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Purpose: Optimization of the AIR-algorithm for improved convergence and performance., Methods: The AIR method is an iterative algorithm for CT image reconstruction. As a result of its linearity with respect to the basis images, the AIR algorithm possesses well defined, regular image quality metrics, e.g. point spread function (PSF) or modulation transfer function (MTF), unlike other iterative reconstruction algorithms. The AIR algorithm computes weighting images α to blend between a set of basis images that preferably have mutually exclusive properties, e.g. high spatial resolution or low noise. The optimized algorithm uses an approach that alternates between the optimization of rawdata fidelity using an OSSART like update and regularization using gradient descent, as opposed to the initially proposed AIR using a straightforward gradient descent implementation. A regularization strength for a given task is chosen by formulating a requirement for the noise reduction and checking whether it is fulfilled for different regularization strengths, while monitoring the spatial resolution using the voxel-wise defined modulation transfer function for the AIR image., Results: The optimized algorithm computes similar images in a shorter time compared to the initial gradient descent implementation of AIR. The result can be influenced by multiple parameters that can be narrowed down to a relatively simple framework to compute high quality images. The AIR images, for instance, can have at least a 50% lower noise level compared to the sharpest basis image, while the spatial resolution is mostly maintained., Conclusions: The optimization improves performance by a factor of 6, while maintaining image quality. Furthermore, it was demonstrated that the spatial resolution for AIR can be determined using regular image quality metrics, given smooth weighting images. This is not possible for other iterative reconstructions as a result of their non linearity. A simple set of parameters for the algorithm is discussed that provides the mentioned results., (Copyright © 2017. Published by Elsevier GmbH.)

The detection of spherical markers in x-ray projections is an important task in a variety of applications, e.g. geometric calibration and detector distortion correction. Therein, the projection of the sphere center on the detector is of particular interest as the used spherical beads are no ideal point-like objects. Only few methods have been proposed to estimate this respective position on the detector with sufficient accuracy and surrogate positions, e.g. the center of gravity, are used, impairing the results of subsequent algorithms. We propose to estimate the projection of the sphere center on the detector using a simulation-based method matching an artificial projection to the actual measurement. The proposed algorithm intrinsically corrects for all polychromatic effects included in the measurement and absent in the simulation by a polynomial which is estimated simultaneously. Furthermore, neither the acquisition geometry nor any object properties besides the fact that the object is of spherical shape need to be known to find the center of the bead. It is shown by simulations that the algorithm estimates the center projection with an error of less than [Formula: see text] of the detector pixel size in case of realistic noise levels and that the method is robust to the sphere material, sphere size, and acquisition parameters. A comparison to three reference methods using simulations and measurements indicates that the proposed method is an order of magnitude more accurate compared to these algorithms. The proposed method is an accurate algorithm to estimate the center of spherical markers in CT projections in the presence of polychromatic effects and noise.

Purpose: To introduce and evaluate an increment matrix approach (IMA) describing the signal statistics of energy-selective photon counting detectors including spatial-spectral correlations between energy bins of neighboring detector pixels. The importance of the occurring correlations for image-based material decomposition is studied., Methods: An IMA describing the counter increase patterns in a photon counting detector is proposed. This IMA has the potential to decrease the number of required random numbers compared to Monte Carlo simulations by pursuing an approach based on convolutions. To validate and demonstrate the IMA, an approximate semirealistic detector model is provided, simulating a photon counting detector in a simplified manner, e.g., by neglecting count rate-dependent effects. In this way, the spatial-spectral correlations on the detector level are obtained and fed into the IMA. The importance of these correlations in reconstructed energy bin images and the corresponding detector performance in image-based material decomposition is evaluated using a statistically optimal decomposition algorithm., Results: The results of IMA together with the semirealistic detector model were compared to other models and measurements using the spectral response and the energy bin sensitivity, finding a good agreement. Correlations between the different reconstructed energy bin images could be observed, and turned out to be of weak nature. These correlations were found to be not relevant in image-based material decomposition. An even simpler simulation procedure based on the energy bin sensitivity was tested instead and yielded similar results for the image-based material decomposition task, as long as the fact that one incident photon can increase multiple counters across neighboring detector pixels is taken into account., Conclusions: The IMA is computationally efficient as it required about 10(2) random numbers per ray incident on a detector pixel instead of an estimated 10(8) random numbers per ray as Monte Carlo approaches would need. The spatial-spectral correlations as described by IMA are not important for the studied image-based material decomposition task. Respecting the absolute photon counts and thus the multiple counter increases by a single x-ray photon, the same material decomposition performance could be obtained with a simpler detector description using the energy bin sensitivity.

