How to Compare Noisy Patches? Patch Similarity Beyond Gaussian Noise
International Journal of Computer Vision
Denoising by second order statistics
Signal Processing
A new similarity measure for nonlocal filtering in the presence of multiplicative noise
Computational Statistics & Data Analysis
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
A New Poisson Noise Filter Based on Weights Optimization
Journal of Scientific Computing
Poisson Noise Reduction with Non-local PCA
Journal of Mathematical Imaging and Vision
| Hi-index | 0.01 |
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.