  This work is concerned with linear inverse problems where a distributed
parameter is known a priori to only take on values from a given discrete set.
This property can be promoted in Tikhonov regularization with the aid of a
suitable convex but nondifferentiable regularization term. This allows applying
standard approaches to show well-posedness and convergence rates in Bregman
distance. Using the specific properties of the regularization term, it can be
shown that convergence (albeit without rates) actually holds pointwise.
Furthermore, the resulting Tikhonov functional can be minimized efficiently
using a semi-smooth Newton method. Numerical examples illustrate the properties
of the regularization term and the numerical solution.
