Sparsity-driven deterministic sampling strategy for coded aperture x-ray computed tomography

Abstract

Abstract The sub-sampling strategies in x-ray computed tomography (CT) have gained importance due to their practical relevance. In this direction of research, also known as coded aperture x-ray computed tomography (CAXCT), both random and deterministic strategies have been proposed in the literature. Of the techniques available, those based on compressive sensing (CS) have recently gained more traction because CS-based ideas efficiently exploit inherent duplication present in the system. The quality of the reconstructed CT images nevertheless depends on the sparse signal recovery properties of the sub-sampled Radon matrices. In the present work, we optimize CAXCT deterministically in such a way that the corresponding sub-sampled Radon matrices remain close to the equiangular tight frames for better numerical behaviour. We show that this optimization, involving the Khatri–Rao product, leads to a non-negative sparse approximation. While comparing and contrasting our method with its existing counterparts, we show that the proposed algorithm is computationally less involved. Finally, we demonstrate efficacy of the proposed deterministic sub-sampling strategy in recovering CT images in both noiseless and noisy cases.