We study weighted `2 fidelity in variational models for Poisson noise related image restoration problems. Gaussian approximation to Poisson noise statistic is adopted to deduce weighted `2 fidelity. Different from the traditional weighted `2 approximation, we propose a reweighted `2 fidelity with sparse regularization by wavelet frame. Based on the split Bregman algorithm introduced in [22], th...

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the variance function of this family.

Motivated by non-Poisson stochastic variability found in service system arrival data, we extend established service system staffing algorithms using the square-root staffing formula to allow for non-Poisson arrival processes. We develop a general model of the non-Poisson non-stationary arrival process that includes as a special case the non-stationary Cox process (a modification of a Poisson pr...

The standard switching from one set of diffusion coefficients to another occurs at random times corresponding the moments jumps a Poisson process independent initial diffusion. paper deals with Brownian motion variance taking two values by depending on trajectories process. most attractive computational point view is moment inverse local time.

In this note, we explore the rich information about inference that the Poisson distribution has. The source of this information is mainly the fact that the mean and variance of this distribution are equal. c © 2007 Elsevier B.V. All rights reserved.

A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.

In this paper, we introduce a new combined integer-valued moving average model of order 2 with poisson innovation, denoted by PCINMA(2). We consider some properties of this process, such as expectation, variance, autocovariance function. Stationary and ergodicity are obtained. We estimate the unknown parameters by using Yule-Walker estimation, and use simulation to assess the performance of Yul...

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function of the first kind. We also study the generated natural exponential family. We determine the domain of the means and the variance function of this family.

Approximations of the estimation variances of kernel estimators of the pair correlation function and the product density of a planar Poisson process are given. Furthermore, a heuristic approximation of the estimation variance of an estimator of the pair correlation function of a "general" planar point process is suggested. All formulae have been tested by simulation experiments.

SUMMARY Using replicated human serum samples, we applied an error model for proteomic differential expression profiling for a high-resolution liquid chromatography-mass spectrometry (LC-MS) platform. The detailed noise analysis presented here uses an experimental design that separates variance caused by sample preparation from variance due to analytical equipment. An analytic approach based on ...