  In this paper we introduce and study fused lasso nearly-isotonic signal
approximation, which is a combination of fused lasso and generalized
nearly-isotonic regression. We show how these three estimators relate to each
other, derive solution to the general problem, show that it is computationally
feasible and provides a trade-off between piecewise monotonicity, sparsity and
goodness-of-fit. Also, we derive an unbiased estimator of the degrees of
freedom of the approximator.
