Patent ID: 7039252
Filing Date: 2006-05-02
Classification: G02B,G06T

Abstract:
1. A method for approximating the evolution of images propagating through a physical medium by calculating a fractional power of a numerical operator, said numerical operator being defined by said physical medium and comprising a diagonalizable numerical linear operator raised to a power (α), said method comprising: (a) representing a plurality of images using an individual data array for each of said plurality of images; (b) representing said numerical operator with a linear operator formed by multiplying an ordered similarity transformation operator (P) by a correspondingly-ordered diagonal operator (Λ), the result of which is multiplied by an approximate inverse (P (c) raising diagonal elements of said correspondingly-ordered diagonal operator (Λ) to said power (α) to produce a fractional power diagonal operator; (d) multiplying said fractional power diagonal operator by an approximate inverse of said ordered similarity transformation operator (P (e) multiplying a data array of one of said plurality of images by said ordered similarity transformation operator (P) to produce a modified data array; (f) multiplying said modified data array by said first partial result to produce said fractional power of said numerical operator; and (g) repeating operations (e) and (f) for each of said plurality of images.