This book considers methods for the optimal processing of random fields. In particular, it studies spatio-temporal filtering problems such as the problem of optimal signal detection (Bayes' approach) and estimating angles of arrival of local signals. The exposition of the problem of optimal filtering is presented with the help of insights from probability theory, functional analysis and mathematical physics. An algorithmic form of the net results facilitates computer-aided applications. <br/> <em>Audience:</em> This volume will be of interest to experts in the design of signal processing and theorists in functional analysis, probability theory, functional analysis and mathematical physics.