A Continuous-Domain Solution for Computed Tomography with Hessian Total-Variation Regularization

We formulate computed-tomography reconstruction as a continuous-domain optimization problem with Hessian total variation (HTV) as the regularizer. HTV is a sparsity-promoting regularizer that favors continuous and piecewise-linear functions with few affine pieces. We develop a computational scheme that yields a solution with arbitrary precision. We model the unknown signal using a box-spline basis. Our contributions involve exact formulas for the x-ray transform, HTV, and the refinement of the proposed model. We adopt a multiresolution optimization scheme that solves the continuous-domain problem. We validate our framework with numerical experiments.