Random processes of considerable importance in signal processing often exhibit short-term stationary statistical attributes although in the long term they appear to behave in a nonstationary manner. Image signals belong to this category. In this work we introduce a class of composite-source models as a means of representing consistently signals of this nature. A composite likelihood function is derived, the subsequent maximisation of which yields estimates of the parameters that are associated with the composite-source model. It is a fact, that maximisation of the composite likelihood function is almost intractable by analytical means. However, by introducing optimisation techniques based on dynamic programming, maximum-likelihood estimation of composite-source models is simplified drastically. A graph-theoretic approach is adopted to demonstrate how the principle of optimality enables efficient algorithms for recursive maximum-likelihood estimation to be developed. Algorithms applied for one-dimensional as well as two-dimensional signals are presented. In both cases it is shown that the estimation problem is equivalent to the problem of identifying the maximumlikelihood path which traverses a directed graph of specific structure. Finally, it is shown that composite source models so estimated can be used in image coding systems which require the least transmission rate for prespecified levels of average distortion of the transmitted image signals.