| Ten years after the introduction of the myriad filter, myriad filtering has evolved into a mature method for efficient non-Gaussian signal processing in impulsive environments. Despite its practical success and the richness of the theory behind it, little is known about the sensitivity of the filter to the underlying numerical algorithms used for its computation. Computing the myriad filter requires the minimization of a difficult objective function built from the filter input data. The typical approach is to apply a "black box" minimization routine from a numerical library. To date, a sensitivity study describing how the filter's performance is affected by the minimization algorithm used has not been done.; This thesis presents results that show that, in effect, the minimization algorithm plays a (sometimes dramatic) role on the design of myriad filters and should not be overlooked. Minimization operations at the interior of nonlinear operations are sensitive components that have a direct impact on the performance of the filtering algorithms, and poorly chosen algorithms compromise the good behavior of the filter. The use of a global search method for the computation of the myriad can guarantee high accuracy of the filter, but the cost may be too high in terms of computational speed, as typical global search algorithms complexity dramatically increases as the order of the filter grows.; An alternative for the accelerated minimization of the objective function in the computation of the myriad filter is introduced. This solution exploits general concepts in global optimization and adapts them to the particular case of myriad filtering. This technique improves accuracy and speed in the computation of the myriad filter, making the method feasible in many problems. |
