Purpose: X-ray scattering leads to CT images with a reduced contrast, inaccurate CT values as well as streak and cupping artifacts. Therefore, scatter correction is crucial to maintain the diagnostic value of CT and CBCT examinations. However, existing approaches are not able to combine both high accuracy and high computational performance. Therefore, we propose the deep scatter estimation (DSE): a deep convolutional neural network to derive highly accurate scatter estimates in real time. Methods: Gold standard scatter estimation approaches rely on dedicated Monte Carlo (MC) photon transport codes. However, being computationally expensive, MC methods cannot be used routinely. To enable real-time scatter correction with similar accuracy, DSE uses a deep convolutional neural network that is trained to predict MC scatter estimates based on the acquired projection data. Here, the potential of DSE is demonstrated using simulations of CBCT head, thorax, and abdomen scans as well as measurements at an experimental table-top CBCT. Two conventional computationally efficient scatter estimation approaches were implemented as reference: a kernel-based scatter estimation (KSE) and the hybrid scatter estimation (HSE). Results: The simulation study demonstrates that DSE generalizes well to varying tube voltages, varying noise levels as well as varying anatomical regions as long as they are appropriately represented within the training data. In any case the deviation of the scatter estimates from the ground truth MC scatter distribution is less than 1.8% while it is between 6.2% and 293.3% for HSE and between 11.2% and 20.5% for KSE. To evaluate the performance for real data, measurements of an anthropomorphic head phantom were performed. Errors were quantified by a comparison to a slit scan reconstruction. Here, the deviation is 278 HU (no correction), 123 HU (KSE), 65 HU (HSE), and 6 HU (DSE), respectively. Conclusions: The DSE clearly outperforms conventional scatter estimation approaches in terms of accuracy. DSE is nearly as accurate as Monte Carlo simulations but is superior in terms of speed (%10 ms/projection) by orders of magnitude.

X-ray scatter is a major cause of image quality degradation in dimensional CT. Especially, in case of highly attenuating components scatter-to-primary ratios may easily be higher than 1. The corresponding artifacts which appear as cupping or dark streaks in the CT reconstruction may impair a metrological assessment. Therefore, an appropriate scatter correction is crucial. Thereby, the gold standard is to predict the scatter distribution using a Monte Carlo (MC) code and subtract the corresponding scatter estimate from the measured raw data. MC, however, is too slow to be used routinely. To correct for scatter in real-time, we developed the deep scatter estimation (DSE). It uses a deep convolutional neural network which is trained to reproduce the output of MC simulations using only the acquired projection data as input. Once trained, DSE can be applied in real-time. The present study demonstrates the potential of the proposed approach using simulations and measurements. In both cases the DSE yields highly accurate scatter estimates that differ by < 3% from our MC scatter predictions. Further, DSE clearly outperforms kernel-based scatter estimation techniques and hybrid approaches, as they are in use today.

Temporal-correlated image reconstruction, also known as 4D CT image reconstruction, is a big challenge in computed tomography. The reasons for incorporating the temporal domain into the reconstruction are motions of the scanned object, which would otherwise lead to motion artifacts. The standard method for 4D CT image reconstruction is extracting single motion phases and reconstructing them separately. These reconstructions can suffer from undersampling artifacts due to the low number of used projections in each phase. There are different iterative methods which try to incorporate some a priori knowledge to compensate for these artifacts. In this paper we want to follow this strategy. The cost function we use is a higher dimensional cost function which accounts for the sparseness of the measured signal in the spatial and temporal directions. This leads to the definition of a higher dimensional total variation. The method is validated using in vivo cardiac micro-CT mouse data. Additionally, we compare the results to phase-correlated reconstructions using the FDK algorithm and a total variation constrained reconstruction, where the total variation term is only defined in the spatial domain. The reconstructed datasets show strong improvements in terms of artifact reduction and low-contrast resolution compared to other methods. Thereby the temporal resolution of the reconstructed signal is not affected.