Purpose: Cardiac in vivo micro-CT imaging of small animals typically requires double gating due to long scan times and high respiratory rates. The simultaneous respiratory and cardiac gating can either be done prospectively or retrospectively. In any case, for true 5D imaging, i.e., three spatial dimensions plus one respiratory-temporal dimension plus one cardiac temporal dimension, the amount of information corresponding to a given respiratory and cardiac phase is orders of magnitude lower than the total amount of information acquired. Achieving similar image quality for 5D than for usual 3D investigations would require increasing the amount of data and thus the applied dose to the animal. Therefore, the goal is phase-correlated imaging with high image quality but without increasing the dose level., Methods: To achieve this, the authors propose a new image reconstruction algorithm that makes use of all available projection data, also of that corresponding to other motion windows. In particular, the authors apply a motion-compensated image reconstruction approach that sequentially compensates for respiratory and cardiac motion to decrease the impact of sparsification. In that process, all projection data are used no matter which motion phase they were acquired in. Respiratory and cardiac motion are compensated for by using motion vector fields. These motion vector fields are estimated from initial phase-correlated reconstructions based on a deformable registration approach. To decrease the sensitivity of the registration to sparse-view artifacts, an artifact model-based approach is used including a cyclic consistent nonrigid registration algorithm., Results: The preliminary results indicate that the authors' approach removes the sparse-view artifacts of conventional phase-correlated reconstructions while maintaining temporal resolution. In addition, it achieves noise levels and spatial resolution comparable to that of nongated reconstructions due to the improved dose usage. By using the proposed motion estimation, no sensitivity to streaking artifacts has been observed., Conclusions: Using sequential double gating combined with artifact model-based motion estimation allows to accurately estimate respiratory and cardiac motion from highly undersampled data. No sensitivity to streaking artifacts introduced by sparse angular sampling has been observed for the investigated dose levels. The motion-compensated image reconstruction was able to correct for both, respiratory and cardiac motion, by applying the estimated motion vector fields. The administered dose per animal can thus be reduced for 5D imaging allowing for longitudinal studies at the highest image quality.

Many applications in medical imaging include image registration for matching of images from the same or different modalities. In the case of full data sampling, the respective reconstructed images are usually of such a good image quality that standard deformable volume-to-volume (3D-3D) registration approaches can be applied. But research in temporal-correlated image reconstruction and dose reductions increases the number of cases where rawdata are available from only few projection angles. Here, deteriorated image quality leads to non-acceptable deformable volume-to-volume registration results. Therefore a registration approach is required that is robust against a decreasing number of projections defining the target position. We propose a deformable volume-to-rawdata (3D-2D) registration method that aims at finding a displacement vector field maximizing the alignment of a CT volume and the acquired rawdata based on the sum of squared differences in rawdata domain. The registration is constrained by a regularization term in accordance with a fluid-based diffusion. Both cost function components, the rawdata fidelity and the regularization term, are optimized in an alternating manner. The matching criterion is optimized by a conjugate gradient descent for nonlinear functions, while the regularization is realized by convolution of the vector fields with Gaussian kernels. We validate the proposed method and compare it to the demons algorithm, a well-known 3D-3D registration method. The comparison is done for a range of 4-60 target projections using datasets from low dose tomographic fluoroscopy as an application example. The results show a high correlation to the ground truth target position without introducing artifacts even in the case of very few projections. In particular the matching in the rawdata domain is improved compared to the 3D-3D registration for the investigated range. The proposed volume-to-rawdata registration increases the robustness regarding sparse rawdata and provides more stable results than volume-to-volume approaches. By applying the proposed registration approach to low dose tomographic fluoroscopy it is possible to improve the temporal resolution and thus to increase the robustness of low dose tomographic fluoroscopy.

