On the processing of piecewise-constant signals by hierarchical models with application to single ion channel currents

A new approach for the processing of piecewise-constant signals is proposed. It is based on modeling the observed data as a sum of a random signal and noise. The random signal has a Gibbs distribution, and the noise is Gaussian. A MAP criterion is derived for joint estimation of the number of signal levels and reconstruction of the signal. The criterion comprises of three terms, one corresponding to the likelihood of the data and two to penalties. One penalty term penalizes for unnecessary transitions, and the other, for unnecessary levels. The method has been tested on synthesized data and applied to single ion channel recordings.