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摘要
X-Ray propagation-based computerized tomography (CT) is a non-destructive and useful method to study the size, shape, 3D pore structures and interconnections of pores in shale. However, it remains a challenging task to adequately calculate the location and size of pores. Synchrotron radiation makes it possible to realize reconstruction of the shale structure on multiple scales. Conventionally, computerized tomography relies on the absorption contrast of the sample. This process can be formulated in Radon transform. When we only consider absorption contrast, we may face a phenomenon of the "edge enhancement" effect. It is caused by the effect of phase shift and we need to correct it with phase retrieval. Under the assumption of phase-attenuation duality, the process of phase retrieval can be described in the transport-of-intensity equation (TIE). But this is an ill-posed inverse problem essentially. The existing methods usually focus on how to deal with phase retrieval by filtration in the frequency domain. The method we propose in this paper is a novel approach, trying to solve this problem in the space domain. @@@ First, we study a model with the size of 512 X 512 pixels based on real shale. We give each pixel of the model a numerical linear absorption index. Second, we execute the process of Radon transform and make the deviation caused by phase to simulate the actual projection data. Then we use three methods to retrieval the phase: the filter method in the frequency domain, direct method in the space domain, and iterative Tikhonov regularization method in the space domain. After we finish the process of phase retrieval, we use the standard filtered back-projection (FBP) method to present the outcome. By analyzing the results from different methods, the effects of different methods can be shown. @@@ Numerical simulations demonstrate that the results calculated by the method proposed in this paper are stable and with less artifacts. In the case of noiseless data, the direct method and the iterative Tikhonov regularization method perform much better than the filter method in the frequency domain. It is obvious that there exist artifacts around the pixels with larger index calculated by the frequency-domain method. When we add 1% Gaussian noise, the direct method performs bad because of the ill-posed property of the linear system. The iterative Tikhonov regularization method and the frequency-domain method can eliminate the noise disturbance. However, we still find the artifact around the pixels with larger index from the detail of the results calculated by the frequency-domain method. And this phenomenon does not exist in our new method. @@@ Our proposed iterative Tikhonov regularization method can tackle the "edge enhancement" effect. With appropriate choice of the regularization parameter, we can get more stable and accurate results under the interference of different level of noise. Numerical results show that the residual of the new method is nearly 1% of the traditional method in the frequency domain, and hence the new method is promising for processing of real data.
- 出版日期2017-5
- 单位中国科学院地质与地球物理研究所; 中国科学院大学; 中国科学院地质与地球物理研究所兰州油气资源研究中心
