Posterior regularization method for phase removal of shale nano-structure imaging in space domain

Abstract

X-Ray computed tomography is a non-destructive method that is used, among many applications, to study the size, shape, 3D structures and interconnections of pores in shale. We use phase retrieval methods to deal with the “edge enhancement” effect caused by phase shift. The process of phase retrieval can be described by the transport-of-intensity equation (TIE). But this is an ill-posed problem. The existing methods focus on phase retrieval in the frequency domain. To tackle the ill-posedness, we propose a new method whose main idea is to solve this problem in space domain with a regularization technique. We study a synthetic shale model and simulate the projection data. Then we apply three methods to retrieve the phase: conventional method in frequency domain, direct solving method and iterative Tikhonov regularization method in space domain. Finally, we use the standard filtered back-projection (FBP) method to present the outcome. By analyzing the results, we find advantages of the new method: more stability and fewer artifacts under noise perturbations. The study shows that relative errors of the new method are nearly 1% of that of the traditional method based on frequency domain, and hence the new method is promising for the practical data processing.