Microstatistic LMS filtering

Adaptive microstatistic filters are developed for applications in which the second-order statistics of the thresholded signals are not known or may be nonstationary. A multilevel threshold decomposition such that real-valued stochastic processes can be filtered is used, and the computational complexity of the algorithm can be arbitrarily specified by the designer. The adaptation uses the least-mean-squares error approach of the least-mean-square (LMS) algorithm. The convergence of the adaptive algorithm is proved. Due to the nonhomogeneous statistical characteristic of the threshold signals, a different step-size adaptation parameter can be assigned to each threshold level. Simple design guidelines are developed for finding the set of nonhomogeneous step sizes which in practice yield better convergence characteristics