Estimation and comparison of the image noise levels via subsampling

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.