A Closed-Form Approximation of the Exact Unbiased Inverse of the Anscombe Variance-Stabilizing Transformation

Abstract

We presented an exact unbiased inverse of the Anscombe variance-stabilizing transformation in [M. Mäkitalo and A. Foi, "Optimal inversion of the Anscombe transformation in low-count Poisson image denoising," IEEE Trans. Image Process., vol. 20, no. 1, pp. 99-109, Jan. 2011.] and showed that when applied to Poisson image denoising, the combination of variance stabilization and state-of-the-art Gaussian denoising algorithms is competitive with some of the best Poisson denoising algorithms. We also provided a MATLAB implementation of our method, where the exact unbiased inverse transformation appears in nonanalytical form. Here, we propose a closed-form approximation of the exact unbiased inverse in order to facilitate the use of this inverse. The proposed approximation produces results equivalent to those obtained with the accurate (nonanalytical) exact unbiased inverse, and thus, notably better than one would get with the asymptotically unbiased inverse transformation that is commonly used in applications.

Poisson-gaussian denoising using the exact unbiased inverse of the generalized anscombe transformation

“…Moreover, we demonstrate that our approach leads to state-of-the-art results. This paper generalizes our earlier work [3], [4], in which we presented an exact unbiased inverse of the Anscombe transformation [5] and showed its importance in obtaining accurate denoising results for the case of pure Poisson noise.…”

“…We have generalized our earlier work [3], [4] by proposing an exact unbiased inverse of the generalized Anscombe transformation for Poisson-Gaussian noise. We showed that the denoising performance associated with this inverse, in conjunction with a state-ofthe-art Gaussian noise removal algorithm, is competitive with that of a state-of-the-art algorithm designed specifically for the removal of Poisson-Gaussian noise.…”

“…Taking into account the asymptotic result (9), and given that I0 is already available (either in accurate numerical form or as closedform analytical approximation [3], [4]), to compute Iσ it is sufficient to tabulate E{fσ(z) |y, σ} (8) only for a finite grid of values, and resort to interpolation (between the grid values) and to the asymptotic form I0(D) − σ 2 (outside of the grid). In particular, for our experiments, we considered 96 non-equispaced values σ ∈ {0.01, .…”

Gaussian Priors for Image Denoising

“…In digital cameras, the two major sources of noise during the acquisition process are the thermal agitation, which produces an almost white and Gaussian noise, and the discrete nature of light, which is behind the photon shot noise, modeled as a Poisson variable (for a complete description of the sources of noise in a digital camera, see [2]). Stabilizing the noise variance by a generalized Anscombe transform [13] results in a noise model well approximated by a white Gaussian noise ε ∼ N (0, σ 2 I m ). The vast majority of works on image denoising focus on this simplified model and it is also our assumption in this chapter.…”

The Effects of Total Variation (TV) Technique for Noise Reduction in Radio-Magnetic X-ray Image: Quantitative Study

“…Appropriate filter and algorithm were required to reduce the noise in images. Although the median filter based on median value in the designated area was frequently used in the medical imaging field, different techniques for the noise reduction have been recently developed [1][2][3] [4][5][6]. Especially, Anscombe noise reduction technique is useful in various inverse problems with Poisson noise contamination.…”