Providing a New Approach for Modeling and Parameter Estimation of Probability Density Function of Noise in Digital Images

Abstract

The main part of the noise in digital images arises when taking pictures or transmission. There is noise in the images captured by the image sensors of the real world. Noise, based on its causes can have different probability density functions. For example, such a model is called the Poisson distribution function of the random nature of photon arrival process that is consistent with the distribution of pixel values measured. The parameters of the noise probability density function (PDF) can be achieved to some extent the properties of the sensor. But, we need to estimate the parameters for imaging settings. If we assume that the PDF of noise is approximately Gaussian, then we need only to estimate the mean and variance because the Gaussian PDF with only two parameters is determined. In fact, in many cases, PDF of noise is not Gaussian and it has unknown distribution. In this study, we introduce a generalized probability density function for modeling noise in images and propose a method to estimate its parameters. Because the generalized probability density function has multiple parameters, so use common parameter estimation techniques such as derivative method to maximize the likelihood function would be extremely difficult. In this study, we propose the use of evolutionary algorithms for global optimization. The results show that this method accurately estimates the probability density function parameters.