A CHARACTERIZATION OF POISSON NOISE

摘要

We shall compare Gaussian (white) and Poisson noises in order to characterize the latter. First, their characteristics are discussed, then we show that approximations of the two noises indicate significant difference between them from the viewpoints of invariance under transformation group and optimality of information. There one can recongnize dissimilarity in addition to similarity. The dissimilarity is more significant. In fact, there are many different properties between the two noises in parallel, so that we can see the contrast which is most interesting for us. Then, we shall come to a characterization of the so-called fractional power distribution with the help of the significant properties of Poisson noise. It is our hope that special methods of approximation to the two noises would further reflect a duality between them. One is related to the rotation group which is continuous, while the other is to the symmetry group which is discrete.