  Popular methods for finding regularized solutions to inverse problems include
sparsity promoting $\ell_1$ regularization techniques, one in particular which
is the well known total variation (TV) regularization. More recently, several
higher order (HO) methods similar to TV have been proposed, which we generally
refer to as HOTV methods. In this letter, we investigate problem of the often
debated selection of $\lambda$, the parameter used to carefully balance the
interplay between data fitting and regularization terms. We theoretically argue
for a scaling of the parameter that works for all orders for HOTV methods,
based off of a single selection of the parameter for any one of the orders. We
also provide numerical results which justify our theoretical findings.
