Superimposed Wavefront Imaging of Diffraction-enhanced X-rays: sparsity-aware CT reconstruction from limited-view projections

Purpose: In this paper, we describe an algebraic reconstruction algorithm with a total variation regularization (ART + TV) based on the Superimposed Wavefront Imaging of Diffraction-enhanced X-rays (SWIDeX) method to effectively reduce the number of projections required for differential phase-contrast CT reconstruction.

Methods: SWIDeX is a technique that uses a Laue-case Si analyzer with closely spaced scintillator to generate second derivative phase-contrast images with high contrast of a subject. When the projections obtained by this technique are reconstructed, a Laplacian phase-contrast tomographic image with higher sparsity than the original physical distribution of the subject can be obtained. In the proposed method, the Laplacian image is first obtained by applying ART + TV, which is expected to reduce the projection with higher sparsity, to the projection obtained from SWIDeX with a limited number of views. Then, by solving Poisson's equation for the Laplacian image, a tomographic image representing the refractive index distribution is obtained.

Results: Simulations and actual X-ray experiments were conducted to demonstrate the effectiveness of the proposed method in projection reduction. In the simulation, image quality was maintained even when the number of projections was reduced to about 1/10 of the originally required views, and in the actual experiment, biological tissue structure was maintained even when the number of projections was reduced to about 1/30.

Conclusion: SWIDeX can visualize the internal structures of biological tissues with very high contrast, and the proposed method will be useful for CT reconstruction from large projection data with a wide field of view and high spatial resolution.