Estimation and comparison of the image noise levels via subsampling
Abstract
As the amount of digital data has increased critically in the last decade, image data has become
more and more important. Noise is a random signal which always present in an image during image
acquisition, coding and, transmission. Image noise leads to pixels representing incorrectly the color
or the exposure of the scene. The noise level is an important component for measuring the quality of
an image.
In the literature, very little work has been done in statistical inference for image noise. Most existing methods deal with the point estimation of the noise level, but the sampling distribution of these
point estimates are unknown in general. In this project, we propose sub-sampling methods for image
data to approximate the sampling distribution for the point estimates. Also, we develop some methods
to compare the noise level of two images. First, we review different models of image noise including
independent noise, dependent noise and bivariate noise models. Usually the probability models for
image noise are not simple and the variance estimates are complicated. The estimates themselves
require sampling distributions for statistical inference. Second, we approximate the sampling distributions via subsampling methods. In statistics, bootstrap and resampling methods are widely used
to construct the sampling distributions and estimate the variances of different statistics. Here, we
generalize resampling methods for one dimensional data to deal with two dimensional images. From
these, confidence intervals for the noise level are constructed. Also, some methods for comparing the
image variance in paired images are evaluated for different types of noise such as independent noise
and dependent bivariate Gaussian noise. The results of the estimation noise level and hypothesis
tests on variance comparison are provided. It seems that the proposed subsampling methods provide
reasonable results while both the F-test and the Pitman t-test may not work well.