Dictionary-based decomposition of linear mixtures of Gaussian processes

We consider the problem of detecting and classifying an unknown number of multiple simultaneous Gaussian processes with unknown variances given a finite length observation of their sum and a dictionary of candidate models for the signals. The optimal minimum description length (MDL) detector is presented. Asymptotic and quadratic approximations of the MDL criterion are derived, and regularization algorithms for their efficient implementation are described. The performance of the algorithms is illustrated by numerical simulations. Interpretations in terms of vector quantization and in model-based spectral analysis are discussed together with applications and possible extensions.