An EM Estimation Algorithm of Iterated Random Function System Parameters from Noisy Observations

In this paper, a new solution to the inverse problem of iterated random function systems is presented. The solution is based on a generalized hidden Markov model formalism to model the process generated by an iterated random function system. Instead of the assumption of conditional independence of observation sequence elements given the state sequence, the new model assumes the existence of short term dependency between successive observations. An expectationmaximization (EM) algorithm is derived to estimate the parameters of the transformations used in the generation of the process. Regeneration of the process is possible given the model parameters and the initial observation by using the Veterbi algorithm. This suggests the use of the model in signal compression, encoding and detection. Increasing the order of the observation process opens the door for many pattern recognition and machine learning applications. KeywordsIterated random function-Fractals-EMAlgorithm-IRFHMM-HMM-Veterbi-Denoising.