Research On The Reconstruction Algorithm Of X-ray Differential Phase-contrast Computed Tomography

For weakly absorbing objects, x-ray phase-contrast-imaging methods use the phase shift rather than the absorption as the imaging signal and offer more details regarding the internal structure. Until now, several x-ray phase-contrast-imaging methods have been proposed, including interferometer, propagation, analyzer-crystal and analyzer-grating methods. The first three methods rely on the spatial coherence or temporal coherence of the x-ray source. However, such x-ray sources are often expensive, which is the main obstacle for the phase-contrast-imaging methods to application. The grating-based methods seem more promising than others in realizing practical phase-contrast imaging systems by using conventional x-ray tube. Unlike other methods, DEI-and grating-based imaging methods measure the gradient of the phase distribution, which is called differential phase-contrast (DPC) imaging technology. The Computed-Tomography using DEI and/or grating-based imaging methods are usually called differential phase-contrast CT (DPC-CT).DPC-CT reconstruction usually requires the refraction angle at each view should be extracted from several raw measurements captured at the identical view, which leads to unacceptably long exposure time and huge X-ray doses. In synchrotron radiation-based DPC-CT experiments, the radiation beams can be well approximated as parallel beams, and the reconstruction problem can be solved by the use of parallel-beam algorithms. In conventional x-ray tube based experiments, the x-ray tube emits spherical wave, the fan or cone-beam algorithms are more suitable. For rod-shaped samples, due to the limitation of the grating size, the fan or cone beams cannot recover the whole object at the same time. Thus, if a rod-shaped sample is required to be reconstructed by above algorithms, one should alternately perform translation and rotation on this sample. Helical cone-beam CT allows the translation and rotation operations to be performed simultaneously, which may be more efficient than other algorithms in the case of rod-shaped samples. However, few researches on helical DPC-CT were reported. In order to solve the fewer data reconstruction and helical DPC-CT problems, we carried out our search along the following three aspects:First, we introduce the Compressed Sensing theory into DPC-CT reconstruction to solve the fewer data reconstruction problem. We compare several classic algorithms such as Orthogonal Matching Pursuit (OMP) algorithm, GPSR algorithm, Proximal-Point algorithm and Bregman Operator Splitting (BOS) algorithm in DPC-CT reconstruction. After that, we introduce the Proximal-Point algorithm and Bregman Operator Splitting (BOS) algorithm into DPC-CT reconstruction and propose two alternating iteration algorithms, ART-PP and ART-BOS algorithm to reconstruct the gradient of refractive index decrement, for sparse angular DPC-CT. The ART-BOS algorithm is also extended to reconstruct the refractive index decrement, whose convergence speed is faster than that of ART-POCS-TV algorithm. The numerical simulation and experiment results show that the proposed algorithm can provide higher quality reconstructions in sparse angular condition.Second, we propose an approximate strategy for helical fan-beam DPC-CT reconstruction by combining the "Forward-Backward projection method" and the helical scanning mode. The main idea of this strategy is approximating the helical fan/cone-beam geometry by single/multiple parallel fan-beams such that the2D sinogram of a given slice can be synthesized from the neighboring fan-beams by interpolation methods. Once the sinogram has been synthesized, the given slice can be reconstructed using any2D reconstruction methods. The main advantage of this algorithm is that only one helical scanning is required. However, as approximate one, this strategy suffers the problem of strict theoretical support.Third, an approximate algorithm and a theoretically exact algorithm for helical cone-beam DPC-CT are proposed, which are both based on the concept of PI-line. The approximate algorithm treats cone-beam as a combination of many oblique fan-beams, and the refractive index decrements are directly reconstructed by modifying fan-beam algorithm. The exact algorithm establishes a general relationship between the derivative data required by Katsevich algorithm and the two-dimension refraction angle data. Thus, the Katsevich algorithm, which is for absorption-based helical cone-beam CT, can be implemented to solve the helical cone-beam DPC-CT reconstruction problem. Due to the theoretical support, the exact algorithm may play a guiding role in the research and application of helical cone-beam DPC-CT.