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An Unbiased Risk Estimator for Image
Denoising in the Presence of Mixed Poisson–
Gaussian Noise
Abstract—The behavior and performance of denoising algorithms are governed by one or several
parameters, whose optimal settings depend on the content of the processed image and the
characteristics of the noise, and are generally designed to minimize the mean squared error
(MSE) between the denoised image returned by the algorithm and a virtual ground truth. In this
paper, we introduce a new Poisson–Gaussian unbiased risk estimator (PG-URE) of the MSE

2. applicable to a mixed Poisson–Gaussian noise model that unifies the widely used Gaussian and
Poisson noise models in fluorescence bioimaging applications. We propose a stochastic
methodology to evaluate this estimator in the case when little is known about the internal
machinery of the considered denoising algorithm, and we analyze both theoretically and
empirically the characteristics of the PG-URE estimator. Finally, we evaluate the PG-URE-driven
parametrization for three standard denoising algorithms, with and without variance
stabilizing transforms, and different characteristics of the Poisson–Gaussian noise mixture.
Existing method:
An exhaustive review of the existing unbiased risk estimators applied to image restoration
problems is beyond the scope of this paper, and we focus in this work just on pure denoising
problems involving noise models encountered in microscopy imaging applications.

3. Proposed method:
The paper is built around the resolution of two issues that restrict in practice the use of SURE for
automatic parameter tuning. First, SURE relies on the hypothesis of additive white Gaussian
noise, which may not account for situations encountered in bio-imaging applications: for
example, in this case, noise intensity may not be uniform in the whole image as assumed in, but
rather depend on the presence of biological objects, and more generally on the value on the
underlying signal. The extension of SURE to a more realistic mixed Poisson-Gaussian noise
model is thus proposed.
Merits:
1. Noise level is very high
Demerits:
1. Noise level is low compared to existing systems.
2. PSNR values is very high.
3. BER rate is very low.
Results:

4. Fig. Comparison between the denoised images ˆxMSE and ˆxPG-URE obtained for the original
image Disks, with four different noise levels and denoising methods. PSNR values are also
reported in the bottom right corner of each image.