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A current topic of great interest is the multi-resolution analysis of signals and the devel-opment of multi-scale or multigrid algorithms. In this paper we describe part of a research effort aimed at developing a corresponding theory for stochastic processes described at mul-tiple scales and for their efficient estimation or reconstruction given partial and/or noisy measurements which may also be at several scales. The theories of multi-scale signal rep-resentations and wavelet transforms lead naturally to models of signals(in one or several dimensions) on trees and lattices. In this paper we focus on one particular class of processes defined on dyadic trees. The central results of the paper are three algorithms for optimal estimation/reconstruction for such processes: one reminiscent of the Laplacian pyramid and the 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 and involves a new discrete Ric-cati equation, which in this case has three steps: predict, merge, and measurement update