Tomographic image reconstruction, such as the reconstruction of computed tomography projection values, of tomosynthesis data, positron emission tomography or SPECT events, and of magnetic resonance imaging data is computationally very demanding. One of the most time-consuming steps is the backprojection. Recently, a novel general purpose architecture optimized for distributed computing became available: the cell broadband engine (CBE). To maximize image reconstruction speed we modified our parallel-beam backprojection algorithm [two dimensional (2D)] and our perspective backprojection algorithm [three dimensional (3D), cone beam for flat-panel detectors] and optimized the code for the CBE. The algorithms are pixel or voxel driven, run with floating point accuracy and use linear (LI) or nearest neighbor (NN) interpolation between detector elements. For the parallel-beam case, 512 projections per half rotation, 1024 detector channels, and an image of size 512(2) was used. The cone-beam backprojection performance was assessed by backprojecting a full circle scan of 512 projections of size 1024(2) into a volume of size 512(3) voxels. The field of view was chosen to completely lie within the field of measurement and the pixel or voxel size was set to correspond to the detector element size projected to the center of rotation divided by square root of 2. Both the PC and the CBE were clocked at 3 GHz. For the parallel backprojection of 512 projections into a 512(2) image, a throughput of 11 fps (LI) and 15 fps (NN) was measured on the PC, whereas the CBE achieved 126 fps (LI) and 165 fps (NN), respectively. The cone-beam backprojection of 512 projections into the 512(3) volume took 3.2 min on the PC and is as fast as 13.6 s on the cell. Thereby, the cell greatly outperforms today's top-notch backprojections based on graphical processing units. Using both CBEs of our dual cell-based blade (Mercury Computer Systems) allows to 2D backproject 330 images/s and one can complete the 3D cone-beam backprojection in 6.8 s.

We have developed a new approximate Feldkamp-type algorithm that we call the extended parallel backprojection (EPBP). Its main features are a phase-weighted backprojection and a voxel-by-voxel 180 degrees normalization. The first feature ensures three-dimensional (3-D) and 4-D capabilities with one and the same algorithm; the second ensures 100% detector usage (each ray is accounted for). The algorithm was evaluated using simulated data of a thorax phantom and a cardiac motion phantom for scanners with up to 256 slices. Axial (circle and sequence) and spiral scan trajectories were investigated. The standard reconstructions (EPBPStd) are of high quality, even for as many as 256 slices. The cardiac reconstructions (EPBPCI) are of high quality as well and show no significant deterioration of objects even far off the center of rotation. Since EPBPCI uses the cardio interpolation (CI) phase weighting the temporal resolution is equivalent to that of the well-established single-slice and multislice cardiac approaches 180 degrees CI, 180 degrees MCI, and ASSRCI, respectively, and lies in the order of 50 to 100 ms for rotation times between 0.4 and 0.5 s. EPBP appears to fulfill all required demands. Especially the phase-correlated EPBP reconstruction of cardiac multiple circle scan data is of high interest, e.g., for dynamic perfusion studies of the heart.

Purpose: Scattered radiation is one of the major problems facing image quality in flat detector conebeam computed tomography (CBCT). Previously, a new scatter estimation and correction method using primary beam modulation has been proposed. The original image processing technique used a frequency-domain-based analysis, which proved to be sensitive to the accuracy of the modulator pattern both spatially and in amplitude as well as to the frequency of the modulation pattern. In addition, it cannot account for penumbra effects that occur, for example, due to the finite focal spot size and the scatter estimate can be degraded by high-frequency components of the primary image. Methods: In this paper, the authors present a new way to estimate the scatter using primary modulation. It is less sensitive to modulator nonidealities and most importantly can handle arbitrary modulator shapes and changes in modulator attenuation. The main idea is that the scatter estimation can be expressed as an optimization problem, which yields a separation of the scatter and the primary image. The method is evaluated using simulated and experimental CBCT data. The scattering properties of the modulator itself are analyzed using a Monte Carlo simulation.

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In the beginning of 2004 medical spiral-CT scanners that acquire up to 64 slices simultaneously became available. Most manufacturers use a straightforward acquisition principle, namely an x-ray focus rotating on a circular path and an opposing cylindrical detector whose rotational center coincides with the x-ray focus. The 64-slice scanner available to us, a Somatom Sensation 64 spiral cone-beam CT scanner (Siemens, Medical Solutions, Forchheim, Germany), makes use of a flying focal spot (FFS) that allows for view-by-view deflections of the focal spot in the rotation direction ( FFS) and in the -direction ( FFS) with the goal of reducing aliasing artifacts. The FFS feature doubles the sampling density in the radial direction (channel direction, FFS) and in the longitudinal direction (detector row direction or -direction, FFS). The cost of increased radial and azimuthal sampling is a two-or four-fold reduction of azimuthal sampling (angular sampling). To compensate for the potential reduction of azimuthal sampling the scanner simply increases the number of detector read-outs (readings) per rotation by a factor two or four. Then, up to four detector readings contribute to what we define as one view or one projection. A significant reduction of in-plane aliasing and of aliasing in the -direction can be expected. Especially the latter is of importance to spiral CT scans where aliasing is known to produce so-called windmill artifacts. We have derived and analyzed the optimal focal spot deflection values and as they would ideally occur in our scanner. Based upon these we show how image reconstruction can be performed in general. A simulation study showing reconstructions of mathematical phantoms further provides evidence that image quality can be significantly improved with the FFS. Aliasing artifacts, that manifest as streaks emerging from high-contrast objects, and windmill artifacts are reduced by almost an order of magnitude with the FFS compared to a simulation without FFS. Patient images acquired with our 64-slice cone-beam CT scanner support these results.