Recursive and iterative estimation algorithms for multiresolution stochastic processes

A particular class of processes defined on dyadic trees is treated. Three algorithms are given for optimal estimation/reconstruction for such processes: one reminiscent of the Laplacian pyramid and making efficient use of Haar transforms, a second that is iterative in nature and can be viewed as a multigrid relaxation algorithm, and a third that represents an extension of the Rauch-Tung-Striebel algorithm to processes on dyadic trees. The last involves a discrete Riccati equation, which in this case has three steps: prediction, merging and measurement update. Related work and extensions are briefly discussed