Fast and Accurate Computation of the Myriad Filter via Branch-and-Bound Search

The myriad filter has demonstrated to be a robust countermeasure against the negative effect that impulsive noise has over electronic systems. However, its use is still limited in systems where processing speed is critical, as is the case of radar, sonar, and real-time audio and video processing. This limitation has its roots in the challenges imposed by the numerical approximation of the myriad filter. In particular, minimization operations at the interior of nonlinear operations are sensitive components that have a direct impact on the performance of the filtering algorithms. In the case of the myriad filter, the minimization of functions with multiple local minima is a common operation, and poorly chosen algorithms compromise the good behavior of the filter. In this correspondence, we present an alternative for the minimization of the objective function in the computation of the myriad filter. 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.