State variable representation of a class of linear shift-variant systems

Certain types of linear shift-variant systems are rendered shift-invariant by appropriate coordinate transformations (changes of variable). Examples occur in aerial photography, restoration of images degraded by coma, and reconstruction of two-dimensional functions from line integrals. The matrices in the continuous state variable representations of such systems may be written as constant matrices multiplied by scalar functions of the independent variables; while the discretized models do not appear to share this feature, one system discussed in this paper does have a simple discrete-time structure. Given a shift-variant impulse response and the corresponding coordinate transformations, it is shown how to construct a state variable representation. Experimental results from an application to image processing are presented.