Sparse Regularized CT Reconstruction: An Optimization Perspective

In Computed Tomography (CT), decreasing the X-rays dose is essential to reduce the negative effects of radiation exposure on the human health. One possible way to accomplish it is to reduce the number of projections acquired, hence the name of sparse CT. Traditional methods for image reconstruction cannot recover reliable images in this case: the lack of information due to the missed projections produces strong artifacts. Alternatively, optimization frameworks are flexible models where incorporated regularization functions impose regularity constraints on the solution, thus avoiding unwanted artifacts and contrasting noise propagation. Since the iterative methods solving the optimization problem calculate more accurate solutions as iterations (and computational time) increase, it is possible to choose a better reconstructed image at the expense of execution time, or viceversa. Parallel implementations of the iterative solvers significantly reduce the computational time, allowing for a large number of iterations in a prefixed short time. Here, the effectiveness of the optimization approach is shown on the case study of 3D reconstruction of breast images from tomosynthesis with tests on real projection data.