Abstract-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-theart 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 ef cient ltering solution that is competitive with some of the best existing methods for Poisson image denoising.

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.

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.

In digital imaging, there is often a need to produce estimates of the parameters that define the chosen noise model. We investigate how the mismatch between the estimated and true parameter values affects the stabilization of variance of signal-dependent noise. As a practical application of the general theoretical considerations, we devise a novel approach for estimating Poisson–Gaussian noise parameters from a single image, combining variance-stabilization and noise estimation for additive Gaussian noise. Furthermore, we construct a simple algorithm implementing the devised approach. We observe that when combined with optimized rational variance-stabilizing transformations, the algorithm produces results that are competitive with those of a state-of-the-art Poisson–Gaussian estimator.

Path tracing produces realistic results including global illumination using a unified simple rendering pipeline. Reducing the amount of noise to imperceptible levels without post-processing requires thousands of samples per pixel (spp), while currently it is only possible to render extremely noisy 1 spp frames in real time with desktop GPUs. However, post-processing can utilize feature buffers, which contain noise-free auxiliary data available in the rendering pipeline. Previously, regression-based noise filtering methods have only been used in offline rendering due to their high computational cost. In this article we propose a novel regression-based reconstruction pipeline, called Blockwise Multi-Order Feature Regression (BMFR), tailored for path-traced 1 spp inputs that runs in real time. The high speed is achieved with a fast implementation of augmented QR factorization and by using stochastic regularization to address rank-deficient feature data. The proposed algorithm is 1.8× faster than the previous state-of-the-art real-time path-tracing reconstruction method while producing better quality frame sequences.

No abstract

The characteristic errors of many digital imaging devices can be modelled as Poisson-Gaussian noise, the removal of which can be approached indirectly through variance stabilization. The generalized Anscombe transformation (GAT) is commonly used for stabilization, but rigorous studies regarding its unbiased inverse transformation have been neglected. We introduce the exact unbiased inverse of the GAT, show that it is of essential importance for ensuring accurate denoising, and demonstrate that our approach leads to state-of-the-art results. This paper generalizes our earlier work, in which we presented an exact unbiased inverse of the Anscombe transformation for the case of pure Poisson noise removal.

No abstract