Lattice partition recovery with dyadic CART Oscar Hernan Madrid Padilla

We study piece-wise constant signals corrupted by additive Gaussian noise over a d-dimensional lattice. Data of this form naturally arise in a host of applications, and the tasks of signal detection or testing, de-noising and estimation have been studied extensively in the statistical and signal processing literature. In this paper we consider instead the problem of partition recovery, i.e. of estimating the partition of the lattice induced by the constancy regions of the unknown signal, using the computationally-efficient dyadic classification and regression tree (DCART) methodology proposed by [14].