Sparsity driven deterministic sampling strategy for coded aperture X-ray Computed Tomography
The subsampling strategies in X-ray Computed Tomography (CT) 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 were proposed in the literature. Of the techniques available, the ones based on Compressive Sensing (CS) recently gained more traction as 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 (SRPs) of the sub-sampled Radon matrices. In the present work, we determine CAXCT deterministically in such a way that the corresponding sub-sampled Radon matrices remain close to the incoherent unit norm tight frames (IUNTFs) for better numerical behaviour. We show that this optimization, via Khatri-Rao product, leads to 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 both in noiseless and noisy cases.