TVReg

"TVReg" is a software package for 3D tomography using Total Variation regularization. The work was carried out as part of the project CSI: Computational Science in Imaging, funded by the Danish Research Council for Technology and Production Sciences, and headed by Prof. Per Christian Hansen, DTU Informatics. The collaborators are DTU Informatics, Dept. of Electronic Systems at Aalborg University, and MOSEK ApS. The main algorithm (UPN) is our practical implementation of an optimal first-order method for strongly convex functions, due to Nesterov, tailored to large-scale total variation regularization. Nesterov's algorithm requires knowledge of both the Lipschitz constant and the strong convexity parameter, both of which are usuall unknown, and our implementation incorporates mechanisms to estimate these important parameters during the iterations - thus making the algorithm suited for practical use. The package also includes two other first-order methods: a method by Nesterov, Beck, and Teboulle (UPN_0) for the case of a zero strong convexity parameter, and the Barzilai-Borwein accelerated gradient projedction method (GPBB).