Title: An Expectation-Maximization Algorithm for the Fractal Inverse Problem,
Abstract: We present an Expectation-Maximization algorithm for the fractal inverse
problem: the problem of fitting a fractal model to data. In our setting the
fractals are Iterated Function Systems (IFS), with similitudes as the family of
transformations. The data is a point cloud in ${\mathbb R}^H$ with arbitrary
dimension $H$. Each IFS defines a probability distribution on ${\mathbb R}^H$,
so that the fractal inverse problem can be cast as a problem of parameter
estimation. We show that the algorithm reconstructs well-known fractals from
data, with the model converging to high precision parameters. We also show the
utility of the model as an approximation for datasources outside the IFS model
class.