Introduction of stochastic dictionaries

Previous chapter highlighted the influence of a dyadic dictionary structure on resulting MP decomposition. In fact, any structure of a dictionary, i.e. constant subsampling of the space of dictionary's atoms parameters, will influence statistical properties of resulting decomposition. As a solution of this problem we propose MP with stochastic dictionaries. Instead of choosing some fixed positions of dictionary atoms (from dyadic or any other grid), we draw the parameters of Gabor functions from uniform distributions within the acceptable ranges, so that each signal's expansion is computed in a dictionary based on a different grid. The MP procedure based on stochastic dictionaries is more time-consuming than in case of dyadic dictionaries, however, recent developments in computer technology decrease the importance of this problem.