MICROSTATISTIC LMS FILTERING

Signal decomposition has shown to be a useful tool for the design of robust and efficient estimators. Stack and microstatistic filters are among the filters that use the threshold decomposition architecture. The microstatistic filter, in particular, uses linear combinations on the set of decomposed (thresholded) signals to produce its estimate. Thus, stack and microstatistic filters can be regarded as Boolean and linear threshold filters, respectively. The design of the optimal microstatistic filter requires the statistical characterization of the decomposed signal set (microstatistics). In this paper, we develop adaptive microstatistic filters for applications where the second-order statistics of the thresholded signals are not known, or when they may be nonstationary. A multilevel threshold decomposition is used such that real valued stochastic processes can be filtered and such that the computation 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 characteristics of the thresholded signals, we can assign a different step-size adaptation parameter to each threshold level. We develop simple design guidelines for the set of nonhomogeneous step sizes which in practice yield better convergence characteristics.