Optimal 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 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 introduce optimal inverses for the Anscombe transformation, in particular the exact unbiased inverse, a maximum likelihood (ML) inverse, and a more sophisticated minimum mean square error (MMSE) inverse. We then present an experimental analysis using a few state-of-theart denoising algorithms and show that the estimation...

• Type: Journal
• Year: 2011
• Where: TIP
• Authors: Markku Makitalo, Alessandro Foi
• Keywords: Additive White Gaussian Noise, Exact Unbiased Inverse, Inverse Transformation, TIP 2011