Vector Space Formulation of Two-Dimensional Signal Processing Operations

Abstracts Signal processing operations on two-dimensional fields of data can be cast into a vector space formulation. This formulation often leads to a simplified analysis of two-dimensional processing systems and to the discovery of more efficient computational algorithms. This paper considers the general representation of two-dimensional fields as vectors and discusses common types of operators on these data vectors. Particular emphasis is given to various forms of the superposition operation. Computation of superposition operations using unitary transform techniques is analyzed.