Tube methods for BV regularization

In this paper tube methods for reconstructing discontinuous data from noisy and blurred observation data are considered. It is shown that discrete bounded variation (BV)-regularization ( commonly used in inverse problems and image processing) and the taut-string algorithm ( commonly used in statistics) select reconstructions in a tube. A version of the taut-string algorithm applicable for higher dimensional data is proposed. This formulation results in a bilateral contact problem which can be solved very efficiently using an active set strategy. As a by-product it is shown that the Lagrange multiplier of the active set strategy is an efficient parameter for edge detection.