A Deep Learning Reconstruction Framework for Differential Phase-Contrast Computed Tomography with Incomplete Data

Differential phase-contrast computed tomography (DPC-CT) is a powerful analysis tool for soft-tissue and low-atomic-number samples. Limited by the implementation conditions, DPC-CT with incomplete projections happens quite often. Conventional reconstruction algorithms are not easy to deal with incomplete data. They are usually involved with complicated parameter selection operations, also sensitive to noise and time-consuming. In this paper, we reported a new deep learning reconstruction framework for incomplete data DPC-CT. It is the tight coupling of the deep learning neural network and DPC-CT reconstruction algorithm in the phase-contrast projection sinogram domain. The estimated result is the complete phase-contrast projection sinogram not the artifacts caused by the incomplete data. After training, this framework is determined and can reconstruct the final DPC-CT images for a given incomplete phase-contrast projection sinogram. Taking the sparse-view DPC-CT as an example, this framework has been validated and demonstrated with synthetic and experimental data sets. Embedded with DPC-CT reconstruction, this framework naturally encapsulates the physical imaging model of DPC-CT systems and is easy to be extended to deal with other challengs. This work is helpful to push the application of the state-of-the-art deep learning theory in the field of DPC-CT

Automatic alignment for three-dimensional tomographic reconstruction

In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to reconstruct the object. Given noisy and incomplete measurements, the inverse problem is typically solved through a regularized least-squares approach. A challenge for both approaches is that in practice the exact directions and offsets of the x-rays are only known approximately due to, e.g. calibration errors. Such errors lead to artifacts in the reconstructed image. In the case of sufficient sampling and geometrically simple misalignment, the measurements can be corrected by exploiting so-called consistency conditions. In other cases, such conditions may not apply and we have to solve an additional inverse problem to retrieve the angles and shifts. In this paper we propose a general algorithmic framework for retrieving these parameters in conjunction with an algebraic reconstruction technique. The proposed approach is illustrated by numerical examples for both simulated data and an electron tomography dataset