Model and optimal filtering of linearly-additive spatially-invariant continuous-measurement imaging

A spatially-invariant image sequence is a collection of images, each of which is taken from the same object or scene. The variation of the images in the sequence is due to changes in the imaging properties of the image formation processes (or image features), not their spatial movement. In applications involving this class of image sequences, it may be desired to process (filter) the image sequence in a way that some image feature is emphasized while other features are suppressed. An explicit mathematical model for linearly-additive spatially-invariant image sequences as well as the general formulation and derivation for the linear filter has been reported. This paper extends the previous analysis to provide a general description of continuous imaging (measurement) rather than a discrete sequence of distinct images. Also included is the filter derivation for the continuous case in which the filter formulation based on the energy ratio of a desired image feature to an undesired image feature and noise involves the inner product as the definite integral of two functions. This new formulation provides a representation of spatially-invariant imaging and the corresponding linear filtering method for continuous imaging (measurement) situations.