On the inversion of the Anscombe transformation in low-count Poisson image denoising

The removal of Poisson noise is often performed through the following three-step procedure. First, the noise variance is stabilized by applying the Anscombe root transformation to the data, producing a signal in which the noise can be treated as additive Gaussian noise with unitary variance. Second, the noise is removed using a conventional denoising algorithm for additive white Gaussian noise. Third, an inverse transformation is applied to the denoised signal, obtaining the estimate of the signal of interest. The choice of the proper inverse transformation is crucial in order to minimize the bias error which arises when the nonlinear forward transformation is applied. We present an experimental analysis using a few state-of-the-art denoising algorithms and show that the estimation can be consitently improved by applying the exact unbiased inverse, particularly at the low-count regime.