Explicit mathematical results for the representation and filtering of spatially-invariant image sequences

Linearly additive spatially invariant image sequences are defined, and an explicit mathematical model for describing them is presented. In such a sequence, all objects are positionally invariant in each image of the sequence but have varying gray-scale contributions to the successive images of the sequence. Three important types of spatially invariant image sequences are functional, parametric, and multispectral. The various components (features or processes) of the scene or object contribute additively to each image of the sequence, but each component has a characteristic variation (signature) from image to image due to the variation of the function, parameter, or spectral band over the sequence. Also presented are the general formulation, derivation, and explicit expression for the linear filter, called the simultaneous-diagonalization filter, that calculates a single new image from the sequence such that a desired process is emphasized and any number of undesired processes is suppressed in the filtered image.<>