Gradient-based sparse approximation for computed tomography

Limited-data Computed Tomography (CT) presents challenges for image reconstruction algorithms and has been an active topic of research aiming at reducing the exposure to X-ray radiation. We present a novel formulation for tomo-graphic reconstruction based on sparse approximation of the image gradients from projection data. Our approach leverages the interdependence of the partial derivatives to impose an additional curl-free constraint on the optimization problem. The image is then reconstructed using a Poisson solver. The experimental results show that, compared to total variation methods, our new formulation improves the accuracy of reconstruction significantly in few-view settings.