Edge illumination is a phase sensitive X-ray imaging technique, compatible with lab-based X-ray sources. Phase information can be retrieved by displacing two masks relative to each other with the object positioned in between. Phase retrieval then allows the three contrasts, absorption, refraction and dark field, to be individually reconstructed with FBP. In this work, a novel joint reconstruction method is proposed using a combined forward model, allowing the three contrasts to be reconstructed simultaneously, without a retrieval step. This allows for more freedom in the acquisition scheme. The proposed objective function is minimized using a split Barzilai-Borwein gradient method. Improved convergence speed and reconstruction quality on an experimental dataset, compared to existing methods, is shown.
KEYWORDS: Ray tracing, Sensors, Projection systems, X-rays, Computer simulations, Monte Carlo methods, X-ray imaging, Signal attenuation, Refraction, 3D modeling
X-ray based inspection often relies on triangular meshes, for example to inspect objects that were manufactured from CAD models. In this work, we present three complementary implementations of X-ray mesh projectors, obtained by adapting state-of-the-art rendering techniques to the simulation of X-ray imaging. The first technique is rasterization, where the interaction of each triangle with the X-ray beam is simulated in parallel using the NVIDIA CUDA toolkit. The second approach is ray tracing, where the interaction of each ray with the mesh is simulated in parallel using the NVIDIA OptiX framework. Both recursive and non-recursive versions of ray tracing are described. The simulated XCT setup is described in terms of a cone beam projection geometry that is compatible with the corresponding geometry in the ASTRA toolbox. All three projectors were benchmarked on a series of tests with varying resolution of both the mesh and the detector. The rasterizer exhibited the best computation time in most benchmark scenarios, coupled with the best scalability w.r.t. both the mesh size and the detector size. However, the recursive ray tracing approach offers more capabilities towards implementing additional optical effects such as refraction.
This work presents an efficient technique for simultaneously reconstructing an image of a moving object from X-ray projections along with estimating the motion parameters. Current state-of-the-art iterative methods rely on objective functions that contain the solution of an iterative procedure as one of its terms. This complicates the reconstruction process as it leads to nested iterations and makes analytic differentiation impractical. The presented technique relies on an objective function that simultaneously depends on the image and the motion parameters. The derivatives of this objective function towards the image and the motion parameters are known exactly and implemented matrix free and in parallel. Moreover, the stepsizes of both the iterative reconstruction and motion parameter estimation schemes are chosen following a mathematical formulation that guarantees a fast convergence speed. The result is a method that not only needs less iterations, but also removes the need to tune the finite differences stepsize and the number of inner iterations, which allows for efficient, scalable reconstruction using modern optimizers, without nested iterations.
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