Volterra-type nonlinear image restoration of medical imagery using principal dynamic modes

This paper introduces a new methodology of medical image restoration using the nonlinear Volterra system identification method, which rests on the theory of functional expansions of nonlinear dynamic operators. The task is achieved by identifying inverse linear and nonlinear transformations or kernels from a training medical image data set. The kernels are further represented by their principal dynamic modes (PDMs) and following static nonlinearities. We validate the methods through computer simulation studies where the restoration operators identified from a training MR image set are applied to test MR image sets.