Inversion
When the Anscombe transform is used in denoising (i.e. when the goal is to obtain from an estimate of ), its inverse transform is also needed in order to return the variance-stabilized and denoised data to the original range. Applying the algebraic inverse
usually introduces undesired bias to the estimate of the mean, because the forward square-root transform is not linear. Sometimes using the asymptotically unbiased inverse
mitigates the issue of bias, but this is not the case in photon-limited imaging, for which the exact unbiased inverse given by the implicit mapping
should be used. A closed-form approximation of this exact unbiased inverse is
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