Purpose: Iterative image reconstruction gains more and more interest in clinical routine, as it promises to reduce image noise (and thereby patient dose), to reduce artifacts, or to improve spatial resolution. Among vendors and researchers, however, there is no consensus of how to best achieve these aims. The general approach is to incorporate a priori knowledge into iterative image reconstruction, for example, by adding additional constraints to the cost function, which penalize variations between neighboring voxels. However, this approach to regularization in general poses a resolution noise trade-off because the stronger the regularization, and thus the noise reduction, the stronger the loss of spatial resolution and thus loss of anatomical detail. The authors propose a method which tries to improve this trade-off. The proposed reconstruction algorithm is called alpha image reconstruction (AIR). One starts with generating basis images, which emphasize certain desired image properties, like high resolution or low noise. The AIR algorithm reconstructs voxel-specific weighting coefficients that are applied to combine the basis images. By combining the desired properties of each basis image, one can generate an image with lower noise and maintained high contrast resolution thus improving the resolution noise trade-off., Methods: All simulations and reconstructions are performed in native fan-beam geometry. A water phantom with resolution bar patterns and low contrast disks is simulated. A filtered backprojection (FBP) reconstruction with a Ram-Lak kernel is used as a reference reconstruction. The results of AIR are compared against the FBP results and against a penalized weighted least squares reconstruction which uses total variation as regularization. The simulations are based on the geometry of the Siemens Somatom Definition Flash scanner. To quantitatively assess image quality, the authors analyze line profiles through resolution patterns to define a contrast factor for contrast-resolution plots. Furthermore, the authors calculate the contrast-to-noise ratio with the low contrast disks and the authors compare the agreement of the reconstructions with the ground truth by calculating the normalized cross-correlation and the root-mean-square deviation. To evaluate the clinical performance of the proposed method, the authors reconstruct patient data acquired with a Somatom Definition Flash dual source CT scanner (Siemens Healthcare, Forchheim, Germany)., Results: The results of the simulation study show that among the compared algorithms AIR achieves the highest resolution and the highest agreement with the ground truth. Compared to the reference FBP reconstruction AIR is able to reduce the relative pixel noise by up to 50% and at the same time achieve a higher resolution by maintaining the edge information from the basis images. These results can be confirmed with the patient data., Conclusions: To evaluate the AIR algorithm simulated and measured patient data of a state-of-the-art clinical CT system were processed. It is shown, that generating CT images through the reconstruction of weighting coefficients has the potential to improve the resolution noise trade-off and thus to improve the dose usage in clinical CT.

Purpose: Phase-correlated microcomputed tomography (micro-CT) imaging plays an important role in the assessment of mouse models of cardiovascular diseases and the determination of functional parameters as the left ventricular volume. As the current gold standard, the phase-correlated Feldkamp reconstruction (PCF), shows poor performance in case of low dose scans, more sophisticated reconstruction algorithms have been proposed to enable low-dose imaging. In this study, the authors focus on the McKinnon-Bates (MKB) algorithm, the low dose phase-correlated (LDPC) reconstruction, and the high-dimensional total variation minimization reconstruction (HDTV) and investigate their potential to accurately determine the left ventricular volume at different dose levels from 50 to 500 mGy. The results were verified in phantom studies of a five-dimensional (5D) mathematical mouse phantom., Methods: Micro-CT data of eight mice, each administered with an x-ray dose of 500 mGy, were acquired, retrospectively gated for cardiac and respiratory motion and reconstructed using PCF, MKB, LDPC, and HDTV. Dose levels down to 50 mGy were simulated by using only a fraction of the projections. Contrast-to-noise ratio (CNR) was evaluated as a measure of image quality. Left ventricular volume was determined using different segmentation algorithms (Otsu, level sets, region growing). Forward projections of the 5D mouse phantom were performed to simulate a micro-CT scan. The simulated data were processed the same way as the real mouse data sets., Results: Compared to the conventional PCF reconstruction, the MKB, LDPC, and HDTV algorithm yield images of increased quality in terms of CNR. While the MKB reconstruction only provides small improvements, a significant increase of the CNR is observed in LDPC and HDTV reconstructions. The phantom studies demonstrate that left ventricular volumes can be determined accurately at 500 mGy. For lower dose levels which were simulated for real mouse data sets, the HDTV algorithm shows the best performance. At 50 mGy, the deviation from the reference obtained at 500 mGy were less than 4%. Also the LDPC algorithm provides reasonable results with deviation less than 10% at 50 mGy while PCF and MKB reconstruction show larger deviations even at higher dose levels., Conclusions: LDPC and HDTV increase CNR and allow for quantitative evaluations even at dose levels as low as 50 mGy. The left ventricular volumes exemplarily illustrate that cardiac parameters can be accurately estimated at lowest dose levels if sophisticated algorithms are used. This allows to reduce dose by a factor of 10 compared to today's gold standard and opens new options for longitudinal studies of the heart.