Optimal Inversion of the Generalized Anscombe Transformation for Poisson-Gaussian Noise

• Published in: IEEE transactions on image processing Vol. 22; no. 1; pp. 91 - 103
• Main Authors: Makitalo, M., Foi, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Algorithms; Applied sciences; Approximation methods; Denoising; Detection, estimation, filtering, equalization, prediction; Devices; Exact sciences and technology; Exact solutions; Gaussian noise; Image processing; Information, signal and communications theory; Inverse; Mathematical analysis; Noise; Noise reduction; Optimization; photon-limited imaging; Photonics; Poisson-Gaussian noise; Signal and communications theory; Signal processing; Signal, noise; Studies; Telecommunications and information theory; Transformations; variance stabilization; State of the art; Noise reduction; Stabilization; Imager; Inverse transformation; photon-limited imaging; Algorithm; Computational complexity; Poisson process; Poisson-Gaussian noise; variance stabilization; Denoising; Gaussian noise; Imaging; Signal processing; Maximum likelihood; Electrons
• DOI: 10.1109/TIP.2012.2202675
• ISSN: 1057-7149; 1941-0042

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.