Scalable Double Regularization for 3D Nano-CT Reconstruction
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Nano-CT (computerized tomography) has emerged as a non-destructive high-resolution cross-sectional imaging technique to effectively study the sub-μm pore structure of shale, which is of fundamental importance to the evaluation and development of shale oil and gas. Nano-CT poses unique challenges to the inverse problem of reconstructing the 3D structure due to the lower signal-to-noise ratio (than Micro-CT) at the nano-scale, increasing sensitive to the misaligned geometry caused by the movement of object manipulator, limited sample size, and a larger volume of data at higher resolution. In this paper, we propose a scalable double regularization (SDR) method to utilize the entire dataset for simultaneous 3D structural reconstruction across slices through total variation regularization within slices and L_1 regularization between adjacent slices. SDR allows information borrowing both within and between slices, contrasting with the traditional methods that usually build on slice by slice reconstruction. We develop a scalable and memory-efficient algorithm by exploiting the systematic sparsity and consistent geometry induced by such Nano-CT data. We illustrate the proposed method by simulation and a real data application using shale rocks acquired in the Sichuan Basin.
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