Abstract: This paper introduces a new point estimation algorithm, with particular focus on coherent noise suppression, given several measurements of the device under test where it is assumed that 1) the noise is first-order stationery and 2) the device under test is linear and time-invariant. The algorithm exploits the robustness of the Pitman estimator of the Cauchy location parameter through the initial scaling of the test signal by a centred Gaussian variable of predetermined variance. It is illustrated through mathematical derivations and simulation results that the proposed algorithm is more accurate and consistently robust to outliers for different tailed density functions than the conventional methods of sample mean (coherent averaging technique) and sample median search.
Abstract: 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.