Talbot-Lau X-ray phase-contrast imaging is a novel imaging modality, which provides not only an X-ray absorption image, but also additionally a differential phase image and a dark-field image. The dark-field image is related to small angle scattering and has an interesting property when canning oriented structures: the recorded signal depends on the relative orientation of the structure in the imaging system. Exactly this property allows to draw conclusions about the orientation and to reconstruct the structure. However, the reconstruction is a complex, non-trivial challenge. A lot of research was conducted towards this goal in the last years and several reconstruction algorithms were proposed. A key step of the reconstruction algorithm is the inversion of a forward projection model. Up until now, only 2-D projection models are available, with effectively limit the scanning trajectory to a 2-D plane. To obtain true 3-D information, this limitation requires to combine several 2-D scans, which leads to quite complex, impractical acquisitions schemes. Furthermore, it is not possible with these models to use 3-D trajectories that might allow simpler protocols, like for example a helical trajectory. To address these limitations, we propose in this work a very general 3-D projection model. Our projection model defines the dark-field signal dependent on an arbitrarily chosen ray and sensitivity direction. We derive the projection model under the assumption that the observed scatter distribution has a Gaussian shape. We theoretically show the consistency of our model with more constrained existing 2-D models. Furthermore, we experimentally show the compatibility of our model with dark-field measurements of two matchsticks. We believe that this 3-D projection model is an important step towards more flexible trajectories and imaging protocols that are much better applicable in practice.
This orientation-dependency of the dark-field signal introduces a notable difference to traditional X-ray computed tomography. The well-known filtered backprojection (FBP) algorithm is able to reconstruct the signal in a voxel by solving a linear system of equations. However, the use of FBP requires that the signal from a voxel is constant, and thus independent from the viewing direction. To this end, Schaff al @cite_1 proposed to align the grating bars parallel to a 2-D trajectory. In this case, the sensitivity direction is perpendicular to the imaged plane, and the signal in each voxel is constant.
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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 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 . X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse-view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets , the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U-Net variants such as dual frame and tight frame U-Nets satisfy the so-called frame condition which makes them better for effective recovery of high frequency edges in sparse-view CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance. High radiation dose in computed tomography (CT) scans increases the lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with total variation (TV) regularization have been developed to reconstruct CT images from highly undersampled data acquired at low mAs levels in order to reduce the imaging dose. Nonetheless, the low-contrast structures tend to be smoothed out by the TV regularization, posing a great challenge for the TV method. To solve this problem, in this work we develop an iterative CT reconstruction algorithm with edge-preserving TV (EPTV) regularization to reconstruct CT images from highly undersampled data obtained at low mAs levels. The CT image is reconstructed by minimizing energy consisting of an EPTV norm and a data fidelity term posed by the x-ray projections. The EPTV term is proposed to preferentially perform smoothing only on the non-edge part of the image in order to better preserve the edges, which is realized by introducing a penalty weight to the original TV norm. During the reconstruction process, the pixels at the edges would be gradually identified and given low penalty weight. Our iterative algorithm is implemented on graphics processing unit to improve its speed. We test our reconstruction algorithm on a digital NURBS-based cardiac-troso phantom, a physical chest phantom and a Catphan phantom. Reconstruction results from a conventional filtered backprojection (FBP) algorithm and a TV regularization method without edge-preserving penalty are also presented for comparison purposes. The experimental results illustrate that both the TV-based algorithm and our EPTV algorithm outperform the conventional FBP algorithm in suppressing the streaking artifacts and image noise under a low-dose context. Our edge-preserving algorithm is superior to the TV-based algorithm in that it can preserve more information of low-contrast structures and therefore maintain acceptable spatial resolution. Dark-field imaging is a scattering-based X-ray imaging method that can be performed with laboratory X-ray tubes. The possibility to obtain information about unresolvable structures has already seen a lot of interest for both medical and material science applications. Unlike conventional X-ray attenuation, orientation dependent changes of the dark-field signal can be used to reveal microscopic structural orientation. To date, reconstruction of the three-dimensional dark-field signal requires dedicated, highly complex algorithms and specialized acquisition hardware. This severely hinders the possible application of orientation-dependent dark-field tomography. In this paper, we show that it is possible to perform this kind of dark-field tomography with common Talbot-Lau interferometer setups by reducing the reconstruction to several smaller independent problems. This allows for the reconstruction to be performed with commercially available software and our findings will therefore help pave the way for a straightforward implementation of orientation-dependent dark-field tomography.