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Learning an Overcomplete Dictionary using a Cauchy Mixture Model for Sparse Decay

An algorithm for learning an overcomplete dictionary
using a Cauchy mixture model for sparse decomposition of an underdetermined
mixing system is introduced. The mixture density
function is derived from a ratio sample of the observed mixture
signals where 1) there are at least two but not necessarily more
mixture signals observed, 2) the source signals are statistically
independent and 3) the sources are sparse. The basis vectors of the
dictionary are learned via the optimization of the location parameters
of the Cauchy mixture components, which is shown to be more
accurate and robust than the conventional data mining methods
usually employed for this task. Using a well known sparse
decomposition algorithm, we extract three speech signals from two
mixtures based on the estimated dictionary. Further tests with
additive Gaussian noise are used to demonstrate the proposed
algorithm-s robustness to outliers.