Analysis and Extension of the PCA Method, Estimating a Noise Curve from a Single Image

Abstract

Given a white Gaussian noise signal Non a sampling grid, its variance � 2 can be estimated from a small w × w pixels sample. However, in natural images we observe ˜ U = U + N�, the combination of the geometry of the scene that is photographed and the added noise. In this case, estimating directly the standard deviation of the noise from w × w samples of ˜ U is not reliable since the measured standard deviation is not explained just by the noise but also by the geometry of U. The Percentile method tries to estimate the standard deviationfrom w × w blocks of a high-passed version of ˜ U by a small p-percentile of these standard deviations. The idea behind is that edges and textures in a block of the image increase the observed standard deviation but they never make it decrease. Therefore, a small percentile (0.5%, for example) in the list of standard deviations of the blocks is less likely to be affected by the edges and textures than a higher percentile (50%, for example). The 0.5%-percentile is empirically proven to be adequate for most natural, medical and microscopy images. The Percentile method is adapted to deal with signal-dependent noise, which is realistic with the Poisson noise model obtained by a CCD device in a digital camera.