Priority-based Mojette reconstruction from sparse noisy projections

Sparse-view Computed Tomography (CT) plays an important role in industrial inspection and medical diagnosis. However, the established reconstruction equations based on traditional Radon transform are ill-posed and obtain an approximate solution in the case of finite sampling angles. By contrast, Mojette transform is considered as the discrete geometry of the projection and reconstruction lattice. It determines the geometrical conditions for ensuring a unique solution instead of solving an ill-posed problem from the start. Therefore, Mojette transform results in theoretical exact image reconstruction in the discrete domain, and approximately gets the minimum number of projections, as well as their directions. However, the reconstruction method utilizing Mojette transform is very sensitive to noise. To address the problem, the paper proposes a sparse-view Mojette inversion algorithm based on the minimum noise accumulation by selecting the prioritized projections for an image reconstruction. Experimental results show that the proposed method can effectively suppress the noise accumulation without increasing the number of projections and produce better reconstruction results than traditional corner-based Mojette inversion (CBI).