Standard deviation of the transformed Poisson random variable as a function of the mean .
In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The Anscombe transform is widely used in photon-limited imaging (astronomy, X-ray) where images naturally follow the Poisson law. The Anscombe transform is usually used to pre-process the data in order to make the standard deviation approximately constant. Then denoising algorithms designed for the framework of additive white Gaussian noise are used; the final estimate is then obtained by applying an inverse Anscombe transformation to the denoised data.
Anscombe transform animated. Here is the mean of the Anscombe-transformed Poisson distribution, normalized by subtracting by , and is its standard deviation (estimated empirically). We notice that and remains roughly in the range of over the period, giving empirical support for
![{\displaystyle [0,10]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/af219c8f0e8e0381e7b35e63dd7093e86d83a540)
