  We consider a class of quasi-variational inequalities (QVIs) for adaptive
image restoration, where the adaptivity is described via solution-dependent
constraint sets. In previous work we studied both theoretical and numerical
issues. While we were able to show the existence of solutions for a relatively
broad class of problems, we encountered problems concerning uniqueness of the
solution as well as convergence of existing algorithms for solving QVIs. In
particular, it seemed that with increasing image size the growing condition
number of the involved differential operator poses severe problems. In the
present paper we prove uniqueness for a larger class of problems and in
particular independent of the image size. Moreover, we provide a numerical
algorithm with proved convergence. Experimental results support our theoretical
findings.
