Anscombe transform ~ INDAHNYA BERBAGI

Selasa, 10 Juni 2014

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 thestandard 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.

For the Poisson distribution the mean

m

and variance

v

are not independent:

m = v

. The Anscombe transform^[1]

A:x \mapsto 2\sqrt{x+\tfrac{3}{8}} \,

aims at transforming the data so that the variance is set approximately 1 whatever the mean. It transforms Poissonian data

x

(with mean

m

) to approximately Gaussian data of mean

2\sqrt{m + 3/8} - 1/(4\sqrt{m})

and standard deviation 1. This approximation is valid provided that

m

is larger than 4.^{[citation needed]}

Sumber : http://en.wikipedia.org/wiki/Anscombe_transform

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