The generalized lasso is reducible to a subspace constrained lasso

We investigate connections between the generalized lasso and the standard lasso problem. We show by an efficient direct construction, that the generalized lasso problem is reducible to a subspace constrained lasso. We then derive the dual of the subspace constrained lasso. This dual problem can be projected to the dual of a standard lasso problem with a modified dictionary. Finally, we discuss the application of these ideas to image approximation using the 2D fused lasso.