We proposed an algorithm for alignment of neighbouring physical slices with ruptures in microscopy, based on iterative minimization of the problem dual to the L1-TV functional using the method of subgradients.

Michálek, J. - Čapek, M.: A piecewise monotone subgradient algorithm for accurate L1 -TV based registration of physical slices with discontinuities in microscopy. IEEE Transactions on Medical Imaging (2013)