The transfer of distributions by LULU smoothers

[摘要] LULU smoothers is a class of nonlinear smoothers and they are compositionsof the maximum and minimum operators. By analogy to the discrete Fouriertransform and the discrete wavelet transform, one can use LULU smoothersto create a nonlinear multiresolution analysis of a sequence with pulses. Thistool is known as the Discrete Pulse Transform (DPT).Some research have been done into the distributional properties of the LULUsmoothers. There exist results on the distribution transfers of the basicLULU smoothers, which are the building blocks of the discrete pulse transform.The output distributions of further smoothers used in the DPT, interms of input distributions, has been a challenging problem.We motivate the use of these smoothers by first considering linear filters aswell as the median smoother, which has been very popular in signal andimage processing. We give an overview of the attractive properties of theLULU smoothers after which we tackle their output distributions.The main result is the proof of a recursive formula for the output distributionof compositions of LULU smoothers in terms of a given input distribution.

[发布机构] Stellenbosch University