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

Abstract

Given a white Gaussian noise signal on a sampling grid, its variance can be estimated from a small block sample. However, in natural images we observe the combination of the geometry of the scene being photographed and the added noise. In this case, estimating directly the standard deviation of the noise from block samples is not reliable since the measured standard deviation is not explained just by the noise but also by the geometry of the image. The Percentile method tries to estimate the standard deviation of the noise from blocks of a high-passed version of the image and 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 signal-dependent noise, which is realistic with the Poisson noise model obtained by a CCD device in a digital camera.