of obtaining component images by minimizing the discrepancy between the data and the mean estimates, LIAM allows for a tunable discrepancy between the basis material projections and the basis sinograms. A parameter is introduced that controls the size of this discrepancy, and with this parameter the new algorithm can continuously go from a two-step approach to the joint estimation approach. LIAM alternates between iteratively updating the line integrals of the component images and reconstruction of the component images using an image iterative deblurring algorithm. An edge-preserving penalty function can be incorporated in the iterative deblurring step to decrease the roughness in component images. Images from both simulated and experimentally acquired sinograms from a clinical scanner were reconstructed by LIAM while varying the regularization parameters to identify good choices. The results from the dual-energy alternating minimization algorithm applied to the same data were used for comparison. Using a small fraction of the computation time of dual-energy alternating minimization, LIAM achieves better accuracy of the component images in the presence of Poisson noise for simulated data reconstruction and achieves the same level of accuracy for real data reconstruction.

PIRPLE: a penalized-likelihood framework for incorporation of prior images in CT reconstruction

Over the course of diagnosis and treatment, it is common for a number of imaging studies to be acquired. Such imaging sequences can provide substantial patient-specific prior knowledge about the anatomy that can be incorporated into a prior-image-based tomographic reconstruction for improved image quality and better dose utilization. We present a general methodology using a model-based reconstruction approach including formulations of the measurement noise that also integrates prior images. This penalized-likelihood technique adopts a sparsity enforcing penalty that incorporates prior information yet allows for change between the current reconstruction and the prior image. Moreover, since prior images are generally not registered with the current image volume, we present a modified model-based approach that seeks a joint registration of the prior image in addition to the reconstruction of projection data. We demonstrate that the combined prior-image- and model-based technique outperforms methods that ignore the prior data or lack a noise model. Moreover, we demonstrate the importance of registration for prior-image-based reconstruction methods and show that the prior-image-registered penalized-likelihood estimation (PIRPLE) approach can maintain a high level of image quality in the presence of noisy and undersampled projection data.

A hybrid metal artifact reduction algorithm for x-ray CT

PURPOSE

Presence of metal artifacts is a major reason of degradation of computed tomography image quality and there is still no standard solution to this issue. A class of recently investigated metal artifact reduction (MAR) methods based on forward projection of a prior image that is artifact-free to replace the metal affected projection data have shown promising results. However, usually it is hard to get a good prior image which is close to the true image without artifacts. This work aims at creating a good prior image so that the forward projection can replace the metal affected projection data well.

METHODS

The proposed method consists of four steps based on the forward projection MAR framework. First, metal implants in the reconstructed image are segmented and the corresponding metal traces in the projection domain are identified. Then the prior image is obtained by two steps. A processed precorrected image is generated as an initial prior image first and then in the next step it is used as the initial image of the iterative reconstruction from the unaffected projection data to generate a better prior image. In order to deal with severe artifacts, the iteration incorporates the total variation minimization constraint as well as a novel constraint which forces the soft tissue region near metal to be as flat as possible. Finally, the projection is completed using forward projection of the prior image and the corrected image is reconstructed by FBP. A linear interpolation MAR method and two recently reported forward projection based methods are performed simultaneously for comparison.

RESULTS

The proposed method shows outstanding performance on both phantoms' and patients' datasets. This approach can reduce artifacts dramatically and restore tissue structures near metal to a large extent. Unlike competing MAR methods, it can effectively prevent introduction of new artifacts and false structures. Moreover, the proposed method has the lowest RMSE in regions of both soft tissue and bone tissue among the corrected images and is ranked as the best method for evaluation, by radiologists.

CONCLUSIONS

Both subjective and quantitative evaluations of the results demonstrate the superior performance of the proposed algorithm, compared to that of the competing methods. This method offers a remarkable improvement of the image quality.

Limited angle C-arm tomography and segmentation for guidance of atrial fibrillation ablation procedures

Angiographic projections of the left atrium (LA) and the pulmonary veins (PV) acquired with a rotational C-arm system are used for 3D image reconstruction and subsequent automatic segmentation of the LA and PV to be used as roadmap in fluoroscopy guided LA ablation procedures. Acquisition of projections at high oblique angulations may be problematic due to increased collision danger of the detector with the right shoulder of the patient. We investigate the accuracy of image reconstruction and model based roadmap segmentation using limited angle C-arm tomography. The reduction of the angular range from 200 degrees to 150 degrees leads only to a moderate increase of the segmentation error from 1.5 mm to 2.0 mm if matched conditions are used in the segmentation, i.e., the model based segmentation is trained on images reconstructed with the same angular range as the test images. The minor decrease in accuracy may be outweighed by clinical workflow improvement, gained when large C-arm angulations can be avoided.

Statistical interior tomography

This paper presents a statistical interior tomography (SIT) approach making use of compressed sensing (CS) theory. With the projection data modeled by the Poisson distribution, an objective function with a total variation (TV) regularization term is formulated in the maximization of a posteriori (MAP) framework to solve the interior problem. An alternating minimization method is used to optimize the objective function with an initial image from the direct inversion of the truncated Hilbert transform. The proposed SIT approach is extensively evaluated with both numerical and real datasets. The results demonstrate that SIT is robust with respect to data noise and down-sampling, and has better resolution and less bias than its deterministic counterpart in the case of low count data.

Localizing intracavitary brachytherapy applicators from cone-beam CT x-ray projections via a novel iterative forward projection matching algorithm

PURPOSE

To present a novel method for reconstructing the 3D pose (position and orientation) of radio-opaque applicators of known but arbitrary shape from a small set of 2D x-ray projections in support of intraoperative brachytherapy planning.

