Optimal Inversion of the Anscombe Transformation in Low-Count Poisson Image Denoising
Optimal Inversion of the Anscombe Transformation in Low-Count Poisson Image Denoising
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DOI：
10.1109/tip.2010.2056693
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发表时间：
2011-01-01
影响因子：
10.6
通讯作者：
Foi, Alessandro
中科院分区：
文献类型：
--
作者：
Makitalo, Markku;Foi, Alessandro
泊松噪声的去除通常通过以下三个步骤来执行。首先，通过对数据应用Anscombe根变换来稳定噪声方差，产生一个信号，其中噪声可以被处理为具有酉方差的加性高斯。其次，利用加性高斯白噪声的传统去噪算法去除噪声。第三，对去噪后的信号进行逆变换，得到感兴趣信号的估计。为了最大限度地减小应用非线性正变换时产生的偏差，选择合适的逆变换是至关重要的。我们介绍了Anscombe变换的最优逆，特别是精确无偏逆、最大似然(ML)逆和更复杂的最小均方误差(MMSE)逆。然后，我们给出了使用几种最先进的去噪算法的实验分析，并表明通过应用精确的无偏逆可以一致地改善估计，特别是在低计数区域。这导致了一种非常有效的滤波解决方案，它与现有的一些最好的泊松图像去噪方法具有竞争力。
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-the-art denoising algorithms and show that the estimation can be consistently improved by applying the exact unbiased inverse, particularly at the low-count regime. This results in a very efficient filtering solution that is competitive with some of the best existing methods for Poisson image denoising.