Learning Splines for Sparse Tomographic Reconstruction

In a few-view or limited-angle computed tomography (CT), where the number of measurements is far fewer than image unknowns, the reconstruction task is an ill-posed problem. We present a spline-based sparse tomographic reconstruction algorithm where content-adaptive patch sparsity is integrated into the reconstruction process. The proposed method leverages closed-form Radon transforms of tensor-product B-splines and non-separable box splines to improve the accuracy of reconstruction afforded by higher order methods. The experiments show that enforcing patch-based sparsity, in terms of a learned dictionary, on higher order spline representations, outperforms existing methods that utilize pixelbasis for image representation as well as those employing wavelets as sparsifying transform.