METHODS

The generalized iterative forward projection matching (gIFPM) algorithm finds the six degree-of-freedom pose of an arbitrary rigid object by minimizing the sum-of-squared-intensity differences (SSQD) between the computed and experimentally acquired autosegmented projection of the objects. Starting with an initial estimate of the object's pose, gIFPM iteratively refines the pose parameters (3D position and three Euler angles) until the SSQD converges. The object, here specialized to a Fletcher-Weeks intracavitary brachytherapy (ICB) applicator, is represented by a fine mesh of discrete points derived from complex combinatorial geometric models of the actual applicators. Three pairs of computed and measured projection images with known imaging geometry are used. Projection images of an intrauterine tandem and colpostats were acquired from an ACUITY cone-beam CT digital simulator. An image postprocessing step was performed to create blurred binary applicators only images. To quantify gIFPM accuracy, the reconstructed 3D pose of the applicator model was forward projected and overlaid with the measured images and empirically calculated the nearest-neighbor applicator positional difference for each image pair.

RESULTS

In the numerical simulations, the tandem and colpostats positions (x,y,z) and orientations (alpha, beta, gamma) were estimated with accuracies of 0.6 mm and 2 degrees, respectively. For experimentally acquired images of actual applicators, the residual 2D registration error was less than 1.8 mm for each image pair, corresponding to about 1 mm positioning accuracy at isocenter, with a total computation time of less than 1.5 min on a 1 GHz processor.

CONCLUSIONS

This work describes a novel, accurate, fast, and completely automatic method to localize radio-opaque applicators of arbitrary shape from measured 2D x-ray projections. The results demonstrate approximately 1 mm accuracy while compared against the measured applicator projections. No lateral film is needed. By localizing the applicator internal structure as well as radioactive sources, the effect of intra-applicator and interapplicator attenuation can be included in the resultant dose calculations. Further validation tests using clinically acquired tandem and colpostats images will be performed for the accurate and robust applicator/sources localization in ICB patients.

Comparison of extended field-of-view reconstructions in C-arm flat-detector CT using patient size, shape or attenuation information

In C-arm-based flat-detector computed tomography (FDCT) it frequently happens that the patient exceeds the scan field of view (SFOV) in the transaxial direction because of the limited detector size. This results in data truncation and CT image artefacts. In this work three truncation correction approaches for extended field-of-view (EFOV) reconstructions have been implemented and evaluated. An FDCT-based method estimates the patient size and shape from the truncated projections by fitting an elliptical model to the raw data in order to apply an extrapolation. In a camera-based approach the patient is sampled with an optical tracking system and this information is used to apply an extrapolation. In a CT-based method the projections are completed by artificial projection data obtained from the CT data acquired in an earlier exam. For all methods the extended projections are filtered and backprojected with a standard Feldkamp-type algorithm. Quantitative evaluations have been performed by simulations of voxelized phantoms on the basis of the root mean square deviation and a quality factor Q (Q = 1 represents the ideal correction). Measurements with a C-arm FDCT system have been used to validate the simulations and to investigate the practical applicability using anthropomorphic phantoms which caused truncation in all projections. The proposed approaches enlarged the FOV to cover wider patient cross-sections. Thus, image quality inside and outside the SFOV has been improved. Best results have been obtained using the CT-based method, followed by the camera-based and the FDCT-based truncation correction. For simulations, quality factors up to 0.98 have been achieved. Truncation-induced cupping artefacts have been reduced, e.g., from 218% to less than 1% for the measurements. The proposed truncation correction approaches for EFOV reconstructions are an effective way to ensure accurate CT values inside the SFOV and to recover peripheral information outside the SFOV.

Statistical projection completion in X-ray CT using consistency conditions

Projection data incompleteness arises in many situations relevant to X-ray computed tomography (CT) imaging. We propose a penalized maximum likelihood statistical sinogram restoration approach that incorporates the Helgason-Ludwig (HL) consistency conditions to accommodate projection data incompleteness. Image reconstruction is performed by the filtered-backprojection (FBP) in a second step. In our problem formulation, the objective function consists of the log-likelihood of the X-ray CT data and a penalty term; the HL condition poses a linear constraint on the restored sinogram and can be implemented efficiently via fast Fourier transform (FFT) and inverse FFT. We derive an iterative algorithm that increases the objective function monotonically. The proposed algorithm is applied to both computer simulated data and real patient data. We study different factors in the problem formulation that affect the properties of the final FBP reconstructed images, including the data truncation level, the amount of prior knowledge on the object support, as well as different approximations of the statistical distribution of the available projection data. We also compare its performance with an analytical truncation artifacts reduction method. The proposed method greatly improves both the accuracy and the precision of the reconstructed images within the scan field-of-view, and to a certain extent recovers the truncated peripheral region of the object. The proposed method may also be applied in areas such as limited angle tomography, metal artifacts reduction, and sparse sampling imaging.

Alternating minimization algorithms for transmission tomography

A family of alternating minimization algorithms for finding maximum-likelihood estimates of attenuation functions in transmission X-ray tomography is described. The model from which the algorithms are derived includes polyenergetic photon spectra, background events, and nonideal point spread functions. The maximum-likelihood image reconstruction problem is reformulated as a double minimization of the I-divergence. A novel application of the convex decomposition lemma results in an alternating minimization algorithm that monotonically decreases the objective function. Each step of the minimization is in closed form. The family of algorithms includes variations that use ordered subset techniques for increasing the speed of convergence. Simulations demonstrate the ability to correct the cupping artifact due to beam hardening and the ability to reduce streaking artifacts that arise from beam hardening and background events.