A Haar-Fisz Algorithm for Poisson Intensity Estimation

By Piotr Fryzlewicz, Guy P. Nason. 2004

176 citations recorded by the source corpus.

Subfields: Applied Mathematics, Atmospheric Science, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/4c2b7537abc4e99e7ddf10148a916506f93f731c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Thierry Blu
2. Guy P. Nason
3. Maarten Jansen
4. Michael A. Unser
5. Bo Zhang
6. Jean-Luc Starck
7. Mohamed-Jalal Fadili
8. Florian Luisier

In Atmospheric Science

1. Florian Luisier
2. Thierry Blu
3. Mohamed-Jalal Fadili
4. Jean-Luc Starck
5. Maarten Jansen
6. Rebecca M. Willett
7. Bernard Walter Silverman
8. Bo Zhang

In Computer Vision and Pattern Recognition

1. Luc Van Gool
2. Andrew Zisserman
3. Xiaogang Wang
4. Thierry Blu
5. Li Fei-Fei
6. Cordelia Schmid
7. Kristen Grauman
8. Jitendra Malik

Citations in the corpus

• Multiscale methods for data on graphs and irregular multidimensional situations (2009, methodology): “In future the Haar–Fisz transform (see Fryzlewicz and Nason (2004) or Jansen (2006)) might be used.”
• Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences (2010, background): “In the case of very low count situations ( 1 photons in average), the more sophisticated Fisz transform allows one to better stabilize Poisson noise [7], [8].”
• Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2008, methodology): “Haar-Fisz transform is another widely used VST [ 7 ][8], which combines the Fisz”
• Object categorization by learned universal visual dictionary (2005, background): “This is the variance stabilizing transformation [6] of a multinomial (or equivalently a Poisson distribution) which has the effect of making the variance constant, rather than linearly dependent on the mean ¯ H.”
• Image Denoising in Mixed Poisson–Gaussian Noise (2011, background): “Fryzlewicz et al. have proposed a VST based on the observation that the scaling coefficients at a given scale are good local estimates of the noise variances of the same-scale wavelet coefficients [10].”
• This is SPIRAL-TAP: Sparse Poisson Intensity Reconstruction ALgorithms—Theory and Practice (2010, methodology): “Variance-stabilizing transforms (VSTs), such as the Anscombe transform [14] and the Haar-Fisz [15], [16] transform, are widely used to address this issue and to approximate the Poisson observations by Gaussian random variables [17], [18].”
• The SURE-LET Approach to Image Denoising (2007, methodology): “Due to the non shift-invariance of the Haar-Fisz transform, some “external” cycle-spins are also performed to the whole algorithm (HaarFisz VST + TI-SUREshrink + Haar-Fisz inverse VST), as suggested in [156].”