Images are fast becoming a mainstream source of data in many fields from medicine to ecology. The analysis of image data poses special problems due to large sample sizes, highly correlated structures and structured sparseness. This presentation focuses on the motivating problem of analysing high dimensional multivariate time series from remotely sensed (satellite) data as part of a landscape monitoring project with the Qld Department of Natural Resources. Bayesian multivariate linear Gaussian state space models and spatial dynamic factor models are developed that allow description of trends in vegetation, extraction of landtype information and identification of associated common factors. Efficient simulation algorithms based on Markov chain Monte Carlo (MCMC) are proposed, including capitalisation on the univariate representation of the state space model to make substantial gains in computational efficiency, and employment of Krylov subspace models to take advantage of inherent sparse matrix structures. The merger of expertise in statistical modelling and computational mathematics has resulted in a viable practical approach to answering important applied questions based on this type of data.