Modeling and estimation of multiscale processes

The authors introduce a class of stochastic processes motivated by the wavelet transform. These processes are represented by Markovian state models in which scale plays the role of a time-like variable. This class of processes is rich enough to model 1/f-type behavior as well as such standard processes as those belonging to the Gauss-Markov class. The authors present an efficient smoothing algorithm which makes it possible to compute estimates based on multiscale data. The authors give numerical examples to show how these models can be used to smooth noisy data as well as examples of fusing multiscale data