Department of Signal Processing, Tampere University of Technology, Tampere 33101, Finland.
IEEE Trans Image Process. 2013 Jan;22(1):91-103. doi: 10.1109/TIP.2012.2202675. Epub 2012 Jun 5.
Many digital imaging devices operate by successive photon-to-electron, electron-to-voltage, and voltage-to-digit conversions. These processes are subject to various signal-dependent errors, which are typically modeled as Poisson-Gaussian noise. The removal of such noise can be effected indirectly by applying a variance-stabilizing transformation (VST) to the noisy data, denoising the stabilized data with a Gaussian denoising algorithm, and finally applying an inverse VST to the denoised data. The generalized Anscombe transformation (GAT) is often used for variance stabilization, but its unbiased inverse transformation has not been rigorously studied in the past. We introduce the exact unbiased inverse of the GAT and show that it plays an integral part in ensuring accurate denoising results. We demonstrate that this exact inverse leads to state-of-the-art results without any notable increase in the computational complexity compared to the other inverses. We also show that this inverse is optimal in the sense that it can be interpreted as a maximum likelihood inverse. Moreover, we thoroughly analyze the behavior of the proposed inverse, which also enables us to derive a closed-form approximation for it. This paper generalizes our work on the exact unbiased inverse of the Anscombe transformation, which we have presented earlier for the removal of pure Poisson noise.
许多数字成像设备通过连续的光子到电子、电子到电压和电压到数字转换来运行。这些过程受到各种依赖于信号的误差的影响，这些误差通常被建模为泊松-高斯噪声。通过对噪声数据应用方差稳定化变换 (VST)、用高斯去噪算法对稳定化数据进行去噪、最后对去噪数据应用逆 VST，可以间接地去除这种噪声。广义安斯考姆变换 (GAT) 常用于方差稳定化，但过去并没有对其无偏逆变换进行严格研究。我们引入了 GAT 的精确无偏逆变换，并表明它在确保准确去噪结果方面起着不可或缺的作用。我们证明，与其他逆变换相比，这种精确逆变换可以达到最新的结果，而计算复杂度没有明显增加。我们还表明，这种逆变换是最优的，因为它可以被解释为最大似然逆变换。此外，我们对提出的逆变换的行为进行了彻底分析，这也使我们能够为其推导出一个封闭形式的近似。本文推广了我们之前针对纯泊松噪声去除的安斯考姆变换精确无偏逆变换的工作。
