Image reconstruction in cone beam computed tomography using controlled gradient sparsity

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for cone beam computed X-ray tomography (CBCT) has been limited so far, mainly due to heavy computational loads at practically relevant 3D resolutions and the difficulty in choosing the regularization parameter. Here an efficient minimization algorithm is presented, combined with a dynamic parameter adjustment based on control theory. The result is a fully automatic 3D reconstruction method. The input on top of projection data and system geometry is the desired degree of gradient magnitude sparsity of the reconstruction. This can be determined from an atlas of CT scans, or alternatively used as an easily adjustable parameter with straightforward interpretation.