DISCRETE FRACTIONAL FOURIER NUMERICAL ENVIRONMENTS FOR COMPUTER MODELING OF IMAGE PROPAGATION THROUGH A PHYSICAL MEDIUM IN RESTORATION AND OTHER APPLICATIONS

A system for numerically modeling evolution of an image propagating through a medium includes image using image data and a propagation medium model. The propagation medium model aligns a propagation centerline of the propagation medium model relative to the center of the image data. The propagation medium model has a numerical operator for applying an index-shifted numerical fractional Fourier transform operation on the image data, and aligning the zero original-domain origin relative to the center of the image data. The image data has spatially-indexed amplitude values and a center located relative to the spatially-indexed amplitude values. The propagation medium model has quadratic phase properties which are defined relative to a propagation centerline of the propagation medium model. Aligning the zero original-domain origin relative to the center of the image data to produces transformed image data having a zero frequency-domain origin that is centered within the transform-domain indices.