Pointwise Approximation for Linear Combination of Probabilistic Operators on Local Averages
Shouyuan Yang · Journal of Tianjin University Science and Technology · 2005
Modern digital data processing of functions (include signals and images) can be carried out with a discrete version of the original signal f(x) obtained by sampling a discrete set of local averages. The influence of high frequency noise can be suppressed by the local average sampling. Probabilistic operators on local averages, which are constructed by binomial processes, Poisson processes and negative binomial processes, are a kind of local averages at the time point by integration. Study on the pointwise approximation for linear combinations of these operators shows the equivalence between the order of error and the new modulus of Ditzian.