Solving the Inverse Problem Forfunction / Image Approximationusing Iterated Function

In this paper, we provide an algorithm for the construction of IFSM approximations to a target set v 2 L 2 + (X;), where X R D and = m (D) (Lebesgue measure). The algorithm minimizes the squared \collage distance" k v?Tv k 2 2. We work with an innnite set of xed aane IFS maps w i : X ! X satisfying a certain density and nonoverlapping condition. As such, only an optimization over the grey level maps i : R + ! R + is required. If aane maps are assumed, i.e. i = i t+ i , then the algorithm becomes a quadratic programming (QP) problem in the i and i. We can also deene a \local IFSM" (LIFSM) which considers the actions of contractive maps w i on subsets of X to produce smaller subsets. Again, aane i maps are used, resulting in a QP problem. Some approximations of functions on 0,1] and images in 0; 1] 2 are presented.