Exact variance-stabilizing transformations for image-signal-dependent Rayleigh and other Weibull noise sources

Variance-stabilizing transforms for families of Rayleigh and, more generally, for Weibull random variables are derived and shown to be exact. These transforms, when applied to appropriate noisy images, render signal-dependent noise signal-independent. Their utility is that, after applying the transforms, classical estimation procedures devised for additive, signal-independent noise can be brought to bear. The results are expected to find use in image filtering, in photon counting, and in the processing of optical field magnitudes and intensities generated by chaotic sources.