SOLVING THE INVERSE PROBLEM FOR FUNCTION/IMAGE APPROXIMATION USING ITERATED FUNCTION SYSTEMS I: THEORETICAL BASIS

Abstract

We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over ℒ p (X, µ): An N-map IFS with grey level maps (IFSM), to be denoted as (w, Φ), is a set w of N contraction maps w i : X → X over a compact metric space (X, d) (the "base space") with an associated set Φ of maps ϕ i : R → R. Associated with each IFSM is a contractive operator T with fixed point [Formula: see text]. We provide a rigorous solution to the following inverse problem: Given a target υ ∈ ℒ p (X, µ) and an ∊ > 0, find an IFSM whose attractor satisfies [Formula: see text].