Signal restoration with controlled piecewise monotonicity constraint

A signal restoration problem can be formulated as a least-squares inversion subject to a constraint that the signal has no more than k piecewise monotonic segments. We refer to the associated constraint as controlled piecewise monotonicity or CPM. We show that this constraint alone is powerful enough to stabilize an ill-posed inversion and enables us to incorporate knowledge about the waveform geometry of the signal. This leads to a new algorithm for constrained signal restoration. We describe a highly efficient iterative scheme for computing the CPM constrained least-squares restoration. We also present experimental results and discuss issues related to the new algorithm