  We give a comprehensive survey on a class of higher order variational
problems which are motivated by applications in mathematical imaging. The
overall aim of this note is to investigate if and in which manner results from
the first author's previous work on variants of the TV-regularization model
(see e.g. [BF1], [BF2], [BF3] and [FT]) can be extended to functionals which
involve higher derivatives. This seems to be not only of theoretical interest,
but also relevant to applications since higher order TV-denoising appears to
maintain the advantages of the classical model as introduced by Rudin, Osher
and Fatemi in [ROF] while avoiding the unpleasant "staircasing" effect (see
e.g. [BKP] or [LLT]). Our paper features results concerning generalized
solutions in spaces of functions of higher order bounded variation, dual
solutions as well as partial regularity of minimizers.
