The authors define linearly additive spatially invariant image sequences and present an explicit mathematical model for describing them. 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. 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. Objects with different spectral characteristics will have different image sequence signatures which can be used to distinguish them. Also presented are the general formulation, derivation, and explicit expression for the linear filter, called the simultaneous diagonalization (SD) 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.