Least-squares optimal prediction, minimum variance control and generalized minimum variance control algorithms for a two-dimensional CARMA process are developed. Each algorithm involves the algebraic solution of a two-dimensional diophantine equation, and may be embedded within ’classical’ two-dimensional systems theory. We show how the algorithms must be modified for any practical implementation to take into account the edges of the data field. In this case we show how we may analyse the process using multivariable theory, and explore the linkages between multivariable representations and two-dimensional systems.