Department of Signal Processing, Tampere University of Technology, PO Box 553, 33101 Tampere, Finland.
IEEE Trans Image Process. 2011 Jan;20(1):99-109. doi: 10.1109/TIP.2010.2056693. Epub 2010 Jul 8.
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.
去除泊松噪声通常通过以下三个步骤完成。首先，通过对数据应用安斯科姆平方根变换来稳定噪声方差，生成一个噪声可以被视为具有单位方差的加性高斯噪声的信号。其次，使用传统的加性白高斯噪声去噪算法去除噪声。最后，对去噪后的信号应用逆变换，得到感兴趣信号的估计。选择合适的逆变换对于最小化非线性正向变换应用时出现的偏差误差至关重要。我们为安斯科姆变换引入了最优逆变换，特别是精确无偏逆变换、最大似然（ML）逆变换和更复杂的最小均方误差（MMSE）逆变换。然后，我们使用几种最先进的去噪算法进行了实验分析，结果表明，通过应用精确无偏逆变换，可以始终如一地提高估计，特别是在低计数情况下。这导致了一种非常有效的滤波解决方案，与现有的一些用于泊松图像去噪的最佳方法具有竞争力。
